MOPFAQ (My Own Personal Frequently Asked Questions) for SAA Brian Tung <brian.y.tung@gmail.com> URL: http://www.astronomycorner.net/reference/faq.txt http://www.astronomycorner.net/reference/faq.html Latest update (2008-07-23) * most amateur telescopes can only reveal four satellites of Jupiter The following is a list of questions that I see asked reasonably often on sci.astro.amateur. It's certainly not an exhaustive list. When I see a question I think I can answer pretty well, I make a note of it and add it to this list. If I can't, I discard it and let someone else answer it. There may be some overlap with the other SAA FAQs (although I bet it's pretty small, actually), but that's OK, since only in this FAQ list do these questions get answered in my own inimitable (or is it inimical?) style. +-------------------------------------------------------------+ | Note: Many of the answers include a so-called ASCII or text | | diagram. You should use a constant-width font when you | | read this FAQ so these diagrams come out right. If the box | | around this text looks right, your font choice is fine. | +-------------------------------------------------------------+ The List of Questions Q. What causes the seasons? Q. What is the purpose of an equatorial mount? Q. If I have a correctly aligned equatorial mount, why do I need a hand controller/auto-guider/other device to keep my telescope pointed in the right direction? Q. What causes field rotation? Q. What are some good telescope choices? Q. Are there any good introductory astronomy books? Q. What are some good inexpensive planetarium programs? Q. How should I select a star atlas? Q. How do you measure distances in the sky? Q. What is the distinction between true field of view and apparent field of view? Q. How can I measure the apparent field of view of my eyepiece? Q. What is an orthoscopic eyepiece? Q. What does "parfocal" mean? Q. What is a Barlow lens, and how do I use it? And how does it work, anyhow? Q. Is a fast telescope (small f/ratio) brighter than a slow telescope (large f/ratio)? Q. What is the limiting magnitude for my scope? Q. How is seeing related to twinkling? Q. What does "diffraction-limited" mean? Q. I often seen optical quality measured as "1/8-wave or better." What does this mean? Is, for example, 1/8-wave better than 1/4-wave? Q. What is the star test, and how does it work? Q. What do "over-corrected" and "under-corrected" mean? Q. What is astigmatism, and what causes it? Q. What do the terms achromat, apochromat, and semi-apochromat mean? Q. Does a central obstruction damage image quality or not? Q. Does a Newtonian's spider damage image quality or not? Q. What is prime focus? Q. What does [insert nutty acronym] mean? Q. What is the deal with [insert nut]? Q. How do mirrors keep their shape? I thought glass was a liquid. Q. My mirror/lens is scratched--is this going to be a problem? Q. What's the difference between a mirror diagonal and a prism diagonal? Q. What does it mean to offset a secondary, and why would I want to do that? Q. How the heck is my image oriented? Q. How much magnification can I get out of my telescope? Q. How do I figure out the magnification when I take an astrophoto? Q. What can I expect to see when I use my telescope for the first time? Q. Did I just see Jupiter's satellites in my binoculars? Q. Did I see a fifth (sixth, seventh) satellite of Jupiter in my telescope? Q. What are these words "following" and "preceding" (or "leading" and "trailing") and what do they have to do with directions? Q. Is it true that looking at the Moon through a telescope will harm your eyes? Q. What interesting astronomy-related science projects can my child do? Q. Is Pluto still a planet? Q. What happened before the Big Bang? Q. What causes the seasons? A. The seasonal variation of weather on the Earth is affected by many things, but the principal factor is the tilt of the Earth's axis with respect to its orbital plane. You often hear (correctly) that the Earth's axis is tilted, at an angle of about 23.4 degrees. But--23.4 degrees from what? Up and down? Up and down from what? Up and down from the ecliptic plane. The Earth travels around the Sun in an almost circular ellipse, with a major axis (long diameter) of about 300 million kilometers (about 186 million miles). The average distance of the Earth from the Sun is thus half of that, or 150 million kilometers (about 93 million miles). The orbit is slightly elliptical, though, with the Sun not quite at the center of the ellipse, but offset by about 2.5 million kilometers (1.5 million miles) along the major axis. As a result, the actual distance at any time varies by about 5 million kilometers (3 million miles) throughout the year. It so happens that in our epoch, the distance is at a minimum in early January, and at a maximum in early July. Earth in Earth in o January O Sun o July |<- 147.5 Gm ->|<-- 152.5 Gm -->| Earth and Sun throughout the year (not to scale) In this diagram, the Earth's orbital plane is coming out of the screen, so that in January, the Earth is moving directly "toward you," and then sweeps around, and is moving directly "away from you" in July. The Gm stands for gigameter--another way to say million kilometers. From this diagram, you'd expect the Earth to receive more heat from the Sun in January than in July, which it does, and for the weather to be warmer in January than in July, which is only true for the southern hemisphere. Why is that? Why should the weather be different in the two hemispheres? Because there is another factor--the tilt of the Earth's axis. In the diagram above, we have the Earth revolving around the Sun in a horizontal plane, which we call the ecliptic plane, or simply the ecliptic. The north and south ecliptic poles are up and down from the ecliptic. If the Earth's axis were also straight up and down, the weather would indeed be warmer in January than in July, all over the Earth, since the only thing that changes for any point on the Earth throughout the year is its distance from the Sun. | | o O o | | But the Earth's axis is not aligned with the ecliptic poles--is not straight up and down from the ecliptic. Instead, it's canted at an angle, 23.4 degrees. By coincidence, the north end of the axis points most directly away from the Sun in late December, at the northern winter solstice, and most directly toward the Sun in late June, at the northern summer solstice. Very approximately, then, the northern end of the axis is pointed away from the Sun at a time when the Earth is closest to the Sun, and toward it when the Earth is furthest: \ \ o O o \ \ It's important to note that although either end of the axis points sometimes toward the Sun and sometimes away, that's not because the axis actually "wobbles." The effect is really caused by the relationship between the axis and the Earth's motion around the Sun. Axial tilt has two major effects. One, when a hemisphere's end of the axis is pointed away from the Sun, it receives light from the Sun, when it gets it at all, only obliquely, only at an angle. This oblique heating is less effective than when it strikes a point on the Earth squarely. Two, at such times, the hemisphere pointed away from the Sun is also illuminated for a smaller portion of the day--indeed, the north pole receives no sunlight for several months centered around the winter solstice. Fewer hours of illumination, and less effective illumination when you do get it, means colder weather on the whole. These effects are naturally reversed when the hemisphere points back toward the Sun. We see now why the seasons are reversed in the two hemispheres: it's because when one hemisphere's pole is pointed toward the Sun, the other must be pointed away. There's more to it than that--in particular, the Earth's atmospheric, oceanic, and land heat capacity causes the temperature extremes to lag behind the solstices by a few weeks, depending on location. But the principal driver appears to be the tilt of the Earth's axis. Does this all mean that the variation in the Earth's distance from the Sun has no effect? Not at all! It's just that any variation in weather induced by this variation is mostly swamped by the axial tilt. Q. What is the purpose of an equatorial mount? A. An equatorial mount makes it easier for a telescope to follow the stars as they appear to revolve around us throughout the night. What it is, actually, is the Earth's rotation. If the Earth didn't rotate, then all the stars would stay in place, and observing the night sky at high power would be easy. Of course, day and night would last about 4,380 hours each, leading to baking temperatures during the day and way below freezing at night. But the Earth does rotate ("E pur si muove," as Galileo was alleged to have said), making our days and nights tolerable, for the most part. It also makes the stars appear to revolve around us. That revolution is only an illusion, though. The Earth, you see, is like a carnival carousel. A typical carousel rotates counter-clockwise as seen from above, just like the Earth as seen from high above the north pole. But when you're *on* the carousel, you see the outside world revolving the other way--that is, clockwise. That's why the stars appear to revolve around us. Now, if you try to focus on any outside object--say, a friend taking your picture--you can't do so if you keep still on the carousel. No, you have to swivel your head in order to follow your friend. Moreover, you can't just swivel in any old direction; you have to swivel around the same axis and as fast as the carousel does, only in the opposite direction. If the carousel is rotating counter-clockwise, you have to swivel your head clockwise, to compensate. Notice that it doesn't matter if you're at the center of the carousel or at the edge, nor does it matter where the object is that you're looking at, to first order--all that matters is that you swivel appropriately to counter the carousel's rotation. In the same way, as the Earth rotates once a day, it's necessary to swivel your telescope around to follow any individual object, whether it's a planet, a star, a cluster, or a galaxy. And again, you can't just swivel your telescope any which way--you have to swivel it on the same axis as the Earth, at the rate of one rotation every day, only in the opposite direction. But where *is* the axis of the Earth? If you were at the north pole, the axis of the Earth would point straight up and down; if you were to take a walking stick and spike it straight into the ground, it would be parallel with (in fact, the same as, really) the Earth's axis. If you were to then walk some 110 kilometers (70 miles) away, to a latitude of 89 degrees north, and again plant your walking stick straight into the ground, it would no longer be parallel to the Earth's axis. Instead, because of the Earth's curvature, it would be off by 1 degree. In order to get it parallel to the Earth's axis, you would have to tilt it by that 1 degree, back toward the direction you came from--that is, to the north. A similar situation applies at any other latitude. If you're, say, 50 degrees away from the north pole--that is, at latitude 40 degrees north--you would have to tilt your walking stick down by 50 degrees, and pointing to the north. Since there are 90 degrees between the northern horizon (or any part of the horizon) and the zenith, another way of putting it is that your stick would have to be pointed up from the horizon by 90 minus 50, or 40 degrees. And if you wanted your telescope to remain pointed at a star, you would have to slowly swivel it around an axis that is tilted up from the horizon by 40 degrees. The axis would then be parallel to the Earth's axis. Well, that is all an equatorial mount does--it changes the axis around which a telescope swivels, so that the axis is parallel to the Earth's axis. An ordinary camera tripod swivels left to right, around a vertical axis. Except at the two poles, that would never do. The easiest way to fix that would be to simply tilt the tripod over. However, it ought to be obvious that that situation is completely unstable and will send your telescope crashing to the ground. Generally speaking, then, the tripod stays where it is, it is only the joint where the telescope attaches to the tripod that is tilted over. Depending on how the telescope is attached to this joint, its own weight may cause instability, so a counterweight is often needed, opposite from the telescope, in order to keep everything balanced and stable. Despite all this machinery, the mount doesn't move the telescope on its own. It only makes it easier for you to do it by hand. Alternatively, you can attach a motor drive to the mount, and that *does* move the telescope automatically, to follow or "track" whatever object you choose. Incidentally, the term "equatorial" comes from the fact that the motion of the telescope is parallel to the Earth's equator. Q. If I have a correctly aligned equatorial mount, why do I need a hand controller/auto-guider/other device to keep my telescope pointed in the right direction? A. Because your mount may not be perfectly aligned, because the motor doesn't run perfectly uniformly, and because the Earth has an atmosphere. Suppose the axis of your equatorial mount is not perfectly parallel to the Earth's axis, but is instead off by (say) 1 degree. Then, even if the star you're following is initially centered in the eyepiece or camera field of view, it will gradually drift away from the center, despite your best efforts to follow it across the sky. A hand controller or auto-guider can help adjust the motor drive so that the object stays in the center of the eyepiece or camera field of view. Then, too, motor drives and gears are imperfect. They may be designed to rotate the telescope at a rate of 1 rotation each day, but that is only the average rate. In actuality, the rotation rate of the gears alternately speeds up and slows down. The amount of variation may be tiny, but it is usually enough to make the target object appear to sway back and forth. Again, a hand controller or auto-guider is used to compensate. In some cases, the swaying is periodic, and a feature called periodic error correction can be used instead. Finally, the Earth's atmosphere refracts light as it comes from the distant stars and galaxies. An overhead star is, generally speaking, just about overhead in reality, but a star that ought to be below the horizon by all rights can have its light bent so much by the thick layers of the Earth's atmosphere that it appears above the horizon. The amount by which a star's position appears to be shifted by the atmosphere varies in a complex way from zenith to horizon, so a single speed motor drive cannot accurately track. There are motor drives that have a special rate, called the King rate, designed to partially address this problem, but even the King rate is optimized for a given angle above the horizon and cannot adequately compensate in all cases. For truly accurate tracking, some active correction is still needed. Q. What causes field rotation? A. Field rotation is the effect that even when you accurately keep an object at the center of the field of view, objects at the periphery appear to rotate around it. It is caused by misalignment of the telescope, and can be defined essentially as the difference between north and up. Suppose you're looking at two stars with the same right ascension--say, the westernmost pair of stars in the square of Pegasus. (That's in the northern hemisphere. Find a similar pair of stars in the southern hemisphere.) When they rise in the east, depending on your latitude, those stars are side-by-side, more or less--something like the following: beta * alpha * +-----------------------------------+ horizon When they cross the meridian, though, beta will be nearly directly above (that is, toward the zenith from) alpha, as follows: beta * alpha * And when they set in the west, beta will now be to the upper right of alpha, like so: beta * alpha * +-----------------------------------+ horizon If you were to track alpha Pegasi using a (very wide-FOV) alt-az mounted scope (or a pair of binoculars), you would see beta Pegasi make a broad, circular arc above alpha. That is the field rotation at work. There is nothing magical about being at the same right ascension, by the way; the entire field around alpha will appear, from the point of view of an alt-az scope, to rotate clockwise throughout the night. A GOTO scope essentially figures out the instantaneous alt-az coordinates of a given object. By using the same algorithm to figure out the instantaneous alt-az coordinates of a position just north of that object, it can differentiate and determine the amount of field rotation. (Yes, I know that a GOTO scope can work in equatorial mode--I believe the Celestron Compustar only worked that way--but most of them nowadays are sold to users who will put them in alt-az mode.) Incidentally, you may occasionally see the angle between "up" and "north" referred to as the "parallactic angle." Q. What are some good telescope choices? A. Before I begin, let me lay down some telescope law. Maximum power has little to do with how good a scope is. It's like rating a stereo amplifier by how far the volume knob goes. It's easy to make that make the volume arbitrarily loud, but it does you no good for it to "go to 11" if the sound coming out of the speakers stinks. From a practical perspective, telescope quality is largely determined by its aperture (how wide its main lens or mirror is), its mount stability, and its optical quality--roughly in that order. A run-of-the-mill 6-inch scope will do better than a high-quality 2-inch on just about anything you care to test them on. (One exception is well-corrected wide fields.) The disadvantage with increasing aperture is bulk. A 10-inch telescope may not be the easiest thing in the world to handle for a budding astronomer. With all this in mind, here are some reasonable choices for a first telescope purchase: 1. A 6-inch or 8-inch "dobsonian," which is a reflecting telescope (it uses a mirror as its main light-gathering element), mounted in a rocker box. Its main attributes are that it is reasonably easy to point; the mount is stable and inexpensive, allowing most of the cost to go to the optics; and it is large enough to allow you to see enough objects to keep yourself in astronomical clover for some time. 2. An 80 mm "short tube" refractor, which is a refracting telescope (it uses a lens as its main light-gathering element), typically but not always placed on a simple alt-azimuth mount. Most but not all of these are sold on stable tripods. Its main points are that it is portable; it has a wide field of view, making it easy to find astronomical targets; and it just plain looks like a telescope (which a dobsonian does not, to many people), which is useful for keeping children interested. 3. A 3-1/2 to 5-inch compound scope (which uses both lenses and mirrors). Not exactly my first choice, but these typically do well at high powers, and if you live in the city and cannot get outside it very often, and don't mind focusing (ahem) on the Moon and the planets, it's not a bad selection. Most of these can come with some sort of computerized aid, which will either move the telescope to point at selected targets at the push of a button, or will guide you in pointing at them yourself. These can help, but they naturally add to the cost of the system. In some cases, the computer can be added retroactively, but this is not the usual case (yet), so be sure to ask and make certain. In the U.S., decent telescopes can be had from Celestron, Meade, Orion Telescopes, and Hardin Optical. They can be purchased direct from the web sites, or from a reputable dealer. In many cases, a dealer can be identified as reputable from the manufacturer web sites. Q. Are there any good introductory astronomy books? A. As it so happens, I like astronomy books, to the extent that I'll buy one even if I know most of what's in it already, just because it's well written. This means that I come in contact with most of the good introductory books, as long as they're sold in North America. The current favorite (not just for me, but for many folks) is Terence Dickinson's Nightwatch. It covers both the science and the practice of amateur astronomy, which I find is a good way to maintain the wonder of astronomy. It is fairly specific when it comes to naming brands and models, so it does need to be updated every few years. Dickinson also wrote a somewhat more advanced book, along with Alan Dyer, called The Backyard Astronomer's Guide. BAG covers much of the same ground as Nightwatch, but in greater detail. It has also been more recently revised than Nightwatch (as of this writing in November 2005), so it includes merchandise that was not available when Nightwatch was written. In the pocket book category, I like Ian Ridpath and Wil Tirion's Stars and Planets, which gives a constellation-by-constellation guide to the sky, complete with star maps and an observing guide to the celestial highlights. Finally, for more help in purchasing telescope equipment, I recommend Phil Harrington's Star Ware. It gives a bit of the history and design of telescopes, and also names names on telescopes and accessories. Q. What are some good inexpensive planetarium programs? A. For the Windows platform, two well-regarded free programs are Cartes du Ciel, by Patrick Chevalley, and Hallo Northern Sky, by Han Kleijn. Here are their web sites: http://www.stargazing.net/astropc/ http://www.hnsky.org/software.htm Despite its name, HNS covers the entire celestial sphere. A similar program for the Macintosh platform is Night Sky. http://www.kaweah.com/Products/NightSky/ A program for Windows, Macintosh, and Linux whose emphasis is on photo-realism rather than as a star-mapping utility is Stellarium, with web site at http://www.stellarium.org/ Another program that is not really planetarium software in the usual sense is Celestia. Celestia's strength is not its object coverage, which is quite modest by today's standards, but in its photo-realism and its novel ability to navigate its point of view to any point in the solar neighborhood; you can, for instance, observe the Sun as it would be seen from Sirius. It runs under Windows, Mac, and Linux, and its web site is http://www.shatters.net/celestia/ For PalmOS users, there are a number of inexpensive choices: Planetarium ($24), PleiadAtlas ($10), 2sky ($30), and Astromist ($16), with all prices in U.S. dollars. Their web sites: http://www.aho.ch/pilotplanets/ http://www.astronomycorner.net/pleiadatlas/ http://2sky.org/ http://www.astromist.com/ For PocketPC, the choices are Pocket Deepsky 2000 ($20), Pocket Stars ($15), Pocket Universe ($30), and The Sky Pocket Edition ($49). Their web sites: http://deepsky2000.com/pocket.html http://www.nomadelectronics.com/PocketPC/PocketStars/PocketStarsIntro.htm http://www.sticky.co.uk/puy2k/index.htm http://www.bisque.com/Products/TheSkyPE/TheSkyPE.asp Q. How should I select a star atlas? A. That's a tough and personal question to answer. The right choice depends a lot on how you intend to use it, and what you're interested in observing. One common use of a star atlas is as a guide for star-hopping to various deep-sky objects (DSOs). Now, DSOs are extended objects; unlike stars, their light is spread out over an area, rather than concentrated in a tiny point. This tends to make them harder to see than stars of the same magnitude. For that reason, you might expect that an atlas might contain, say, all stars down to magnitude 8, and all DSOs down to magnitude 6. But in fact, exactly the opposite is true. An atlas that contains all stars down to magnitude 6.5, say, might contain all or most DSOs down to magnitude 10, and some even dimmer than that. Partly, this is because there are far fewer relatively bright DSOs than there are relatively bright stars, but it is also because the atlas publishers don't expect you to match the eyepiece field, star by star, when you're hunting down DSOs. Rather, they give you only what they think is needed to find the target, and using a variety of means. This may frustrate those prospective star-hoppers who don't happen to be particularly good at pattern matching. Because of this, I think it's best to have a star atlas that matches, at least approximately, whatever view of the sky you have when you navigate. For example, if you navigate using the unaided eye (or with a unit-power finder like the Telrad), then your signposts are unaided-eye stars--that is, stars down to magnitude 6.5. You should therefore use an atlas that goes down to about magnitude 6.5, because any atlas that goes deeper is wasted for your purposes. (You can't navigate using 8th-magnitude stars if you can't see any!) Atlases in this category include the Edmund Mag 6 Atlas, Cambridge Star Atlas, Bright Star Atlas, and the Norton Star Atlas. All cost in the neighborhood of $10 to $20 U.S. If, on the other hand, you navigate using a small finderscope (or maybe a larger one under light-polluted skies), then an atlas that goes down to magnitude 8.5 or so will best match your finderscope view. The principal one in this range is Sky Atlas 2000.0. The unaided-eye stars are plotted more prominently than the dimmer ones, so it's still possible to get your bearings with the unaided eye, and then fine-tune your navigation with the 7th and 8th-magnitude stars you see through the finder. Another atlas in this range is the Herald-Bobroff Atlas, which has not one but *six* sets of charts. The main set of charts covers stars down to about magnitude 9.0. A little deeper still is Uranometria 2000.0, which has stars down to magnitude 9.5. These atlases run you in the range of $40 to $120 U.S. Those with larger finders, or possibly navigating through the eyepiece, will want something even deeper. The deepest *paper* atlas is the Millennium Star Atlas, which contains stars down to magnitude 11.0. MSA is a big beast--it comes in three sizable volumes--and costs a similarly hefty $250 U.S.! You can tell that this is about the upper limit when it comes to paper atlases. (One can, of course, use any of the computer planetarium programs to get stars down to about magnitude 15. These can usually print out custom charts. It isn't as convenient in many ways, of course.) However, DSO hunting is only one possible application. Another one is variable star observing. In this case, your targets may not be terribly hard to see, but they might be hard to identify. A 6th-magnitude atlas might put you in the right spot of the sky, but you can't figure out which 9th-magnitude dot is the cataclysmic variable you're looking for. In this case, a dedicated atlas, such as the AAVSO atlas, is probably your best bet. It generally contains stars down to magnitude 9.0 or so, but more importantly, it has the variable stars clearly indicated, with comparison magnitudes of stable stars. Or perhaps you use a GOTO telescope. In that case, you are guided entirely by the selection of objects of interest, not by how you navigate. A typical magnitude-6.5 sky atlas contains objects that can be seen under decent conditions by about a 4-inch scope; Sky Atlas 2000.0 contains objects visible in a 6-inch scope, and MSA those visible in an 8 to 10-inch scope. Under these circumstances, the object guides that are packaged separately in the case of Sky Atlas and Uranometria become all the more important, since it is these books that tell you which objects are of particular interest, among all the thousands of objects visible in such a telescope. Q. How do you measure distances in the sky? A. When people are first asked to describe the separation, say, between two stars, they often say something like, "Oh, they're about a foot apart," because that's the sort of measurement we're used to down on Earth. It makes perfect sense to say that two nails are a foot apart on a piece of wood. However, it doesn't make any sense at all in the night sky, because the sky has no depth of field--all the stars look like they're at about the same distance. If all the stars were a mile away, a foot would appear very small--it would be very difficult for your eye to separate two stars separated by only a foot. And if they were 160 kilometers (100 miles) away, it would be plainly impossible. As it happens, the stars are all more than 40 trillion kilometers (25 trillion miles) away and at all different distances, so the measurement of a foot is useless. What we need is some kind of measurement that doesn't depend on how far away the stars are. One such measurement is the angle of separation. If we draw two lines, one from each star down to us, so that they intersect at our eyes, those lines meet at an angle. The distances to the stars doesn't enter it at all--it doesn't matter where each star is along its line, the angle stays constant. Therefore, the angle of separation is a perfectly suitable measure of distances in the sky. The unit of angular measure is the degree. There are 360 degrees in a circle, and the sky is a hemisphere, so there are 180 degrees from one point on the horizon all the way to the opposite point on the horizon, or 90 degrees from the zenith overhead down to any point on the horizon. If one star is on the horizon, and another is, say, one-fifth of the way up from the horizon to the zenith, then their angular separation is one-fifth of 90 degrees, or 18 degrees. We can also measure sizes this way. About 180 full Moons would fit, stacked end to end, from the horizon to the zenith, so the angular size of the Moon is 90 degrees, divided by 180, or 1/2 degree. Some angles are too small to measure conveniently using degrees, so we split up the degree into smaller units. A minute is 1/60 of a degree, so the Moon can also be said to be 30 minutes across. A second, in turn, is 1/60 of a minute. (It's called a second, because it's the second division of a degree. There is also such a thing as a third, which is--you guessed it--1/60 of a second, but that unit now only exists as a curiosity and isn't used by anyone.) Stars in binary systems can often be distinguished only through a telescope, and their separations are often measured in seconds. For example, the Double Double in the constellation of Lyra the Lyre is composed of two binary systems. In each binary, the two stars are separated by about 2.5 seconds. Because minutes and seconds are also units of time (and of right ascension, too), the angular variety are often called arcminutes (or minutes of arc) and arcseconds (or seconds of arc). Q. What is the distinction between true field of view and apparent field of view? A. In short, the true field of view tells you how much of the sky you see, and the apparent field of view tells you how big that much sky looks when magnified by the telescope (or binoculars). If you look through a telescope at the Moon, say, at 100x, you'll find that the Moon more or less fills the field of view. In wide-angle eyepieces, there may be quite a bit of dark space around the Moon, and in other eyepieces, you may not be able to squeeze the whole Moon in at 100x, but we can ignore these differences for the moment. If the Moon exactly fills the eyepiece field of view, the true field of view is 30 arcminutes, since that is the angular size of the Moon, and the Moon is filling the field of view. That's how much of the sky you can see through the eyepiece. It doesn't make any difference that the patch of sky you happen to be looking at is all Moon--if you rotate the telescope over to a featureless expanse of sky, the true field of view is still the same old 30 arcminutes. However, the Moon certainly doesn't look only 30 arcminutes across. It looks that big to the unaided eye, but the point of using a telescope on the Moon is to make it look bigger. How much bigger? Well, 100x bigger, and 100 times 30 arcminutes, or half a degree, is 50 degrees. That's how big the Moon, or whatever patch of sky you're looking at, seems to you, and that therefore is the *apparent* field of view. That's also the relationship in general: apparent FOV = true FOV * magnification This is only an approximate formula, and to be more precise is affected by a number of optical vagaries, but we don't need to worry about that here. Incidentally, the apparent field of view is inherent in the eyepiece. In fact, if you just look through the eyepiece, without inserting it first into any telescope, you'll see a sharply defined circle. That circle's angular size is the apparent field of view. The true field of view is related to the angular field of view by the magnification, and so it is *not* inherent in the eyepiece--it also depends on the telescope you're using the eyepiece with. Q. How can I measure the apparent field of view of my eyepiece? A. Here's a method that's worked for me. You need a tape measure and the ability to use your two eyes for slightly different purposes. As mentioned in the answer to the preceding question, if you look through an eyepiece just on its own, without a telescope, you'll usually see a sharp edge to the field of view. That's because you're seeing the field stop, which lies at the focal plane of the eyepiece. If the barrel itself is being used as the field stop, the edge might not be as clean, but you can still use this method. Set up in front of an object of known height (or width) h. I use a doorway that's 80 inches tall. Holding both eyes open, look through the eyepiece with one eye. Be sure to keep the eyepiece level with the midpoint of the object. You should see an indistinct field with the eyepiece eye, and the object with your other eye. Now, move back and forth until the object is just as tall (or wide) as the field of view. Measure the distance d between your *eye* (not eyepiece) and the object. The apparent field of view is then measured directly as h aFOV = 2*atan --- 2*d Here's a rough ASCII diagram: ___ / ^ / | / | / | / | / | / eye<EP h \ \ | \ | \ | \ | \ | \ v --- |<-- d -->| For example, my 6 mm Radian yielded a distance d of 69 inches, so the aFOV was 2*atan(80/138) = about 60 degrees. I estimate the error on this method to be on the order of 1.5 degrees, plus or minus. Q. What is an orthoscopic eyepiece? A. An orthoscopic eyepiece is simply one which exhibits no distortion. If an object 2 degrees across looks exactly twice as wide as one that's only 1 degree across, then you're looking through an orthoscopic eyepiece. Otherwise, the eyepiece exhibits distortion. If the 2-degree object looks *less* than twice as wide as the 1-degree object, then the eyepiece has barrel distortion. This is because through such an eyepiece, a square object looks as though its sides were bowed out, like a barrel. On the other hand, if the 2-degree object looks *more* than twice as wide as the 1-degree object, then the eyepiece has pincushion distortion. This is because through that eyepiece, a square object looks as though its sides were bowed in, and this supposedly reminds people of pincushions. (Does that make any sense to you? It doesn't to me.) Anyway, the term "orthoscopic," used generically, doesn't refer to a specific design, but rather a characteristic which any design might or might not have. Plossls, for example, are orthoscopic eyepieces. Tele Vue Radians are nearly orthoscopic, but not quite; they exhibit a small amount of pincushion distortion. Naglers and other wide-angle eyepieces have a relatively large amount of pincushion distortion. This may make navigating while using them a little like walking while wearing coke bottle glasses. The image is clear, so long as you keep the scope pointed at one particular object, but once you start moving it, some people get a little "motion sick." Others aren't bothered by it at all. There is a specific design, called an Abbe orthoscopic (after optical designer Ernst Abbe, who designed it in or around 1800). It consists of a positive triplet field lens (the part nearer the "bottom" of the eyepiece) and a positive singlet eye lens (the part nearer the "top"). It is, of course, orthoscopic in the general sense, and furthermore, it is high in contrast (allegedly because it only has 4 elements and 4 air-glass interfaces). It is a popular choice among planet observers. Q. What does "parfocal" mean? Parfocal essentially means that you don't have to change focus when you change eyepieces. Eyepieces are said to be parfocal to others, or alternatively, two or more eyepieces can be said to be parfocal. One eyepiece on its own cannot be simply parfocal; such a statement makes no sense. For example, suppose you have three eyepieces: a 40 mm, a 25 mm, and a 10 mm. Suppose that whenever you have something in focus with the 25 mm eyepiece, you can swap it out for the 10 mm eyepiece, and the object will still be in focus, without having to adjust anything. Suppose further that that isn't the case with the 40 mm eyepiece; whenever you switch from either the 25 mm or the 10 mm to the 40 mm eyepiece, you have to adjust focus. Then, the 25 mm and 10 mm eyepieces are said to be parfocal (to each other); the 40 mm eyepiece is not parfocal to either of them. This means that parfocality, if I can mangle the word in such a way, is transitive: if A is parfocal to B, and B is parfocal to C, then A is also parfocal to C. There is one special circumstance in which a single eyepiece can be said to be parfocal. A zoom eyepiece may or may not require refocusing as you change the focal length (and hence the magnification); if it doesn't require adjustment, it can reasonably be said to be parfocal (to itself). Q. What is a Barlow lens, and how do I use it? And how does it work, anyhow? A. A Barlow lens is an accessory that boosts the magnification of any eyepiece you use with it. Many Barlows are nominally 2x, meaning that if you normally get 100x with a specific eyepiece in a specific scope, adding the Barlow will get you 200x. However, Barlows (and other power amplifiers) come in a variety of different "magnifications." The normal way of using a Barlow lens is to insert it into the focuser, in place of the usual eyepiece. The eyepiece is then inserted into the Barlow lens. If you compare using an eyepiece in isolation with using it in conjunction with the Barlow, you will ordinarily find that you have to refocus the telescope, often considerably. Occasionally, you may have to refocus too much--your telescope won't reach focus with that particular combination. If you *don't* have to refocus, or at least don't have to refocus very much, the Barlow is often called "parfocal" (see the preceding question). In principle, a Barlow lens is only a negative lens in a long tube. The lens is usually a doublet, although it may be a triplet, as in the Celestron Ultima or the Meade "apochromatic" Barlow, or it may be a combination of a negative doublet and a positive doublet, as in the case of the Tele Vue Powermates. Light approaches the objective of a telescope as a parallel beam, and the objective focuses this beam into a light "cone." This cone has a characteristic shape--some telescopes have fat light cones, and others have thin ones. The fatness or thinness of the light cone is measured by dividing its length by the diameter of the base. The length of the cone is equal to the focal length of the objective, and the diameter of the cone's base is equal to the aperture of the objective. The ratio of these two numbers is called the focal ratio, or f/ratio for short. A telescope objective makes light converge, so we say that it is a positive lens or mirror; it has a positive focal length. A negative lens, such as the one in a Barlow, has a negative focal length; it makes light *diverge*. Therefore light that enters the Barlow in a parallel beam will spread out when it emerges. If the light beam is not quite parallel when it enters the Barlow, but is already converging slightly, then the beam will still spread out upon emerging, but it will spread out more "slowly." If we make the light converge even more before entering the Barlow, we will get to a point where the light is not spreading out at all when it leaves the Barlow, but is instead a parallel beam, or even converging slightly. In such a situation, you might have a light cone going in that is quite fat--that is, with a small focal ratio--but comes out relatively thin, with a large focal ratio. And if you have a larger focal ratio with the same aperture (the Barlow doesn't affect the effective aperture of the telescope), the effective focal length must be increased in proportion. Finally, if the effective focal length is increased, then the power or magnification of any given eyepiece must be increased as well, since the power of an eyepiece is equal to focal length of telescope power = ------------------------- focal length of eyepiece Incidentally, it's a commonly held conception that a Barlow lens, by increasing the effective focal ratio of the telescope, inherently makes most of the (longitudinal) color error go away. That generally isn't the case. In an achromatic telescope, the colors are almost all the way spread out by the time the light gets to the Barlow lens--it just can't get all the colors to focus back into one place at that point. What does appear to be the case is that inserting a Barlow makes it possible to make better use of eyepiece designs that work well only at long focal ratios. These tend to be less expensive than designs that work well at short (and long) focal ratios. Q. Is a fast telescope (small f/ratio) brighter than a slow telescope (large f/ratio)? A. Roughly speaking, the answer is yes if you're talking about taking long-exposure astrophotos, and no if you're talking about actually looking through the telescope at a given magnification. What really determines the amount of light gathered by a telescope is the aperture. There are also certain variations based on the design, involving the central obstruction (which clearly blocks some light from entering the telescope in the first place) and the reflectivity or transmission of the optical elements (which cause light to be lost once it has entered the telescope). Let's ignore those for now, and assume that we are comparing a fast telescope with a slow telescope of roughly the same design. In that case, the amount of light gathered by the telescope varies as the square of the aperture (diameter). For example, a telescope with an aperture twice as wide gathers 2 squared or 4 times as much light. Now, for visual use--looking through the scope with an eyepiece--that's all that matters. If you have an 8-inch f/4 (that's fast) and an 8-inch f/10 (that's slow), and you use both at, say, 100x, then images will look equally bright through both telescopes, because the same amount of light is being gathered by both, and is spread out over the same area in both. Of course, in order to get 100x in the fast telescope, you need about an 8 mm eyepiece, and in the slow one, only a 20 mm eyepiece. If you were to use a 20 mm eyepiece on the fast telescope, that would yield a power of only 40x. Things would look 2/5 as large as they do through the same eyepiece on the slow scope, and since the same amount of light is being squeezed into only 2/5 squared, or 4/25, of the area, things look much brighter (provided you can fit the 5 mm exit pupil of this set-up into your eye). In the case of (prime-focus) astrophotography, there is no eyepiece. What determines the size of the image is the focal *length* of the scope and not the focal ratio. The image scale is directly proportional to the focal length. Since the 8-inch f/4 has a focal length of 32 inches, and the 8-inch f/10 one of 80 inches, images will be only 2/5 times as large in the former as in the latter--precisely as when using a single given eyepiece in visual use. And for the same reason, things will look 25/4 (that is, 6-1/4) times as bright, although they will also cover 6-1/4 times smaller an area. In short, in astrophotography, scopes of the same focal *length* yield images with the same *scale*; scopes of the same focal *ratio* yield images with the same *surface brightness* (see the following question). Astrophotographers can take advantage of this enhanced brightness to reduce the length of exposures. To get the same surface brightness, one can take images in 4/25 the time in any f/4 as in any f/10. (Strictly speaking, because of those other design factors mentioned at the start of this answer, we should be using so-called "t/ratios," which take them into account.) Q. What is the limiting magnitude for my scope? A. That depends a lot on how acute your eyes are, what kind of skies you have, and what kind of object you're looking at. One way to address the first two factors is to figure out what the unaided-eye limiting magnitude is for you on any given night. If you can see to magnitude 6 with the unaided eye on any given night, and we can determine that you should be able to see 7 magnitudes deeper with your telescope than you can without it, then the limiting magnitude is 13 on that night. If, on some other night, the unaided eye limiting magnitude is 5.5, then the limiting magnitude on this second night would be 12.5. The formula for determining how much deeper you should be able to see with your telescope than without it depends a little on your pupil size (the pupil in your eye, that is). However, we can assume a 5 mm pupil without too much error, and give the adjustment as 5 log (D/5) where D is the aperture of your telescope, in millimeters. Thus, a 50 millimeter scope gives an adjustment of 5 log 10, or 5 magnitudes deeper. However, there is another factor to consider, and that is the type of object you're looking at. If you're under magnitude 6 skies--that is, you can see stars down to magnitude 6--then the above formula tells you that you should be able to see down to magnitude 11 with a 50 mm telescope. But those are just magnitude 11 *stars*. You will not be able to see many galaxies, for example, with magnitudes as high as 11, because galaxies are extended objects, not dots. Their light is therefore spread out over an area, and although they would be visible if only that light were squeezed into a dot, spreading it that thin makes them invisible. Under these circumstances, a hard rule simply doesn't exist. You will have to learn from experience what your telescope will see when it comes to extended objects like galaxies and nebulae. There is a rule of thumb, though, that might help. It involves a certain property of the object, called surface brightness, which you can think of as the brightness per unit area, and the unit area in this case is square arcminute. What we ordinarily call the magnitude of the galaxy is more precisely called the *integrated* magnitude--that is, the brightness of the whole galaxy, summed up (or "integrated") over its entire area. If a galaxy is magnitude 10, but has an area of 100 square arcminutes, then each square arcminute contains 100 times less light than the whole galaxy. Since a factor of 100 is equal to 5 magnitudes, the surface brightness of the galaxy is 10+5, or 15. The rule of thumb, which I'll call the Rule of 13 (even though I didn't come up with this rule), states: Add the integrated magnitude to the surface brightness, and subtract 13. The object should then be about as visible as stars whose magnitude is this number. In the case of the galaxy above, its integrated magnitude is 10, and its surface brightness is 15. Add those together, and subtract 13, and you get 12. If you can see stars through your telescope down to magnitude 12, then this rule suggests that you have a decent chance of spotting the galaxy. Again, though, the Rule of 13 is just a guideline, and not really a hard and fast rule. You might use it to prioritize an observing list, but I wouldn't omit a target solely because the Rule of 13 suggests that you won't be able to see it. One particular issue with the Rule of 13 is that most catalogues don't list peak surface brightness numbers. The upshot is that if an object has a strong central condensation, using the average surface brightness will lead to an underestimation of its visibility. Q. How is seeing related to twinkling? A. Seeing and twinkling are related, but they are not the same thing. The term "seeing" refers to the effect of turbulence on the view through the eyepiece, how it distorts the image. Twinkling is the blinking on and off of stars; another name for it is "scintillation." It too is caused by atmospheric turbulence. An oft-quoted rule of thumb states that when the stars twinkle, the seeing is poor, and conversely, when the stars do not twinkle, the seeing is good. That, however, is not always the case, and I'll try to explain why. We can think of a star emitting light rays in all directions, only some of which land here on the Earth, or in our eyes. If we were to trace those rays back where they came from, we would find that they converge, quite naturally, back at the star. However, the stars are so far away from us, and our eyes so small in comparison, that those light rays are as good as parallel by the time we see them. If the Earth had no atmosphere, the light rays would continue to be parallel until the moment they struck the ground, or our eyes. If you could see the places where the light rays struck the ground, you could imagine that the ground would be littered with countless little points of light, and with no atmosphere, the points would be perfectly evenly spaced. However, the Earth *does* have an atmosphere. In any transparent medium that is not a vacuum (such as the atmosphere), light travels slower than it does in a vacuum. This is not a problem so long as the atmosphere is uniform all the way down to the ground. All light rays are equally slowed and their motion is unaffected except for speed. You can see that if the light rays were merely slowed down, they would travel to the ground in exactly the same paths as before, and their points of impact would still be perfectly evenly spaced. Unfortunately, the Earth's atmosphere is not uniform. Some pockets of air are hotter or colder, denser or less dense. This not only slows the light rays down by different amounts as they traverse the atmosphere, but it also bends them, and the more the atmosphere varies in density or temperature, the greater the bending. If the atmosphere changed willy-nilly as the light descended to the Earth, who knows what would happen to the image of the star. But the very fact that we can see the stars at all indicates that that doesn't happen. Luckily for astronomers, the turbulence layers are generally rather limited in extent. Let's consider, for a moment, if there's just one layer of turbulence, high up in the air. When the light rays hit that layer, they are still a long way from hitting the ground (in human terms). The light rays may only be bent a little by the turbulence layer, but since they are so high up, their points of impact may be changed significantly, perhaps as much as a few centimeters. Moreover, the light rays are bent randomly and are not all bent in the same direction. Instead of a pattern of perfectly evenly spaced points of impact, we would see places where more light rays were hitting the ground, and the light there would be brighter. In other places, fewer light rays would strike the ground, and there the light would be dimmer, or perhaps even absent. What does this have to do with twinkling? Stars twinkle because as the atmosphere swirls around, occasionally the light rays get bent so far as to miss your eye entirely, or mostly. Your eye's pupil, or opening, is about 5 millimeters across at nighttime. If your eye happens to be in one of those holes in the pattern, where fewer light rays are meeting, the star will suddenly appear to dim. Then, as the atmosphere moves around again, the light rays will return to your eye and the star will re-brighten. These brightness changes are not inherent in the star; they are a product solely of how the atmosphere brings the light rays to your eye. The changes take place on the order of perhaps a second or so, and this is what we see as twinkling, or scintillation. On the other hand, suppose that the layer of turbulence is close to the ground. In that case, by the time the light rays hit the layer, they are already so close to striking the Earth that their points of impact are changed only slightly, perhaps just a millimeter or so. In that case, you can see that there can't be so much as a single hole 5 mm wide where no light strikes. The holes can only be twice as wide as the bending is--and twice a millimeter is only 2 millimeters. In other words, given the same degree of turbulence, but different heights, high-altitude turbulence causes the stars to twinkle noticeably, while low-altitude turbulence causes them to twinkle only modestly, or not at all. But this is only to the unaided eye. What about telescopes? What about telescopes indeed! A telescope is generally at least 50 millimeters across at the objective, and usually greater than that. Even with high turbulence, the chances that there will be a circle more than 50 millimeters across where no light rays hit is minuscule. I suspect that it is so close to zero that there is essentially no way for stars to entirely twinkle out (though they might appear to dim and brighten). However, just because stars don't twinkle at the eyepiece doesn't mean that the image is unaffected. Suppose you're observing Mars, and you have it centered in the eypiece. Light rays from the center of Mars get to the objective along a line perfectly parallel to the axis of the telescope; these light rays are called on-axis rays. Light rays from the edge of Mars, say, get to the objective along a line at a very slight angle to the axis of the telescope; these light rays we call off-axis rays. If light from Mars hits a turbulence layer, though, all bets are off. The actual shifting of the light may not matter very much, since as we noted, it's very unlikely that there will be a hole as large as the telescope's objective. However, it also gets bent--that is, its angle changes. On-axis light rays become off-axis light rays, off-axis light rays become on-axis light rays, and the image of Mars appears therefore to shift a little in the eyepiece. Worse yet, the bending may happen unequally to the different parts of Mars, meaning that the image appears to wrinkle and sway, almost as though we were observing it from the bottom of a swimming pool, and it is *this* effect that we call seeing. All this leads to the interesting question: How much does the altitude of the turbulence affect seeing? Not very much at all! Since what determines the seeing is the angle through which the light rays are bent, and not their displacement, it doesn't matter whether the turbulence layers are way up there, or all the way down here, the angle of deflection is the same. Seeing is to first order independent of the altitude of the turbulence. The upshot of all this is that if the turbulence is high up but weak, the twinkling may be quite noticeable, but the seeing still reasonably good, whereas if the turbulence is low down but strong, the twinkling may be absent, but the seeing will be poor. Of course, if the turbulence is high and strong, or low and weak, then the two phenomena agree, but that's not always the case. Twinkling just isn't a reliable indicator of seeing. By the way, the fact that bad seeing resembles the view from the bottom of a swimming pool has led some people to the idea that the two phenomena are similar. Other than the visual effect, however, that simply isn't true. Images from the bottom of a swimming pool waver not because of turbulence within the water, but because the surface of the water has waves, and light from outside objects therefore hits the water at constantly changing angles. This affects how much the light is bent, and that's what causes the boiling effect in this case. The same effect on the image of Mars, on the other hand, has little to do with the top "surface" of the atmosphere, and is primarily dependent on turbulence layers within the atmosphere. Q. What does "diffraction-limited" mean? A. Literally, it means that the performance of a set of optics, such as a telescope, is limited by the diffractive nature of light, and not by other factors such as the quality of the optics. However, as we'll see later, this term is so often abused that it is nearly meaningless. Let's consider a Newtonian reflector. The same basic ideas apply in other kinds of telescopes, but then there are other factors that obscure the basic principle at work. Ideally, a Newtonian's primary mirror has a paraboloidal shape--that is, it's the result of rotating a parabola around its axis of symmetry. Why "ideally"? Because when you shine a beam of light rays down on a mirror, all parallel to that axis of symmetry, that is the one shape that will focus all of those rays down to a point, appropriately enough called the focal point. That at least was the hope of its designer, the English scientist Isaac Newton (1646-1727). It was later discovered that because light has a wave nature to it, the light rays interfere with each other noticeably when they get close to the focal point. The result is that instead of getting a neat, infinitesimal point of light at the focus, what you get instead is a ball. This is the effect of light diffraction. It must be emphasized that this has nothing at all to do with not making the mirror good enough. Even if the mirror is absolutely perfect, you can't get a point of light. In other words, you're not fighting imperfect engineering techniques, you're fighting physics--usually a losing battle. When viewed through an eyepiece fitted to the telescope, this ball has the appearance of a disc, surrounded by a series of successively dimmer rings. This disc is named the Airy disc, after George Airy, the English astronomer and physicist who first gave the proper explanation for it, and the entire pattern is sometimes called the Airy pattern. The view of any celestial object (or terrestrial, for that matter) is affected by the Airy pattern. Instead of being a sharp point of light, stars at high power are Airy discs. These discs are *not* the discs of the stars themselves--again, they are only artifacts of the physics of light. This same effect is visited on extended objects such as galaxies and planets, too. Every single point of detail is smeared around according to the Airy pattern, just as the light of a star is. The upshot is that patches of detail that are finer than the size of the Airy disc are washed out--all you get in these cases are uniform patches. This is especially a problem with the planets, which are full of patches of fine detail. The diffraction of light, however, is only one of many ways for detail to be lost. Another is the atmosphere; if the air above the telescope is turbulent, that can cause light rays to bend even before they enter the telescope, and that destroys some detail. (See the preceding question for more information.) The optics themselves may radiate some heat as the night progresses, and that is destructive, too. Finally, even if the optics are properly acclimated, and the atmosphere is steady, the optical quality may also degrade the image. Out of these factors, the one that is under the control of the telescope (or rather, the telescope manufacturer) is optical quality. It is also a major selling point; naturally, higher-quality telescopes will sell better than lower-quality ones, all other things remaining equal. On the other hand, other things do not remain equal: it costs more to make a higher-quality telescope. As the quality increases, at some point, it just doesn't make any sense to put any more money into the optics; the improvement in the image isn't worth it. The question is, at what point does that happen? How do you judge when the optics are "good enough"? The common criterion is the diffractive effect of light. At any given moment, the atmosphere may suddenly calm, the optics may be all cooled, but light diffraction never rests. It is *always* in effect. On the best of nights, the detail you can see is limited by either the optical quality, or the diffraction of light. If it's the latter, then the optics *are* "good enough"; that is, they are "diffraction-limited." This is the first definition of the term. This is, however, just subjective hand-waving. After all, at no point does higher quality lose *all* effect--it's just that the effect may be tiny compared to that of diffraction. For that reason, astronomers and opticians have tried to quantify "diffraction-limited." One way is to specify the necessary accuracy of the curve, or "figure," of the optics. This is the source of the Rayleigh criterion, which states that the telescope is diffraction-limited if the light waves miss focus by no more than 1/4 the wavelength of light. However, this criterion totally ignores the distribution of the error. It considers identical two sets of optics, one which has only two small patches of error, and one that is completely covered with error patches. Another criterion, due to Marechal, considers a telescope diffraction- limited if the RMS--the "root mean square"--of the error is less than 1/14 the wavelength of light. This takes into account the distribution of the error, so that the telescope with two small error patches rates better than the one completely covered with error patches. The Rayleigh and Marechal criteria are a result of observations; that is, experienced astronomers tested a number of telescopes with known quality, and tried to establish a point at which the image was "good." Another way to quantify "diffraction-limited" is to examine how light is distributed in the Airy pattern. In an ideal set of optics, about 84 percent of the light goes into the Airy disc itself. The remaining 16 percent goes into the rings, most of that being in the first ring. The light in the rings means that the intensity at the very center of the Airy disc is limited to a certain theoretical maximum for that particular aperture and design. However, imperfect optics can throw even more light into the rings and away from the center, so that the central intensity drops even further. The *Strehl ratio* of a telescope is the actual intensity at the center as compared to the ideal central intensity. Using this metric, a scope is said to be diffraction-limited if the Strehl ratio is over 80 percent. These various ways to quantify "diffraction-limited" represent, collectively, the second definition of the term. It turns out that they are in remarkable agreement with each other. In other words, under normal circumstances, optics that satisfy one criterion will come at least close to satisfying the others (although there are exceptions). Unfortunately, there is a third definition. This last definition is how the term is used in advertising copy, and here it is so overused as to be nearly meaningless. The nominal definition used is the old peak-to- valley definition (1/4-wave), but this can be interpreted loosely (see the following question). What's more, the old phrase "guaranteed to be diffraction-limited" means just that: we'll exchange it if it isn't diffraction-limited, but it's up to you to initiate the process. In that way, many customers who either don't know or don't care enough end up with subpar telescopes. Many authors who should know better recommend that beginners look for telescopes that are rated as "diffraction-limited." It's not wrong to look for diffraction-limited optics, of course; the problem is that you can't always trust what you read, and you may have to do some hunting around before you find the real deal. Q. I often seen optical quality measured as "1/8-wave or better." What does this mean? Is, for example, 1/8-wave better than 1/4-wave? It depends. All other things being equal, yes, 1/8-wave is better than 1/4-wave. But all other things are not always equal. Light from a distant star arrives at the objective (lens, mirror, or both) in parallel rays. A perfect objective would focus all of these light rays down to one point, but perfection is impossible: invariably, some of the light rays overshoot the mark, some undershoot it. One measure of quality of an objective is how far the light rays miss the mark. The precision of even a so-so set of telescope optics is astonishing: the error is on the order of 0.00001 inches. Now obviously, measuring something that small in inches or even millimeters would be a pain, so instead, the wavelength of light is used. Then that error of 0.00001 inches can be said instead to be about 1/2 wave, since the wavelength of visible light is on the order of 0.00002 inches. Now I'm going to make that same error be about 1/6-wave. The trick is that we forgot to specify the color, or wavelength, of light that we used as our yardstick. Light of a blue-green color is about 500 nanometers, or about 0.00002 inches, and using that wavelength as our yardstick, the error of our objective is indeed 1/2 wave. But let's suppose we use red light of about 700 nanometers. Then the error drops to 1/3-wave, simply because the wave we're using as our yardstick is longer. With me so far? (Actually, it's worse than that in some cases. The above analysis works for reflectors, but in the case of refractors, they're often very well-shaped for some colors, but not for others. For visual use, refractors should be corrected in the middle of the visible light range, about 550 nanometers. Testing them in red light may set you off by much more than the 50 percent or so in the case of mirrors.) Then there's concern over where we're measuring the error. I've measured it at the wavefront--what happens after the light has already passed through the objective. But let's suppose we measure the error at the surface of, say, an objective mirror. If we have a pit of depth x in the mirror, then light hitting that pit is delayed by 2x--x on the way in, and x on the way out. In other words, the surface error is half of the wavefront error. Now our 1/3 wave error drops to just 1/6 wave. (This "half" rule only works for mirrors--it doesn't apply to objective lenses, so refractors aren't subject to quite such a drop.) Wait, it gets better. I've talked about measuring the extent to which light rays overshoot or undershoot the mark, called P-V (peak-to-valley) error. What if what we want to know is how smooth the wavefront is, not in the worst cases, but just on average? Then we measure the error in terms of RMS (root mean square). Because of the way the RMS error is derived, it's impossible to make a hard rule about the relation between it and P-V error, but we might reasonably see that a P-V of 1/6-wave might become a 1/20-wave RMS. So, if you want to be hard on an objective, you measure it P-V, at the wavefront, in a short wavelength like blue-green. If you want to be kind to the objective, you measure it RMS, at the surface, in a long wavelength like red. The difference can be something like an entire order of magnitude, and you need to be sure how your particular error is being measured. Measuring errors RMS without mentioning it is pretty slimy and I don't think anyone big does that, but measuring at the surface in a long wavelength is probably at least somewhat common. Q. What is the star test, and how does it work? A. The star test is a test of optical quality and other factors affecting image quality, and it can be run by anyone. The definitive reference regarding star testing in the amateur community is Harold Suiter's Star Testing Astronomical Telescopes. What follows is a very brief description of how and why it works. In the star test, you start with a star in focus at the center of the field of view, at very high power--ideally something exceeding 40x per inch of aperture. (For example, use 160x or more on a 4-inch telescope.) Now, ever so slightly rack the star in and out of focus, on both sides of focus. When out of focus, where you might expect just a fuzzy ball of light, what you actually get is a small bullseye pattern of a central dot and some concentric rings. This is due to the diffractive nature of light, which for reasons of space we won't get into here. If everything is working properly, the bullseye pattern should look exactly identical on both sides of focus. However, if there is an error somewhere, this will be reflected in a difference between the two out-of-focus images. For example, one possible error is called spherical aberration, and it is caused by a misshapen mirror or lens. In order to focus light to a point, a mirror (say) must be shaped like a paraboloid--that is, a parabola rotated around its axis. If the shape is more like a section of a sphere than a paraboloid, then the rays of light entering near the periphery of the mirror will be focused too close to the mirror, and those that enter near the center will be focused too far from the mirror. The result is that instead of a sharp point of focus, what you get is a kind of oozing funnel, with the broad cup of the funnel pointing toward the mirror and the drain tip pointing away. See the following question for more on this. (There's a name for the funnel, by the way. It's called the "caustic horn." Horn for the shape, clearly, and caustic because it's at the focus, and therefore "hot." I prefer "oozing funnel," myself.) Spherical aberration creates fuzziness in images. When just observing, its effect may be difficult to distinguish from bad focus or atmospheric instability, but it reveals itself in a characteristic way in the star test. Since the light at the center focuses too far away from the mirror, when you go out of focus in one direction, you see the drain tip of the focus "funnel," and the center gets brighter and the outer diffraction rings get dimmer. In the other direction, you see the cup of the "funnel," and the center gets dimmer and the outer rings get brighter. The two out-of-focus images are no longer identical, and this particular effect on the star test can be identified, in isolation, as spherical aberration. Unfortunately, there are many different errors possible, and these combine in some non-intuitive ways, making diagnosis non-trivial. What's worse, the images can also be affected by factors that are not the fault of the optics at all, such as turbulence. The end result is that reading the star test is not easy. It is easy to identify a good telescope, but not so easy to identify a bad one--what you interpret as errors may be factors out of the telescope's control. If you want to be a conscientious user of the star test, you should read Suiter's book. Q. What do "over-corrected" and "under-corrected" mean? A. The terms refer to correction of spherical aberration. The "ideal" reflector mirror is paraboloidal, at least in the case of a Newtonian reflector. Only a paraboloid--that is, the 3-D shape you get by revolving a parabola around its axis--will focus a parallel, on-axis beam of light to a point. (Well, more or less. See the question on diffraction-limited telescopes, above.) However, it is not simple to grind a paraboloidal mirror. It doesn't have equal curvature everywhere; it's less curved on the edges than it is in the center. It's rather easier to grind a spherical mirror, which has the same amount of curvature everwhere on its surface. A spherical mirror, unlike a paraboloidal one, does not focus the on-axis light to a point, however. Instead, the light rays striking the edge of the mirror focus closer in to the mirror than do the rays striking the center. As a result, even point sources do not appear exactly pointlike; instead, what you get is a fuzzy ball, due to the imperfect focusing of the spherical mirror. Because a spherical mirror is easier to make, however, one often begins by grinding a spherical mirror, and then "correcting" its shape to that of a paraboloidal one. If one doesn't correct enough, then the light rays at the edge continue to focus closer in than the ones at the center (although perhaps not as much as with a perfectly spherical mirror). In this case, the image is still a little fuzzy, and the mirror is said to be "under-corrected." On the other hand, if you go too far, and the mirror is too "sharp," then the light rays at the edge now focus further out than the ones in the center. The mirror is then said to be "over-corrected," although the resulting image quality is just about the same as it is with an equivalently under-corrected mirror. Only in between, when the mirror is precisely corrected to a paraboloidal shape, do you get sharp, on-axis images. It should be remarked that even this mirror has an off-axis aberration, called coma, in which stars out from the center of the field of view appear comet-like, with their tails trailing out to the edge of the field of view. Coma is only objectionable in the faster (i.e., smaller focal ratio) scopes--perhaps f/5 or faster--and even then, it can be largely reduced by devices such as Tele Vue's Paracorr. Q. What is astigmatism, and what causes it? A. Astigmatism is a directional flaw in the optics, and therefore in the image presented by those optics. One way to think of the way a telescope works is to imagine parallel rays entering the telescope, which are then focused to a point on the image plane by the objective (whether that's a lens in the case of a refractor, or a mirror in the case of a reflector). That image is then magnified by the eyepiece so that you can see it. That's what happens ideally, at least. What occasionally happens is that the light in one direction (say, up and down) focuses too short, and the light in the other direction (left and right) focuses too far. That's astigmatism. Because the deviation of the optics from the ideal is positive in one direction and negative in the other, this is sometimes called potato-chip error. With astigmatism, at no place is all the light in focus. In the star test (see the preceding two questions), if you focus in, then the up-down light is in focus, but the left-right light is out of focus, and instead of a point, you get a left-right bar. If you focus out, then the left-right light is in focus, but the up-down light is out of focus, so you get an up-down bar. In between, when both are slightly out of focus, you get a plus or cross shape. That's often the point of best focus for that telescope, but it may not be very good, depending on how astigmatic the telescope is. Astigmatism can come from anywhere in the optical system, from your eyes to the objective. You can identify where it's coming from by process of elimination. For example, if you try looking into the scope from two different directions, but the astigmatism still points the same way (with respect to the telescope), then you know the problem is not in your eyes. Next, rotate your eyepiece. If the astigmatism doesn't move, it's not in the eyepiece. If you're using a reflector, then try rotating your primary. If the astigmatism *still* doesn't move, then it's not in your primary. And so on. Astigmatism is sometimes ground into the optics, or come about as a result of the way the glass formed. If so, you're out of luck, I'm afraid--you'll have to either live with the flaw, or get the optics replaced. However, more often than not, it's a result of the way the optics are supported. Mirror sag or pinching support clips on the primary are principal suspects, as are similar clips on the secondary. Q. What do the terms achromat, apochromat, and semi-apochromat mean? A. These terms usually refer to the degree of color correction that a refracting telescope possesses. An achromat is a refractor that has only a little bit of chromatic aberration, in which the colors that make up white light are split up by the objective lens. An apochromat has almost no chromatic aberration at all. A semi-apochromat, to the extent that the term means anything at all, lies somewhere in between. When refracting telescopes were first made, 400 years ago, their objectives were made from a single piece of glass. This lens refracted the incoming light to a focus, so that it could be magnified by the eyepiece. The problem was that different colors or wavelengths of light were refracted by differing amounts, and therefore did not come to focus at the same distance. This problem is called longitudinal chromatic aberration (often shortened to just chromatic aberration). As a result, if you pointed the telescope at a white star, only one of the wavelengths of light could be in focus at any given time. If you focused on the red light, the other wavelengths would all be out of focus, and could be seen as a fuzz of light that gradually grew bluer toward the edges. This robbed the image of considerable detail. The effect could be reduced somewhat by making the telescope longer, and so immensely long telescopes were designed and built, with the high-water mark being represented by Johannes Hevelius's refractor, which measured over 60 meters (about 200 feet) long. Then, in 1733, the English barrister Chester Hall discovered that by making the objective from two pieces of glass with different properties, much of the variation in focus of the different colors could be eliminated. The basic design is still used today, and reduces the chromatic aberration by about 98 percent. What is left, the last 2 percent, is called the secondary spectrum of the objective. Hall's invention (and its subsequent popularization by John Dollond) made it possible to produce well-corrected telescopes that were only a couple of meters long, rather than nearly a hundred. They were *the* telescope of choice for about a century, culminating in Joseph von Fraunhofer's refractors in the early 19th century. Eventually, the cost of making exquisitely fashioned lenses larger than Fraunhofer's caught up to the achromat design, and the heyday of the reflecting telescope began. It wasn't until the late years of the 19th century that the German physicist Ernst Abbe designed the first truly new refractor design in a century and a half, with the apochromat. This design used (typically) three glasses to produce an objective with even better correction for chromatic aberration. It reduced the secondary spectrum of the achromat by a further 80 to 90 percent, so that only a few tenths of a percent of the original aberration in the single-lens design remains--too small to be seen on virtually any target in the night sky. Abbe also gave strict definitions to what qualified as an achromat or an apochromat. These definitions felt the impact of the photographic era, however, so that an Abbe apochromat could actually seem worse than an achromat when used visually, even though this difference couldn't be seen in the film image. Today, most amateur astronomers aren't familiar with Abbe's definitions, and use the terms to refer only to the degree of color correction. (In fact, he first designed apochromatic lenses for microscopes, where chromatic aberration is also a problem, and only later transferred it to telescopes, along with his partner, Carl Zeiss.) Both achromatic and apochromatic telescopes are commercially available, with apochromats commanding a significant premium--a 4-inch apochromat (or "apo," as it is often called) typically costs well over $2,000 U.S., whereas a similarly sized well-executed achromat may cost only $500. It should be pointed out that apochromats convey several benefits besides mere color correction--they produce wide, flat fields, and are also well-corrected for spherical aberration (which see)--which are more important for astrophotography than they are for visual use. The Abbe definitions did not allow for an intermediate class of color correction. An achromat, according to Abbe, brings two wavelengths to focus at the same point; an apochromat, three. Since the terms today refer mostly to the reduction of the secondary spectrum, however, one could define a semi-apochromat to be a telescope that reduces the secondary spectrum of an achromat by about half (or about 1 percent of the original one-lens design). No single-objective design exists with this level of correction, although the compound, Petzval configuration does; this design has been used by Tele Vue in some of its refractors. Q. Does a central obstruction damage image quality or not? A. Yes, it does, but nearly everyone overestimates the damage done, especially those using telescopes without central obstructions. There is a rule of thumb running around (so to speak) to the effect that a reflector is only as good (in terms of contrast and resolution) as a refractor whose aperture is equal to the reflector's aperture minus the diameter of the reflector's central obstruction. I happen to think some of that is what happens when people stop thinking and instead speak only in aphorisms such as "A stitch in time saves nine" and "A reflector is only as good as a refractor of reduced aperture." But I'll leave that alone. It really depends on what you're looking at and what the specific instruments are. It also could depend on what kind of skies you observe under. To reduce it to, "A 6-inch refractor is as good as an 8-inch reflector," say, is to simplify matters beyond sense. The *origin* of that phrase is in the modulation transfer function, or MTF, which just measures how well the optical system preserves feature contrast, as a function of feature size. It's equal to 100 percent at a given feature size (measured in arcseconds) if the brightness difference between feature and background is completely preserved; 50 percent if the brightness difference is reduced to 50 percent; and so forth. The MTF of a telescope with a central obstruction (such as a reflector) is *like* (but not identical to) that of a smaller, unobstructed telescope; the smaller aperture is said to be the aperture of the reflector minus the diameter of the obstruction. Well, consider three telescopes: A. An 8-inch refractor. B. An 8-inch reflector, with a 2-inch obstruction. C. A 6-inch refractor. Let us assume that all three are smooth and well-corrected. Telescopes A and C also have to be well-corrected for color error. The MTF of telescope B will be lower than that of telescope A, and about equal to that of telescope C. That is the origin of that aphorism. This has to be taken with a grain of salt, however. First of all, it is not true for the finest of features. The MTF of an obstructed scope at the highest frequencies is essentially indistinguishable from that of an unobstructed scope. Telescopes A and B will perform just about equally well on small detail--say, smaller than about 1 arcsecond across. Secondly, *all* telescopes do well with larger detail, and this "larger" doesn't have to be very large at all. The MTF of all three telescopes on details of a few arcseconds and larger are high, and while telescope B will perform worse than A (and about the same as C) on these larger details, the difference doesn't hurt that much. The greatest difference is in the mid-frequency (that is, mid-size) range, between perhaps 1 and 3 arcseconds in size, where the MTFs of all three telescopes are falling, and the difference between A and B is most apparent. In this range, telescopes B and C might preserve only 3/4 as much contrast as telescope A. A great many features on Jupiter, for example, fall here--festoons, barges, ovals--but not all. Thirdly, this MTF hurts more on bright objects such as the planets, where the eye doesn't have to work hard on mere detection. With most DSOs, you are working hardest on just seeing the objects, and even on detail, the increased light-gathering power of the 8-inch telescope helps you more than its somewhat decreased contrast hurts you. Fourthly, this rule of thumb is swamped by differences in optical quality. If either telescope has rough optics, that will matter as much as, if not more than, a central obstruction. Reflectors are more prone to turned down edges, but refractors are more prone to chromatic aberration. "All other things being equal" doesn't happen very much in the real world. So, to be a bit more accurate, one should say, "A 6-inch refractor is as good as an 8-inch reflector, but not on fine detail, and really just on the planets, and only if both are made to the same optical standards, and on larger details, it doesn't matter very much." However, that is starting to get a bit wordy, so many people just mention the first part. To be generous, they may *know* the whole thing, but forget to say it. Q. Does a Newtonian's spider damage image quality or not? A. This question gets asked almost as much as the previous one. The truth is that it does, but the overall magnitude of the effect is much smaller than even that of the central obstruction. The reason that it nonetheless gets asked very often is that the effect, although relatively small, is quite noticeable. Bright stars sprout spikes of light which correspond to the spider arms. Each arm creates two diametrically opposed spikes, so that a three-arm spider creates six spikes, while a four-arm spider creates four spikes, not eight, because each of the four spikes is doubly reinforced by a pair of diametrically opposed arms. The explanation for this is beyond the scope of this FAQ; I have written a more extensive explanation of diffraction and its effects at http://www.astronomycorner.net/games/diffraction.html Some people find this irritating; others find it inconsequential or even kind of charming. (I find it charming, myself.) Most people concede that it is largely a matter of personal preference--most everyone except double star observers, that is, for whom the chance that a dim companion star is hiding somewhere behind a bright star's spike is frustrating. What worries more people is the effect on planets. For example, Jupiter may appear to be at the center of a hazy cross of light, and it is clear that a noticeable amount of light is being smeared around as a result of the spider support. Since any smearing results in *some* loss of image contrast and detail, it's quite reasonable to wonder how large that loss is. Because the effects of diffraction are most easily noticed at the edges of obstructions and stops, people get the idea that diffraction is an "edge phenomenon," that diffraction is somehow caused by light striking an edge and "forgetting" where to go. Although that image is not quite entirely wrong, it can easily lead to some mistaken conclusions. One might deduce, for example, that since diffraction is associated with the edge or perimeter of an obstruction, the magnitude of the effect must be proportional to the length of that perimeter. And since a spider's perimeter is long way out of proportion to its area, the perception arises that the spider's contribution to diffraction is much greater than you'd guess based on its area. As a matter of optical fact, however, the fraction of light that goes somewhere where it doesn't belong (due solely to diffraction at the spider) is proportional to the fraction of the aperture's area that the spider blocks. If a spider blocks 0.1 percent of the aperture, by area, then 0.1 percent of the light arriving from a distant planet or star never enters the telescope in the first place. Of the light that does get in, a further 0.1 percent goes where it shouldn't, due to diffraction. It is this latter 0.1 percent that leads to the smearing and resulting loss of contrast; the former 0.1 percent only causes the image to be (unnoticeably) dimmer. It's only because the 0.1 percent smearing is concentrated along very tight lines that it's so easy to see. Note that the same reasoning applies to the central obstruction as well, except that the area covered by the obstruction is typically in the 4 to 15 percent range. As a result, 4 to 15 percent of the light is blocked from entering the system altogether, resulting in a dimmer image; then, 4 to 15 percent of the remaining light is smeared around where it shouldn't go, resulting in a less contrasty image. This effect is an order of magnitude worse than the spider, and since the obstruction's effect is noticeable but hardly fatal, the contrast loss due to the spider can be safely neglected. The aesthetic damage caused by the spider can be resolved using either curved spiders, which typically cause greater diffraction but spread it around more evenly, rather than concentrating it along narrow lines, or by using an optical window to support the secondary. However, optically flat windows (that is, flat to within 1/4 wave, which see) aren't easy to make. Q. What is prime focus? A. Speaking loosely, it is the point where your telescope creates an image, so that you can either view it with your eyepiece, or record it on film. In order to get further into this, it's necessary to explain a little about how a telescope works. When you observe a distant star, the objective of your telescope (whether it's a mirror or a lens) causes light from that star to converge to a point. "After" that point, of course, light begins to diverge, very much as though there were a little carbon copy of that star in your telescope. Your eyepiece magnifies that copy, and the magnified image is what you see when you look through the telescope. Because the image emits light as a star would if it were actually there, the image is called a "real image." Now, light from the star focuses to a point because, for all intents and purposes, the star is a point source. If you observe the Moon, on the other hand, light from that focuses only to a disc; this is the real image of the Moon formed by the objective. Again, your eyepiece magnifies this real image, and when you look through the telescope, you see a magnified image of the Moon. If, rather than magnifying the real image with an eyepiece, you instead capture it with camera film, you can then develop the film to get a big picture of the Moon. Because the image is recorded at the principal focal point of the objective, this is called "prime focus" photography. This is to contrast it with other kinds of astrophotography, such as the following: * Piggyback: The camera is mounted on top of a tracking telescope. This permits it to take a long-exposure, wide-angle photo without recording star trails (which is what you get if you simply take a long-exposure photo with a stationary camera). * Afocal: The camera peers directly into the telescope, just as the human eye would. It is called afocal, because light exiting the eyepiece does not reach focus (in principle). To be austere, prime focus is really the point toward which the objective converges light from an object at infinity; if something, such as another mirror, gets in the way, then the focus is not prime focus. For example, in a Newtonian telescope, the light path is reflected by the secondary mirror toward the eyepiece, which magnifies the image at Newtonian focus; similarly, the focal point of a Schmidt-Cassegrain telescope is called the Cassegrain focus; and there are other focus points called the coude focus, or the Naismyth focus, or whatever. All of these distinctions are vital to a pedant (so it's useful to know of them in case you find yourself in an argument), but generally speaking, most reasonable people will know what you mean by "prime focus," if you reference it to a specific telescope. Q. What does [insert nutty acronym] mean? A. There are a few acronyms and abbreviations that crop up persistently on SAA. I'll try to collect them here as I encounter them. FL = Focal Length. The distance between a mirror or lens and the point at which it focuses parallel light rays to a point. If the mirror or lens diverges rather than converges light, the focal length is negative and represents the distance between the mirror or lens and the point from which the diverging rays appear to emanate. FOV = Field Of View. How much sky can be seen in the eyepiece (true FOV), or alternatively, how big that view looks when magnified by the eyepiece (apparent FOV); measured in degrees or fractions thereof. See also the question elsewhere in this FAQ. FS = Field Stop. The washer-shaped ring in the underside of an eyepiece that determines the field of view. Also the inside diameter (usually in mm) of the field stop. O-III = Doubly-ionized oxygen, with two extra electrons. (O-I refers to un-ionized oxygen.) A common emission line for nebulae, it resides at 500.7 nm, in the blue-green section of the spectrum. OTA = Optical Tube Assembly. The optics, plus the tube that holds them together. Includes the objective and any auxiliary lenses, but not the eyepiece. SAA = Sci.Astro.Amateur. The Usenet newsgroup on amateur astronomy. SCT = Schmidt-Cassegrain Telescope. A compound telescope with a concave primary mirror and a convex secondary mirror that puts the image near the rear of the telescope (that's the Cassegrain part), and a complex correcting lens at the front that allows a spherical primary to be used rather than the more difficult-to-make paraboloid (that's the Schmidt part). TINSFA = There Is No Substitute For Aperture. Aperture determines how much light is collected by the telescope, and somewhat less obviously, it also is the primary determinant of the best resolution and contrast the telescope can achieve. Q. What is the deal with [insert nut]? A. SAA (sci.astro.amateur) has its quota of nuts. Those who have been around the Sun a few times in the newsgroup know who they are (though they might have trouble restraining themselves from responding), but for those who don't, here's a quick recap. Daniel Min is an astrology-obsessed would-be neo-con. I say would-be, because the neo-conservatives would be embarrassed to count him amongst their number. He is a rabid pro-Bush, fundamentalist xenophobe (don't bother pointing out the inconsistency with astrology) who cheerfully supports the extermination of people who don't think the way he does. Daniel posts using anonymous Usenet servers, so that it is difficult to killfile him; however, his posts are always pretty obvious to the eye. He has an odd fondness for posting in (and translating) ecclesiastical Latin, which is always good for a laugh for those of us who actually read Latin. Gerald Kelleher (aka oriel36) is a celestial mechanics nut who thinks that astronomy should have stopped with Kepler, and never gone on to the analytical universe of forces and accelerations put forth by Newton. He seems quite taken with the elegance and beauty of the music of the ellipses that Kepler recorded. Whenever a thread on celestial mechanics (or indeed anything having to do with celestial motions) comes up, he can be counted on to throw in his two cents worth, usually denigrating any competent contributor who's moved beyond the 17th century. He wastes no time reading any rebuttals to his posts, so there's no point wasting any time writing them. He also starts a few threads of his own, whenever it seems that interest in 16th-century celestial mechanics might be flagging. Ed Conrad bursts forth from time to time, ringing the changes on his idea that MAN IS AS OLD AS COAL. (In case you're wondering, most coal deposits are an order of magnitude or two older than the oldest known hominids.) His posts are pretty obvious, inasmuch as he signs them with his own name and his subject lines are generally in all caps. He is known for gratuitously slapping himself on the back for being right (although that never happens to be the actual case). Nancy Lieder, sometimes known as just Nancy, is an alien enthusiast who insists that she channels advanced beings who hail from zeta Reticuli. (Reticulum is a real constellation, by the way; it lies in the far south of the celestial sphere, so that in point of fact, it can't be seen from most of the United States, including where Nancy apparently lives.) She became extraordinarily active when the great comets Hyakutake and Hale Bopp came around, and every now and then, she still promotes her notion of Planet X, the twelfth planet. (Whatever happened to ten and eleven is anyone's guess.) As of this writing (April 2006), it's been a while since she's spoken up, but her name still strikes fear in the hearts of many an old-timer. Brad Guth belongs to the "NASA never landed on the Moon" camp, but with the added wrinkle that he believes that Venus harbors life. It's hard to imagine a more inhospitable place for life, but never mind that. It turns out that Venus's cloudtops may well harbor life, and when that bit of news came out, you can bet that Brad was there to trumpet his earlier "prediction," despite the fact that much of the evidence came from the same organization--NASA--that steadfastly maintains that it *did* land men on the Moon. Like many, he claims to have seen the light of skepticism, but actually, it's the train's lamp of conspiracy. Mick (aka Mike, aka MTA, aka TMA, aka ATM, aka a number of other aliases) is a Canadian gadfly whose usual modus operandi is to take others to task for being sloppy in their posts, despite the fact that he consistently is sloppy in his. Quite frequently he quotes his quarry's entire post, following up with a single line to the effect of "What do you know about this any way?" [sic] Mostly harmless, although he does manage to offend those who haven't been exposed to his peevish ways. He does start some reasonable astronomy-related threads, usually by posting a link with a provocative subject line. Naturally, he has found time to lambaste others for starting reasonable astronomy-related threads by posting a link with a provocative subject line. Q. How do mirrors keep their shape? I thought glass was a liquid. A. Glass isn't a liquid. One fact often cited as evidence that glass flows (and is hence a kind of super-viscous liquid) is that old church windows are thicker at the bottom than they are the top. However, the method used to form these windows was not perfect (I think it was spin casting), and often resulted in uneven sheets of glass. Now, if you were laying glass windows, and you had such an uneven sheet, which end would *you* put on the bottom? Surely not the narrow end. No--in order to improve stability, you would put the thick end at the bottom. What's more, careful examination of these windows fails to reveal telltale signs of downward flow, such as glass piling up around and out of the window casing. That explanation alone doesn't prove that no glass flows measurably in hundreds of years, but the fact is that sensitive experiments *have* been conducted on glass, and it doesn't flow fast enough to be considered a liquid. It can deform elastically (like stretching a rubber band), and it can deform plastically (like bending a metal bar), but only under continuously maintained stress. Also, telescope glass is stronger than ordinary window glass--particularly from the medieval period. Any telescope you buy will be safe over your lifetime as well as those of your descendants for centuries to come. The reason that glass can flow at all is because it is amorphous--it doesn't have a regular crystalline lattice. The various phases inside the glass can therefore (*very* slowly) shift amongst one another and produce creep. But just because glass flows doesn't mean it's not a solid. The alkali metals--lithium, sodium, potassium, and so on--are very malleable and can be said to flow, probably much more so than glass does. Yet they are all considered by chemists to be solid at room temperature, and rightly so. Glass has too many more similarities to solids than to liquids: it can break just like a crystal; it can be melted, although the melting point is really a range of temperatures; left to its own, it doesn't collapse into a puddle; and so forth. It could be considered another state of matter, but *not* a liquid. Q. My mirror/lens is scratched--is this going to be a problem? A. As long as the glass isn't actually cracked, a single scratch is not likely to be a problem. A lot of scratches will eventually render the optics unusable. Your mirror or lens is designed to focus the light that falls on it down to a point. A scratch throws a monkey wrench into that process; it throws the light all over the place, where it doesn't belong. In principle, then, a scratch can ruin the image and its contrast. However, a scratch is essentially a one-dimensional aberration on a two-dimensional surface. Only a tiny percentage of the light falling on the lens is affected--most of it still goes in the right place. All bets are off when a bunch of scratches combine to cover a large fraction of the optical surface, so don't smooth out your lens with 60-grade coarse sandpaper! If you have any doubts about the glass, try it out on the planets. If you can't see at least some detail on Jupiter, for example, you probably have a problem. Q. What's the difference between a mirror diagonal and a prism diagonal? A. Both diagonals reflect light through an angle of 90 degrees to make viewing more comfortable. A mirror diagonal uses a single mirror canted at 45 degrees to do the job, whereas a prism diagonal does it by using the long side of a 45-90-45 prism. ^ ^ | | | / +-|-/ |/ | |/ -------------/ --------------/ / |/ / / mirror diagonal prism diagonal One difference between them is that a mirror usually has a reflectivity in the range of 90 percent, meaning that the remaining 10 percent is lost. A prism diagonal relies on total internal reflection. As long as the prism is made of a glass whose refraction index (a number, greater than 1, that indicates how much light slows down in the glass) is more than the square root of 2 (about 1.414), *all* the light that strikes the long side of the prism will be reflected upward. There is some loss of light from having to go through all that glass in the prism, but it's quite a bit smaller--perhaps 1 or 2 percent--so the light transmission is still larger for the prism, by about 8 or 9 percent. However, a difference of 8 or 9 percent only amounts to about 0.1 magnitudes, so in general, that difference isn't terribly noticeable. Another difference has to do with how the light enters the diagonal. In the diagrams above, I've shown the light coming in straight from the left, and reflecting straight upward. However, not all light comes in that way. Only a bit of the light coming from the center of the field of view comes in that way. The rest of the light comes in mostly from the left, but at a slight angle. With a mirror diagonal, light coming in from the left, plus a slight angle, is simply reflected upward, plus the same slight angle. The slight angles have no effect on a mirror diagonal. With a prism diagonal, though, it's slightly different. The glass, with its refraction index of around 1.5, slows down the light to about 2/3 of its original speed. This also has the effect of bending the light slightly, so that light coming in from the left side, plus a slight angle, is instantly changed, at the first glass surface, to light coming in from the left, plus a somewhat smaller angle. The long side of the prism then reflects this light upward, plus the same somewhat smaller angle. Fortunately, when this light reaches the upper surface of the prism, it speeds up again and bends back outward, so that it becomes light going upward, plus the original slight angle. In other words, the two errors induced by entering and exiting the glass compensate for one another. In passing through the glass, it is shifted somewhat closer to the center than it should be, but that only means that you need to refocus a little. Again, the amount of refocusing is so small as to be unnoticeable by just the eye. There is one more effect of going through glass, though. It turns out that the refraction index for the glass is not constant for all colors. Instead, there is a small dependence on color--that is, frequency. All other things being equal, violet light is bent more than red light. Along the center line, this makes no difference since the light goes straight in and is not bent, but anywhere the light is entering the glass at an angle, the component colors of the light are separated by small angles. These angles persist throughout the glass, are maintained by the total internal reflection, and are *not* compensated for when the light exits the upper surface of the prism. In other words, the prism induces its own color error, aside from any color error that might be present in the rest of the telescope. Is this significant? If the angles of the incident light are small, as they are in slow telescopes (i.e., those with long focal ratios, in excess of f/8 or so), then the separation of colors is small and probably unnoticeable. On the other hand, in very fast telescopes (those with short focal ratios, less than f/5 or so), there is a much greater separation of colors, and the effect may be noticed. In many cases, though, these telescopes are short refractors, which may exhibit color errors of their own, and the one error may be mistaken for the other. In any event, with slow telescopes, you can generally ignore the color effect and concentrate on price and optical quality (that is, whether the glass is smooth--a factor that affects both types). On telescopes of moderate focal ratios, between f/5 and f/8, the effect is small, but perhaps noticeable to you; however, it shouldn't be an overriding factor. Q. What does it mean to offset a secondary mirror, and why would I want to do that? A. Here's a quick explanation of offset. What goes into the telescope, toward the primary mirror, is a cylinder of light. Actually, it's not quite a cylinder of light--that would be just the rays that enter parallel to the axis of the telescope. These are called on-axis rays. If you include all of the off-axis rays, you you get a kind of wobbly cylinder, and bouncing off the primary, you get a wobbly cone. But it doesn't affect the geometric explanation of offsetting. The primary bounces this light back toward the front of the telescope, and also focuses the cylinder toward a point, so that the light coming back from the mirror looks like a cone--in fact, it's often called the "cone of light." The secondary should be placed in order to intercept the whole cone. However, this secondary also blocks light going to the primary, so you don't want to make it any bigger than you need to. So, the secondary should be exactly the same size and shape as a cross-section of the cone of light, but not just any cross-section--it has to be set at a 45-degree angle, so it can reflect the light up to your eyepiece. If you cut a cylinder at a 90-degree angle, you get a circular cross-section, with the center of the circle along the axis of the cylinder. If you instead cut the cylinder at a 45-degree angle, you get an ellipse--a stretched-out circle, whose center is also along the axis of the cylinder. Now, if you cut a *cone* at a 45-degree angle, you also get an ellipse, but now its center is *not* along the axis of the cone. From the point of view of an observer at the eyepiece, the center is *offset* a small distance away from the cone's axis. In order to maximize your coverage of the light cone, you need to offset the secondary by this same amount. It will look approximately centered if you look straight through the focuser, but it won't look centered if you look down the OTA toward the primary. Q. How the heck is my image oriented? A. If you're using a pair of binoculars, it's right-side-up and not mirror-reversed. If you're using a refractor (or Schmidt-Cassegrain, or some other telescope used straight through), without a star diagonal, the image is upside-down and not mirror-reversed. After that, it gets a little complicated; it's not as simple as many introductory astronomy books make it out. The way they talk, you'd guess that images can be either right-side-up and non-reversed (like binoculars), upside-down and non-reversed (like refractors without star diagonals), or right-side-up and reversed (like refractors with star diagonals). In truth, there are other possibilities. It's impossible to give an ironclad rule, because in most cases, there are too many variables. First of all, what's right side up in the sky? Generally speaking, up is toward the zenith, and down is toward the horizon. But what's up in the eyepiece? That depends on how you're looking at the eyepiece. On a Newtonian, for example, how do you orient your head when you look through the telescope? Then, too, there are many other factors outside the observer. Is the telescope equatorial or alt-azimuth? If it has a diagonal, how is it inserted into the focuser--is it sideways, up and down, or somewhere in between? If the telescope is a Newtonian, is the focuser on top, on the side, on the bottom, where? All these can affect the image orientation. About the only further thing that can be said is that if the telescope is a Newtonian, however mounted, the image is non-reversed, and possibly rotated by an arbitrary amount. If it's a refractor or other straight-through telescope, plus a star diagonal, the image is reversed, and possibly rotated by an arbitrary amount. That and the first paragraph should cover most of the cases. Actually, one of the most disorienting things about the image presented in telescopes is not just the way they're oriented, it's the way the image "moves" as you move the telescope. You may find stars moving the opposite direction to the way you moved the telescope (as happens in a pair of binoculars), or they might move the *same* way, or they might move perpendicular to the way you moved the telescope. It can be quite startling the first time you encounter it, and it takes a while to get used to it. Some people, in fact, never get used to it, and it's one of the reasons they have a hard time star-hopping. Q. How much magnification can I get out of my telescope? A. The short answer is that small telescopes are limited by their size--they can get perhaps 50x per inch of aperture, or 2x per mm of aperture. Large telescopes are limited by atmospheric turbulence, which typically (but not always) limits useful magnification to around 200x to 400x, something in that vicinity. It comes as a surprise to many beginners that high magnification is not the most important property of a telescope. The most important is that it has a large aperture, or opening, which allows it to obtain both more light and more detail. However, high magnification is needed for you to be able to see that detail, so let's examine the magnification issue a bit more closely. As I described in the question on diffraction-limited telescopes, each telescope produces an image whose detail is limited by the diffractive nature of light (hence, "diffraction-limited"). That effect can be more effectively countered the more area you gather light across, so larger telescopes are less affected by diffraction than smaller ones. To be more precise, a telescope twice as wide as another will create an image that's smeared around by diffraction just half as much. It will therefore stand to twice as much magnification before the diffractive smearing becomes objectionable. Through trial and error, observers have found that the maximum comes into play at around 50x per inch. You can see that this rule does give a maximum magnification that is twice as high for a telescope that's twice as large. There's nothing theoretical about this rule, by the way (except for the fact that we know it comes about because of diffraction); it's a purely empirical rule. So the fact that you might be able to push it beyond 50x per inch doesn't mean that you or your telescope has somehow defied the laws of nature; it just means that your eye doesn't see the effects of diffraction until the higher magnifications. In fact, the more acute your eye, the *lower* the maximum magnification--not higher. There's a limit to this progression, however, caused by atmospheric turbulence, which causes the effect we call "seeing" (which see). The negative effect of seeing does not depend very strongly on seeing (although its qualitative description does), so it effectively caps the maximum magnification somewhere in the few hundreds. Turbulence is dynamic, so the longer you're willing to wait, the more likely you'll catch a moment of still air, and the higher your maximum magnification. Q. How do I figure out the magnification when I take an astrophoto? A. Astrophotos don't have magnifications, because you don't use an eyepiece. They do have what is called the image scale, and you can figure that out from just the focal length of the objective. To explain that, let's look closely (ahem) at what magnification really means. The object in the sky has a certain angular size (which see). When you look at it through the eyepiece, it has another, bigger angular size. The ratio between those angular sizes is the magnification, and it has no units; it's just a number. The Moon, for instance, has an angular size of about half a degree. If you see an image that's 50 degrees across when you look in the eyepiece, that means the magnification is 50 degrees, divided by half a degree, or 100x. The x is not a unit; it just means "times," as in "100 times larger." What you're looking at, when you observe through the eyepiece, is the real image formed by the objective. That real image has a specific linear size; it's just floating in mid-air at the focal plane of the objective. You look at it through the eyepiece--basically a very well- corrected magnifying glass--just as though it were a real object inside the telescope. When you take an astrophoto, on the other hand, you don't use an eyepiece. You record that real image directly onto film, or using a CCD, or whatever. Your image or photo retains that linear size, but no angular size; if you measure the image size, you get an answer in mm, not degrees. Therefore, the division you used for magnification when you observed through the eyepiece no longer returns a unitless number; now you get mm divided by degrees, or mm/degrees. That's called the image scale. If you image the Moon, for instance, with an objective whose focal length is 1000 mm, you'll get an image about 9 mm across. That means the image scale is 9 mm, divided by half a degree, or 18 mm/degree. You can use the image scale to figure out how big any object will be in the image, by multiplying by the image scale. If you image the Andromeda Galaxy, which has a length of, say, 4 degrees, it'll cover 18 mm/degree, times 4 degrees, or 72 mm--too big for a 35 mm camera, but it'll fit in a medium-format frame. The formula for magnification is, as you may already know, focal length of objective divided by focal length of eyepiece. For image scale, it's focal length of objective divided by 57.3 degrees. That weird number is the number of degrees in a radian, and it's equal to 180 divided by pi. So another way to figure image scale is to multiply the focal length by pi (about 3.14), and divide by 180. I'm sure some of you know pi to more digits, but you won't be able to use that kind of precision (and you won't need it anyway). Q. What can I expect to see when I use my telescope for the first time? A. That depends a lot on what you're looking at, what you're looking through, and where you're looking from. I'll take care of the last factor by assuming that you're observing from a typical suburban setting. That's not true for everybody, of course, but it should give you an idea of what's possible. The light pollution doesn't greatly affect the views of the planets (aside from Pluto)--only galaxies, nebulae, and the like. I'll also assume that you're using a small or medium-sized telescope, 8 inches or smaller. First of all, the Moon will reveal more detail than you can possibly keep track of, in any telescope. By the time you have exhausted the detail visible on the Moon through your telescope, you will no longer need to read this Q&A (or perhaps the rest of this FAQ, either). Secondly, you will not be able to see all the detail all at once. The atmosphere and your personal perception conspire to require patience on your part to make the most out of your observing session. Count on five to ten minutes *minimum* (and probably longer) to see even a tenth of what your telescope will eventually be able to reveal on any specific target. Thirdly, different targets require different magnifications. Details on the planets typically require higher power--start at perhaps 25x per inch of aperture, and use what the atmosphere will give you. Deep sky objects *generally* require lower power, and the larger the object, the lower the power, but there are exceptions. Try starting out at 10x per inch of aperture, and try to frame the object well in the field of view. If you're using a small telescope (4 inches or smaller), you need only a negligible amount of time for the telescope to cool down. You should be able to see at least two belts on Jupiter, its four big satellites (unless these are obscured by Jupiter or its shadow) and the rings around Saturn. Toward the high end, you should also be able to see at least a third belt on Jupiter (the NTB, or north temperate belt), the Cassini division in Saturn's rings (especially in the early years of the 21st century), and some detail on Mars. You should be able to see some of the brighter galaxies: some targets to try are M31 in Andromeda and M81/M82 in Ursa Major. Some nebula are also within your range: M42, the Great Orion Nebula, is of course the first to try, but also M8, a large bright nebula in Sagittarius. There are also the planetary nebulae, the dying breaths of stars: M27, the Dumbbell Nebula in Vulpecula, and M57, the Ring Nebula in Lyra, are the two easiest, especially if you have a nebula filter. Better bets are the open and globular clusters. The Messier catalogue contains almost all of the brighter globulars, and plenty are within your reach: M2, M3, M5, M13, M22, and M53 are good starters for the globulars. For the open clusters, M7, M41, M44, and M45 (the Pleiades) are easily seen in the smallest of telescopes, although M44 in the heart of dim Cancer may be hard to find. If you're using a medium-sized telescope (4 to 8 inches), you may need 15 minutes to an hour for the telescope to cool down properly, depending on the temperature differential between storage and use. You should be able to see at least three belts on Jupiter, the Great Red Spot (or at least the hollow in the south equatorial belt where it resides), details inside the belts, and some incipient granularity in the polar regions. Saturn should show color differences in its subtle banding, the Cassini division, and in the higher end, the Encke minimum, the slight dimming in the outer or A ring. Mars should show a moderate to substantial amount of detail: dark areas such as Syrtis Major, the polar caps, the twilight clouds, and perhaps the larger storms. Under suburban skies, a medium-sized telescope should be able to show you most of the Messier objects, although they might be difficult, especially at the small end of the range. At the high end, you may be able to make out the beginnings of detail in the galaxies, especially with M82 and M51. Many of the nebulae are now visible: try M20, if you have a larger telescope. Most planetary nebulae can be seen with a filter, although most of them are nearly stellar; some good exceptions are the four Messier planetaries, as well as NGC 7009, the Saturn Nebula. Somewhere between half and all of the globulars in the Messier catalogue can be seen, and also most if not all of the open clusters should be visible. With a larger telescope, you may be able to make out some nice combinations, such as M35/NGC 2158, a pairing of two open clusters, similar in size, but with NGC 2158 several times further (and therefore considerably dimmer, too). If you can't see everything you're "supposed" to, don't despair. It may simply be that conditions aren't right, or that your skies aren't dark enough. If you can, have someone experienced test out your telescope. And if you can see *more* than you're supposed to, wonderful! Q. Did I just see Jupiter's satellites in my binoculars? A. Very likely, you did. People are often surprised that a lowly pair of 7x35 or 10x50 binoculars can make out Jupiter's satellites. They usually expect the satellites to be either too dim, or too close to Jupiter. One thing they are not, for certain, is too dim. The four big satellites, from innermost to outermost, are Io, Europa, Ganymede, and Callisto. Each is no dimmer than magnitude 5.5, and therefore quite possible to see, even by the unaided eye, from reasonably dark skies. There are even reports of some people who *have* seen them with the unaided eye. Unfortunately, they are usually too close to Jupiter to see that way, most of the time. Callisto, the outermost, is still never more than about 26.5 arcminutes away from Jupiter--less than the width of the full Moon. And usually, the separation is somewhat less. With Jupiter ordinarily glowing at a respectable magnitude -2 or brighter, the planet's light typically drowns out the satellites. But since you can *just about* see the satellites with the unaided eye, it stands to reason that it should be almost easy with a pair of binoculars. Unless a Jovian satellite is either hidden or in front of Jupiter, or very nearly so, you should be able to see it. The only trick is to hold the binoculars steady, but that can be managed by bracing them against a car or fence or other sturdy object. Q. Did I see a fifth (sixth, seventh) satellite of Jupiter in my telescope? A. Chances are, if you have to ask, you didn't. The four Galilean satellites are easy to see (see preceding question), but after that, there's a long gap to the next brightest satellite, Amalthea. It was discovered visually--the last satellite of any planet to be so discovered--but it is very dim. At magnitude 14.1, it is dimmer than Pluto is currently (in 2008), and since Amalthea is always found close to Jupiter, it is exceedingly difficult to see. It took E.E. Barnard, possibly the most talented visual observer who ever lived, a 36-inch telescope to discover it in 1892. You won't see it by accident. It is common to see what appears to be a fifth satellite of Jupiter, even one that appears to be in line with the other, big four satellites. These are invariably background field stars that are aligned with the satellites by chance. Q. What are these words "preceding" and "following" (or "leading" and "trailing") and what do they have to do with directions? A. They indicate celestial west and east, respectively. The next question is, why not use west and east? But there's a problem. The first time you were introduced to celestial east and west--on a star atlas, say--you may have noticed something unusual about the order of the directions. Specifically, moving clockwise from north, you read north, *west*, south, *east*. This is mirror-reversed from terrestrial maps, where the order is north, east, south, west. The reason for this is that when you're looking at a terrestrial map, you're looking at the Earth from above it--that is, outside it. But when you look at a star atlas, you're looking at the imaginary celestial sphere from within it. (In fact, since the celestial sphere *is* imaginary, you can't possibly look at it from outside, anyway.) So naturally the directions are reversed: if you could look at the Earth from within, the directions would be reversed, too. What has this all got to do with those weird terms? When you look at the planet Jupiter, for example, if north is up, then celestial west is to your right, and celestial east to your left. But we also concern ourselves with features on Jupiter, meaning that we use a system of Jupiter longitudes. (Actually, there are three systems, but never mind that for now.) Following a convention that a planet rotates west to east, Jupiter west is to the *left* and Jupiter east is to the *right*. That makes "east" and "west" ambiguous. How about using "left" and "right"? Alas, those too are ambiguous, for they depend on what instrument you're using. Depending on whether your telescope or binoculars invert, reverse, or rotate the image, "left" could be one way or the other. For these reasons, the unambiguous terms "preceding" and "following" are used. They are interpreted as follows: Observe the planet through the telescope (or binoculars), with any motor drive turned off. The planet will appear to drift because of the rotation of the Earth. The edge of the planet that disappears first is the preceding edge. The edge that disappears last is the following edge. This interpretation also has the advantage that features on Jupiter and Mars, for example, move from following edge to preceding edge, meaning that the preceding features, too, disappear first, and the following features disappear last. Personally, I dislike the terms "preceding" and "following," and use "leading" and "trailing" instead, in my own reports. But following a convention is a good thing in certain circumstances, and if I were to file a report with ALPO, I would be best off using "preceding" and "following," like everyone else. Q. Is it true that looking at the Moon through a telescope will harm your eyes? A. You cannot harm your eyes by looking at the Moon through a telescope. It may be uncomfortably bright, and you may can improve the visibility of detail by either adding a neutral density filter (a gray screw-on filter) to the eyepiece, or by increasing the magnification. But there is no safety risk. You may wonder how this can be, since the telescope gathers so much more light than your eye. However, it also magnifies the Moon, so that the extra light is spread out over a greater area. Each part of the Moon's image is seen by just one portion of your eye, and as far as damage is concerned, the critical factor is the intensity of light falling, per individual portion of your eye. If your eye's pupil is 5 mm across, and your telescope is 100 mm across, then the telescope gathers 20 squared, or 400 times more light than your eye alone. But if you're using a magnification of 20x or greater, then that light is spread out over an image at least 400 times larger, so that the actual brightness seen by any portion of your eye is no greater, and usually less, than when you observe the Moon with the unaided eye. What if you observe the Moon at less than 20x--say, 10x? Shouldn't the light be spread out over a smaller area, and thus more concentrated? At 10x, the 400 times more light is spread out over an image that is only 100 times larger, so it seems as though each part of the image should be 4 times as bright as when seen by the unaided eye. However, consider that each portion of the Moon can be thought of as pouring down light, out of which only a shaft 100 mm across--as wide as your telescope--actually enters the optics. In the process of magnification, that shaft is reduced to fit into your eye's pupil, and the factor of reduction is equal to the magnification. In other words, if you magnify by only 10x, the 100 mm shaft of light is shrunk down to 10 mm. The result is that only part of the light--a smaller shaft that is 5 mm across--as big as your eye's pupil--actually gets in. The rest of it falls uselessly (at least as far as image brightness is concerned) on the surface of your eyeball. Since a circle 5 mm across has 1/4 the area of a circle 10 mm across, only 1/4 of the light gets into your eye, and this precisely compensates for the extra intensity from lowering the magnification. Of course, it *feels* as though the Moon is about to blind us, for two reasons. One is that we typically observe the Moon by night. The same phase by day is just as bright, but it doesn't feel blindingly bright through the telescope because our eyes are then accustomed to daytime light levels. Another reason is that the Moon *is* magnified by the telescope, and at the same intensity throws more total light onto your retina. By way of an analogy, if I shine a flashlight into your eye at a distance of 10 centimeters (4 inches), it's uncomfortably bright, whereas if I put a mask on the flashlight that only lets through a tiny spot of light, it's merely annoying. The total light output is much smaller, but the intensity of that tiny spot is just as great as before. Incidentally, some people may ask, why then is observing the Sun through a telescope so dangerous? After all, although we don't stare at the Sun (at least, we shouldn't), its light still comes through our eye. If looking at the Moon through a telescope is no more dangerous than looking at it without the telescope, why isn't the same true for the Sun? The answer is that the Sun is so bright that each portion of its image is enough to create some heating in the eye. (So does the Moon, but its light is about 400,000 times less intense and the heating is completely negligible.) If any given part of your eye is subjected to that heating for long enough, permanent damage will result. Your eyes avoid this by moving around, so that the image of the Sun doesn't stay in place, and the part of your eye that is getting heated by the Sun one moment has a chance to cool down the next. However, if you were to be so foolish as to observe the Sun through a telescope, each portion of your eye gets heated the same amount, but now moving the eye doesn't help, since it is still likely to be heated by the Sun. Moreover, with a small image of the Sun (as when seeing it with the unaided eye), the fraction of your eye being heated is small, and it can dissipate heat rather easily to slow down the damage. With a magnified image, the fraction of your eye being heated is much larger, and there is now nowhere for the heat to go. You can as a result burn out your retina with startling and tragic speed. Bottom line: DON'T DO IT! DON'T OBSERVE THE SUN THROUGH A TELESCOPE without proper safety precautions, such as an appropriate filter. Do not use solar filters that screw onto the eyepiece. The focused heat at the eyepiece is too intense and will crack the filter, sending all that concentrated light and heat into your eye. The light must be filtered before entering the telescope. (Exception: A Herschel wedge can be safely used. If you don't know what a Herschel wedge is, though, don't guess--just use a proper solar filter.) Q. What interesting astronomy-related science projects can my child do? A. It depends on how old your child is (astronomy requires a decent attention span), and how much equipment you have. I'll try to suggest a few that require only modest equipment (or none at all). Note that the background given below is only a summary. The student is still responsible for gathering the primary sources (such as articles in an encyclopedia set or astronomy magazines). 1. Topic: The eclipsing binary, Algol (beta Persei). Background: Eclipsing binaries are pairs of stars that orbit each other (like a basketball official's fists calling travelling), in such a way that from time to time, one of the stars blocks the other. Ordinarily, we see the light from both stars, blended together, and the brightness of the pair is the brightnesses of the two stars added together. Occasionally, though, the dimmer star blocks the brighter star. (This seems weird, but what's happening is that the dim star is dim and *large*, whereas the brighter star is bright but small.) We then see only the dimmer star, or perhaps the dimmer star plus a fraction of the brighter star, and the combined brightness diminishes. You may also, more rarely, see the brighter star block the dimmer star. However, this is harder to detect, because the reduction in brightness is smaller. Eclipsing binaries seem like variables. However, they are distinguished from true variables (single stars that actually get brighter and dimmer) by two things. First, eclipsing binaries are perfectly regular. Only *some* true variables, such as Cepheids, are regular--others, such as Mira-type variables, are only semi-regular; that is, they go up and down, but sometimes there may be 300 days between peaks, and then other times there are 350 days. Secondly, an eclipsing binary usually stays at a constant brightness, which is the combined brightnesses of the two stars. Only when one star is blocked does the pair dim. In contrast, true variables (other than recurrent novae, which are stars that burp hydrogen fusion every now and then) typically ramp up and down in brightness. Task: Your job here is to observe the brightness of Algol, by comparing it with other stars in the night sky, to see if it's an eclipsing binary or not. (I'll give the parent a hint: It is, and it has a period of about 2.87 days.) Only a pair of binoculars is required--I find it difficult personally to compare brightnesses without them, although you may find differently. 2. Topic: The height of the Moon as the phases change. Background: You may have noticed that the Sun is high in the sky at noon in summer, and low in the sky at noon in winter. That is because the *declination* of the Sun changes throughout the year. If you imagine a plane that cuts through the Earth at the equator, and extends in all directions to infinity, that plane is called the *celestial equator*. The declination of an object such as the Sun is the angle of the object above or below the celestial equator, as viewed from the Earth. The declination of the Sun is around +23.4 degrees on or about June 21 of each year, and around -23.4 degrees on or about December 21. At the equinoxes, on or about March 21 and September 21, the Sun's declination is 0 degrees. This might give you the impression that the Sun is bobbing up and down like a buoy as the year progresses, but that's not the case. If you were to imagine a second plane that cuts the Earth at an angle of 23.4 degrees to the equator, that cut would reach a maximum latitude of 23.4 degrees north, a minimum latitude of 23.4 degrees south, and it would intersect the equator at two points in between, but it would be as straight a cut as you could make on the spherical Earth. It certainly would not bob up and down. This second plane, which the Sun appears to follow throughout the year is called the ecliptic. Along the ecliptic in the sky are the constellations of the zodiac. As you might expect, however, it's hard to tell that the Sun goes through the zodiac constellations, since when the Sun is up, you can't see the stars, and vice versa. All the same, ancient astronomers managed, by keeping careful track of where the various constellations were just before dawn and just after dusk. The Moon, as it turns out, also follows an orbit that, although not *quite* on the ecliptic, is close enough for our purposes. (The difference is about 5 degrees.) The advantage of observing the Moon is that unlike the Sun, it is often up at night and one has an easier time of it tracking exactly where in the sky it is, relative to the stars. (One Persian story has it that a wise old vizier was asked which was more important, the Sun or the Moon. "The Moon," he said, "because the Sun shines during the day, when it's light out anyway.") For that reason, each month, around the time of the new Moon, when the Moon is between the Earth and the Sun, the declination of the Moon is very close to that of the Sun. If the Sun has a positive declination--that is, if it's directly overhead somewhere in the northern hemisphere--then the Moon, very likely, has a positive declination, too, and within 5 degrees of the Sun's declination. And if the Sun's declination is negative, then the Moon's is, too, probably. However, it may be difficult to tell, if the Moon is so close to the Sun. (See the preceding question, about observing the Moon through the telescope.) It's different at full Moon. Then the Moon is on the opposite side of the Earth from the Sun, and it's very easy to see. This also means that if the Sun's declination is positive--again, remember that this means that it's directly overhead somewhere in the northern hemisphere--then the Moon is probably directly overhead on the opposite side of the Earth, in the *southern* hemisphere. That means that it has a *negative* declination. And vice versa: If the Sun's declination is negative, the Moon's is probably positive. In short, the path that the Sun follows throughout the *year*, the Moon follows throughout the *month*. (Therefore, for example, at first quarter, a quarter of a month after the new Moon, the Moon is roughly where the Sun will be in a quarter of a year.) Task: Follow the Moon for a month, whenever you can. This should be easy during the first part of the cycle after the new Moon, when the Moon is up during the early evening. As the month progresses, the Moon rises later and later, until just before the next new Moon, it rises only just before dawn. At that point, you'll have to get up early to see the Moon, in order to see it against the stars. (You can see it during the day, too, but then you can't see the stars.) Plot the position of the Moon on a star atlas (or on a copy), and see how the declination changes throughout the month. What months do you expect the first quarter Moon to be high in the sky? What about the last quarter Moon? I'll add more projects here as I think of them. Q. Is Pluto still a planet? A. Not anymore. To be more precise, as of August 24, 2006, Pluto is no longer considered a major planet by the International Astronomical Union (IAU). However, this classification is still in flux, so the answer to this question may change in the near future. Pluto was discovered by Clyde Tombaugh in 1930, but people first began searching for it in the 19th century after it was noted that Uranus and Neptune weren't behaving quite as they ought to. Instead, they seemed to be under the gravitational influence of some unseen body further out than Neptune. Based on the perturbations seen in the orbits of these two planets, the ninth planet was estimated to be smaller than either of them, but still significantly more massive than the Earth. (Both Uranus and Neptune are about 16 times as massive as the Earth.) Soon after Pluto was discovered, it was found to be smaller than expected. In fact, every new measurement of Pluto seemed smaller than the last! At first, it was thought to be about the size of the Earth, about 13,000 kilometers (8,000 miles) across. By 1960, based on visual appearance and assumptions of actual brightness, its estimated size had dropped to about 6,000 kilometers (3,700 miles). The final straw came in 1978, when Pluto's satellite, Charon, was discovered. By observing the motion of a planet's satellite, scientists can determine the mass of the planet. Pluto turned out to be a whopping 500 times *less* massive than the Earth. It is only 1/6 as massive as our own Moon, in fact. The current best estimate of Pluto's size is about 2,300 kilometers (1,400 miles) in diameter. More recently, the observations of Uranus and Neptune have been re-examined in light of better mass figures for those two planets, and with those corrections, the discrepancies have been completely explained. No further planet is necessary. Back to Pluto. As a result of its diminutive size--Mercury, the next smallest planet, is still about 4,900 kilometers (3,000 miles) in diameter--and its unlikely location out beyond the gas giants, many astronomers proposed changing Pluto's status. The group of planets includes not only the familiar nine from Mercury to Pluto, but also asteroids and comets. These are divided into major planets and minor planets, ostensibly based on size, but also based on tradition. What some people were proposing to do was to declare Pluto a minor planet. This proposal became stronger as it became evident that there were a bunch of similarly composed objects beyond Neptune, at around Pluto's distance from the Sun. None of them was as big as Pluto, but it might just be a matter of time until another body that large was discovered. One version of the proposal suggested that Pluto be labelled minor planet number 10,000 (it would retain its proper name, too, of course, just like the asteroids). The matter never got to a vote. Once word of the proposal got out, there was such a tremendous backlash that the IAU promptly sent out a statement that Pluto's status was unchanged. Apparently, there is still a sense of pride that someone in the 20th century should have discovered a planet. The minor planet number 10,000 was assigned to a different body altogether. However, the matter was re-engaged in 2005 after a larger body *was* discovered, with the unpreposessing name of 2003 UB313. Was it to be the tenth planet? Or would Pluto be removed from the list? What was a planet, anyway--was it something of sufficient size, or did it depend on how it interacted with its environment? After all, the other planets do not revolve around the Sun along with many companions, the way Pluto does. Or, perhaps, was "planet" really a historical term, only to be applied in an informal setting? On August 24, 2006, the IAU formally defined a planet to be an object in orbit around a star, of sufficient size that it was spherical, more or less, and so that it dominated its orbital environment. Pluto qualified on the first two counts, but because of all the other objects that revolve around the Sun in much the same environment as Pluto, some of which were almost as large as Pluto, it was "demoted" to the status of dwarf planet, which are objects that, like Pluto, are spherical and orbit a star, but that do not dominate their environment. The retinue of major planets therefore returns to its condition before 1930. However, there is some dissatisfaction with the hasty manner in which the classification was arrived at. There seems to be some call for revoking the re-classification, so the saga of Pluto the planet is not yet done. Stay tuned! Q. What happened before the Big Bang? A. Nobody knows what happened before the Big Bang. It is even likely that the question doesn't make sense (at least, not as it is usually understood). The usual answer is that the Big Bang is not an explosion in space, at some epoch in time, but an explosion *of* space *and* time. That is to say, the Big Bang created both space and time, with the galaxies and other matter in the universe being largely by-products. For whatever reason, most people find it easier to accept that space was created in the Big Bang than that time was created in the Big Bang, too. Part of the problem is that it's simply not intuitive that there could have been a time without time, as it were. It's revealing that we don't ask what was in front of the Big Bang, or to the left of it, but we do ask what came before it. Part of that must be our curiosity about the ultimate cause of things (something that science really can't answer), but part of it is also that we don't view time as being interchangeable with the other three, spatial dimensions. Einstein's general theory of relativity, however, does treat time as being very closely related with the three spatial dimensions. In a way that only makes sense mathematically, the time dimension is sort of like a spatial dimension times i (the square root of -1). As counter- intuitive as this seems, it gives physicists some confidence that as the Big Bang created space, it also created time. One way to approach this might be to think of the Big Bang as sort of the opposite of a black hole--the ultimate "white hole," so to speak. In everyday terms, once something goes inside an imaginary boundary of a black hole called the event horizon, it can never leave. Physicists would say that within the event horizon, all worldlines end at the singularity at the center of the black hole; everything's future, both in time and in space, ends there. In short, the singularity lies in the infinite future. The curious thing that general relativity tells us about a black hole is that from the perspective of someone outside the black hole, space and time are in some sense inverted; stretches of time become expanses of space, and vice versa. As we approach the event horizon from the outside, a faraway observer will see us less and less falling forward in space, and more and more falling forward in *time*, until they see us frozen in place right at the event horizon. From our own perspective, though, we see space and time behaving as they usually do, as we go on falling until we hit the singularity at some definite point in time. (It's a little like travelling from the north pole to the equator. From the point of view of an observer at the north pole, you go from walking forward to walking "downward," but from your point of view, you're always walking forward.) The Big Bang would be like that, but with everything reversed in time; instead of everything's worldline ending at the singularity that is the Big Bang, they all *start* there. From our own perspective, perhaps, we see space and time behaving as they usually do, so that (for instance) we perceive the Big Bang as having taken place at some definite point in time--about 14 billion years ago--but for an imaginary observer outside our universe, perhaps they see space and time reversed, so that for them, our Big Bang singularity lies in the infinite past. In any case, as successful as it may be, we know that general relativity has striking limitations, conditions under which it *must* break down, and those conditions come into play, unfortunately, at the moment of the Big Bang. At the start of the universe, so much energy was compressed into so small a volume of space that classical laws like general relativity can no longer be valid, and quantum mechanics must be brought to bear. (In physics, the term "classical" simply means non-quantum. Thus, even a difficult theory such as general relativity qualifies as classical.) However, physicists implicitly assume that there was no time at which quantum mechanics stopped governing and general relativity took over. This isn't as big a leap of faith as it might seem. It's akin to assuming that there was no point in time at which you suddenly became an entirely different person; rather, you are and have always been a single person, with one set of behaviors when you were an infant, and another set of behaviors when you became an adult, and a more or less smooth transition between the two (however bumpy it might have seemed at the time!). In the same way, there must be a single theory of gravity, which looks like general relativity in the normal conditions that apply almost everywhere in the universe today, and yet in the high-energy, small-scale limit that applied for the Big Bang, is a wholly quantum- mechanical theory. Similar theories have been created for the other forces in nature (electromagnetism, and the two nuclear forces), but gravity has thus far defied "unification." Ultimately, the synthesis of a quantum theory of gravity will be a watershed moment in physics, and may well permit us to plumb the universe's history, right to the moment of its creation at the Big Bang. ***** Copyright (c) 2001-2008 Brian Tung