Notes from Under Sky

What is a Planet, Anyway?

Yet another definition of planet

As I write this in August 2006, the IAU has convened a general meeting to try to nail down the definition of "planet" once and for all. The provisional idea the IAU has come up with is to predicate planethood on whether the object is massive enough to become spherical under its own gravity. I think that's a fine idea in principle; the problem arises when you try to make it precise. How spherical is spherical? Keep in mind that I'm not talking about deviations from a spherical shape resulting from an object's rotation—just protrusions held up by the strength of electromagnetic forces against the influence of gravity.

On the Earth, the tallest mountains are small in comparison with the overall size of the planet—less than 1/1,000 the diameter of the planet. On a much larger terrestrial planet, gravity might prevent mountains exceeding 1/5,000 the planet's diameter, or 1/10,000. On the other hand, on a much smaller planet, gravity might permit mountains exceeding 1/100 the planet's diameter, or 1/10. At some point, the mountains get so large that we consider the whole thing to be mountains, and we call the planet's shape irregular. But where do we draw the dividing line? That's the hidden trap of the IAU's definition, in my opinion.

Some other folks—such as the team that discovered 2003 UB313, which set off a lot of this concern about defining what a planet is—think the definition should incorporate a notion of how the planet interacts with its environment. With undoubted planets like the Earth, there is nothing else of comparable size in the same or similar orbits. Since Pluto orbits the Sun along with a bunch of other objects of comparable (if somewhat smaller) size, these folks have proposed removing Pluto from the planet lineup.

This definition is attractive, but it's difficult to apply in a timely fashion. It might take some time before we really understand the other objects in a given candidate's environment. Moreover, it seems excessively dependent on the environment of the object. By implication, if Pluto were to switch places with Mercury, say, they would both be considered planets. (Incidentally, Mike Brown, who discovered 2003 UB313—also known informally as Xena—has since recanted somewhat, and offered his support for the IAU's current proposal.)

These days, it seems that everyone has their own idea of what the definition should be, and I'm no exception. I think the idea of sufficient mass is right, but maybe the actual form of the criterion should be different. Ideally, it should be capable of being made precise, yet at the same time, stem from considerations that are essential to our conceptions about planets. In that connection, one possible basis for discrimination arises: how the planets form.

Well, how do planets form? Once they get large enough, by accretion. If a body isn't sufficiently large, then an incoming piece of debris doesn't accrete, it just bounces off. So, in principle, a planet is an object large enough that an incoming object doesn't bounce off.

That's somewhat vague because we haven't said what kind of debris is incoming, nor what it means to bounce off. But consider what happens when a sizable object encounters the Earth. No matter what its initial speed is, the Earth's gravity gives it an additional pull, and its final speed must be at least the Earth's escape velocity: about 11 km/s. Only the Earth's atmosphere may slow it down in the final kilometers, but if the object is large enough, not even the air will have much of an effect.

That substantial speed is enough to melt incoming rock or ice. So maybe that should be the exact statement we're looking for—that the escape velocity, which is also the impact velocity, is enough to melt the incoming body. What kind of body? Why not ice, which is one of the most common molecules in the universe, is the universal solvent, and is generally recognized as a requirement for life as we know it? How massive does a body have to be before an incoming piece of water ice at the triple point—where all three phases of water can co-exist—melts to become water at the triple point, so that it just sits there in a puddle (and possibly refreezes later on)?

The heat of fusion of water is about 335 kJ/kg; in order to melt 1 kg of ice, 335,000 joules of energy has to be applied to it. In order for the impact of 1 kg of ice to deliver 335,000 joules to itself, it has to be moving fast enough:

KE = 1/2 (1 kg) v2 = 335,000 J
v2 = 670,000 m2/s2

which yields a required velocity of about 820 m/s. The convenient aspect of impact energy is that the amount of energy per unit mass is constant: No matter how many kg of ice falls from the sky, if it falls at 820 m/s or faster, each kg gets the 335 kJ needed to melt it. (For comparison, the speed of sound at sea level is about 330 m/s.)


Pluto's escape velocity is 1220 m/s
2003 EL61's escape velocity is about 840 m/s
Sedna's escape velocity is somewhere between 620 and 950 m/s
Quaoar's escape velocity is somewhere between 520 and 710 m/s
Charon's escape velocity is 660 m/s
Ceres's escape velocity is 450 m/s

The mass of 2003 UB313 isn't currently known, but assuming it's at least half that of Pluto, it would have an escape velocity greater than 820 m/s. The mass of another candidate, 2005 FY9, is also not known. Its radius is about 1700 km, so if its mass were at least one-third that of Pluto, it too would have an escape velocity greater than 820 m/s.

So here's my proposed definition of a planet:

A planet is a non-fusor, whose escape velocity is at least 820 m/s, in a bound orbit with a fusor. A fusor is a body that, at some point in its lifetime, exhibited core fusion.

By this criterion, Pluto's a planet, easily. 2003 UB313 is almost certainly a planet, unless by some odd chance it turns out to be less dense than water. Sedna, 2003 EL61, and 2005 FY9 might also be planets, pending a better determination of their size and mass. It's possible that 2003 EL61's escape velocity depends on where on its ellipsoidal body you're trying to escape from.

There's another concern, which is what kind of body should count as a satellite. For instance, the escape velocity on the Moon is 2400 m/s. It would therefore qualify as a planet under the above definition. But hardly anyone really considers the Moon to be a planet, because it orbits the Sun along with the Earth, and the Earth is so much bigger.

The IAU is proposing a distinction: If two objects that are both large enough to be called a planet, using their sphericity criterion, orbit a common center of gravity that is outside both objects, then both objects are considered planets. Otherwise, the smaller is considered a satellite of the larger. Presumably, the IAU thinks this can be extended to cover more than two objects.

The problem with this distinction is that it leads to some—to me, at least—unsavory dependences on time. For instance, the mass of the Moon is about 1/81 that of the Earth. Its distance, on the other hand, is about 60 times the radius of the Earth. The center of gravity of the Earth-Moon system is therefore about 60/81 of an Earth radius from the center of the Earth, which is about 1,000 km under the Earth's surface.

On the other hand, if the Moon were more than 81 Earth radii away, the common center of gravity would be outside the Earth, and the Moon would then be considered a second planet sharing an orbit with the Earth. As it happens, although the Moon isn't that far away yet, it is moving further away. Right now, it is receding from the Earth at about 0.04 meters (4 cm) per year. To move another 21 Earth radii out, it would have to recede by a total of about 135,000 km. At its current rate of recession, it would take about 3.5 billion years to move far enough out.

To be sure, the Moon will not recede at 4 cm per year indefinitely. As it gets further out, the tidal effect will decrease (it will also do this because the Sun will probably vaporize the Earth's oceans), and the recession will likely slow down. Even so, it's not out of the realm of possibility that in the distant future, the Moon will suddenly become a second planet along with the Earth, even though nothing will have changed but the distance between them.

Here's my proposal for something a bit less time-dependent. There are bodies in Jupiter's orbit that are nevertheless safe from being accreted by Jupiter, because they are held in equilibrium at one of the so-called Lagrangian points L4 and L5, 60 degrees ahead of and behind Jupiter in its orbit. Objects can only be held at such points if they are at least 1/25 as massive as the main body—Jupiter, in this case. Otherwise, they may gradually approach the main body and impact it. In fact, this is allegedly exactly what happened to the impactor that created the Moon: The Mars-sized object, about 1/10 the mass of the Earth, wandered slowly in from L4 or L5, and struck the Earth, creating an impact ring, some of which coalesced to form the Moon.

So let's call an object a satellite of a larger companion if it could be held at L4 or L5, provided it started out there:

If there are two or more co-orbiting bodies that would qualify as planets according to the above definition, all those that are at least 1/25 as massive as the largest of the bodies are also considered planets. Everything else is considered a satellite.

The Moon itself is small enough to be classified as a satellite, as we noted above. Interestingly, Charon is as much as 1/7 the mass of Pluto, so if it is massive enough to qualify as a planet, it should be considered a double planet along with Pluto. By the IAU's criteria, it is large enough, but by the escape-velocity criterion, it isn't.

It's crazy, but I don't think it's any crazier than what the IAU is looking at.

Copyright (c) 2006 Brian Tung