# Double Play

#### What's so odd about a sunset on Mercury?

In the Nine Planets Site they mention that a person on Mercury would see this odd behavior: "At some longitudes the observer would see the Sun rise and then gradually increase in apparent size as it slowly moved toward the zenith. At that point the Sun would stop, briefly reverse course, and stop again before resuming its path toward the horizon and decreasing in apparent size. All the while the stars would be moving three times faster across the sky. Observers at other points on Mercury's surface would see different but equally bizarre motions."
Why is this and what is the other "equally bizarre" behavior?

The apparent path of the Sun in the sky of any planet is actually the combination of two separate motions of the planet. In the case of the Earth, the most obvious one is its daily rotation. Once a day, the Earth turns about once on its axis, from west to east. From the point of view of someone standing on the Earth's surface, the Sun therefore appears to cross the sky from east to west.

The Sun repeats its daily apparent motion once every 24 hours, on average. However, the Earth does not rotate once on its axis in exactly 24 hours. Instead, the true rotational period is closer to 23 hours and 56 minutes. So how come the day seems to last 24 hours?

The reason for this is the second planetary motion in question, and that is the revolution of the planet around the Sun. From the point of view of an imaginary and highly heat-resistant observer on the Sun, the Earth appears to revolve from east to west, and as a result, from the Earth, the Sun also appears to revolve from west to east. (In case that seems confusing, imagine going around a column in a clockwise direction while always facing north. The column will appear to you to be revolving in a clockwise direction around you.)

The Sun's daily apparent motion is therefore the sum of two separate and also apparent motions: the east-to-west motion caused by the Earth's rotation, and the much slower west-to-east motion caused by its orbital motion around the Sun. How much slower? About 366 times slower, so that the day is about 1/366 times longer than it would be if the Earth's rotation were the only relevant motion. This brings the 23 hours and 56 minutes up to 24 hours, as expected.

Butâ€”remember that I mentioned that the Sun repeats its daily motion every 24 hours on average. This is because although the Earth's period of rotation doesn't change very much (varying by perhaps 1 part in 1 million throughout the year), its orbital motion does change noticeably. Its orbit is elliptical, and Kepler's laws of planetary motion tell us that the Earth therefore changes speeds as it goes around the Sun. When the Earth is closer to the Sun, it speeds up, and the Sun's apparent west-to-east motion increases. When it recedes from the Sun, it slows down, and the Sun's west-to-east motion decreases.

The amount by which that motion acts against the daily rotation of the Earth therefore is not a constant 4 minutes or so on top of the 23 hours and 56 minutes, but instead varies smoothly throughout the year. There are times of the year when the day, as measured by the Sun's return to the meridian (the north-south line passing directly overhead us), is more than 24 hours, and other times when it is less. Although the daily difference is only a matter of seconds, these differences pile up, so that on some days, the Sun may reach the meridian up to about 15 minutes before or after the time that it "should," based on a constant orbital motion. This variation is called "the equation of time," and it comes up when trying to use sundials to compute the current time accurately, for instance.

The Earth's orbit, however, is only slightly elliptical. Its distance from the Sun varies only by a little more than 3 percent throughout the year. The variation in the Sun's apparent motion doesn't change very much as a result (about 6 percent, twice the variation in distance), and its effect is never so great as to ever be greater than the rotational motion (which, after all, is 366 times greater on average). Generally speaking, we just don't notice.

That is not the case with Mercury. First of all, its orbit is much more elliptical than the Earth's. Its distance from the Sun varies by some 40 percent, and the Sun's apparent motion, as seen from Mercury, therefore varies by almost a factor of 2.

More importantly, Mercury's rotation is not hundreds of times faster than its orbital revolution, but only about 50 percent faster. That means that if the Sun's apparent motion due to orbital motion were to increase by 50 percent, it would be enough to counteract the apparent motion of the Sun due to Mercury's rotation, and the Sun would actually appear to stand still.

As a matter of fact, Mercury's orbital motion varies so much that it sometimes is enough to make the Sun actually appear to move backward. If you are standing in the right place on Mercury's surface, you can actually see a double sunrise or sunset. In the latter case, you would first see the Sun set. Then, as though it weren't sure of itself, it would peep back up a short ways. Finally, making its mind up, it would set back down.

Of course, because Mercury's rotational period is about 59 Earth days, this whole process would take a long time from a human perspective. But it would certainly qualify as "bizarre."