Posted by: Lister | February 11, 2007

Sunrise on Mercury

This page is to explain some astronomy for a friend at AlienLove.

The Sun will sometimes seem to go backwards in Mercury’s sky. The question is, could we ever see the same effect on Earth?

The first thing, is to distinguish this from the Retrograde Motion of planets like Mars. This is easily explained with a picture.


The reverse of the Sun in Mercury’s sky is different.

As you know, the sun only seems to move because the Earth rotates. The same is obviously true for Mercury. But the Earth has an almost circular orbit — so its speed throughout the orbit is constant. And so the Sun’s motion through the Sky is constant. But Mercury’s orbit is more elliptical, and so its speed changes throughout the orbit.

Take a look at this picture, showing 5 Day snapshots of Mercury’s orbit:


Put your first finger on June 24 and your second on July 9th. Then put those fingers on May 25 and May 10th. (You should have two extra planets between your fingers both times). You don’t need a protractor, it’s obvious that Mercury has moved more in the second period than in the first.

Why is this important? It means the Sun will appear to change speed in Mercury’s sky.

Have you noticed that, when you look at the moon, you always see the same face? The Moon is tidally locked. As it orbits the Earth it rotates the right amount to always keep the same face pointing to the Earth.

Earthrise on the Moon

If you are standing on the Moon you will never see the Earth rise or set. The reason is that one side of the Moon always faces the Earth and the other always faces away. So almost anywhere on the Moon you either see the Earth or don’t. I say almost anywhere because I should probably add that the Moon sort of ‘jiggles’ from side to side a bit. A tiny bit more than 50% of the surface is thus visible from the Earth over time and in locations near the edge you therefore might be able to see the Earth go up and down a bit . Without more thinking about it I couldn’t say if the Earth would completely rise and set or if you would be able to see/not see part of it all the time.

Astronomers used to think that Mercury was tidally locked to the Sun. If that were the case, then the Sun would not move in Mercury’s sky. But it turns out that there is a 3:2 ratio between Mercury’s orbit and rotational period. As shown in this picture:

Mercury's orbital resonance.png

The two orbits are 1-4 and then 4 to (well, they should have double labelled 1 with a 7 to show the completion of the 2nd orbit). And there are three rotations (1-2) (3-4) (5-6).

Mercury rotates once every 58.6441 days How long is a day on Mercury? If we measure a day as the length of the cycle of the Sun’s motion, then a Mercury-Day is 2-Mercury years! You can see that in the last picture.

At position 1, the red pole is facing away from the sun. How long before it is facing away from the sun again? You have to wait for Mercury to go all the way back to 1. That is two full orbits.

But even more spectacular is that, as Mercury’s speed of orbit changes, sometimes it is going too slowly to make the Sun appear still, and sometimes it is going too fast. Of course, there is an instant inbetween when the Sun does appear still.

And so the Sun appears to rise, pause, and set where it rose.

As I understand it, if Earth were to become tidally locked with the Sun, then it would have the same side facing the Sun all day. Like the Moon has the same side facing the Earth the entire Lunar day.

The Earth wobbles too, and I don’t know what would happen to that as the Earth becomes tidally locked. So I suppose the Sun may not appear perfectly stationary even with a tidally locked Earth.

The main feature is that Earth’s orbital speed is constant due to the near circular orbit. It is the changing speed of Mercury’s orbit that produces the special movement of the Sun in its sky.

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Responses

  1. I think they put the sun at the wrong focus in the second picture. As it is, Mercury should travel a larger arc between 2 and 3 than between 1 and 2.


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