What are the parameters of a planet having multiple moons?
I'm not sure if this question belongs here or over on Physics Stack Exchange.
The Earth and Moon are unique in the Solar System in that the Moon is a significant size compared to the Earth, at 1/4 the diameter and 1/80 the mass.
In the Solar System planets are distributed in an exponential fashion with each being roughly twice the distance from the Sun. (See the Titus-Bode law.) In each case, the attraction of the Sun is by far stronger compared to the attraction of other planets.
A favorite theme of science fiction illustrators is several large moons hanging in the sky. (Sometimes they even get the phases right.)
Is this possible? Can a planet have a stable configuration of multiple moons, each one large enough to provide a visible disk and signficant ground illumination?
For the sake of discussion, let's call the minimum angle one degree (twice the apparent size of the moon.
So we could use a moon twice the diameter of our Moon. This would be eight times as massive. Our average 6-foot tides would be 50-foot tides. Yikes.
We'll call moon #2 Selene. Make it much smaller but much closer. If it was 1/8 the diameter and 1/4 of the distance it would appear half as large and have 1/500 the mass, but tides go as the third power of distance, so it would have a net effect of 1/8 the tide of our Moon. The orbital period would be about 1/4 the length of our Moon's - about a week.
Now, I'm guessing that if were exactly 1/4 of our Moon's period there would be resonance, and everything would come crashing down around my ears. But now I'm stuck. What determines a stable configuration?
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1 answer
You have to deal with the 3 body problem, specifically the small moon being pulled toward the much larger moon, and then moving away, and how this would destabilize the small moons orbit.
The distances you set up could support this, but calculating the effects of that extra mass is interesting.
Larger planets can support more moons because they have much greater gravity wells, and the moons orbits can be far enough apart to not bother each other.
Mars has two moons, but they are not much more than captured asteroids, and not much gravity.
To answer the second part, The small moon would have its own little tide. When the tides caused by the second moon synced with the first, they would be bigger than the already massive tides as you already thought.
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