# 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?

• You could try to use orbital resonances. See also physics.stackexchange.com/questions/25817/…. Dec 6, 2015 at 15:54
• Dec 6, 2015 at 20:38
• Could you consider having dwarf planets / large asteroids that orbit inside and outside your planets orbit? They won't be consistent "day-night" schedules but they'd put on a spectacular view. I've been playing with it on Universe Sandbox 2 to try to make the large moons work for you, but they keep wreaking havoc. Jan 10, 2016 at 21:30
• @Mikey, I suspect that if they are close enough to actually have an appreciable angular diameter that they will 'cry havoc and let slip the dogs of war' (Possibly moon made of styrofoam -- this would give you roughly 10 times the diameter for the same mass.) Also try a period ratio of, say sqrt(2) or 13/9. Meanwhile, I'm looking up your universe sandbox. Jan 12, 2016 at 19:15

I am a senior physics major, and have access to some pretty cool software. I have been running some simulations on this, and I think that I am getting pretty close to a 3 body stable orbit, but it is very fragile. The small moon the middle seems to keep falling into one of the other bodies eventually. The only way that I can conceive it being stable would be to have the moons orthogonal to each other, but even that should collapse eventually.

One interesting option I found that works is to have two moons of similar size tidally locked with each other in orbit around the planet. It's pretty stable, and would make a neat view.

However, if you want to keep your moons the way they are, that's fine. If I can get it to be stable, I'll send you some numbers.

As a bonus,

Some interesting effects of our moon: -Tides (obviously) -keeping earth's axial tilt stable -slowed the earth down

Tides: You seem to have the right idea here

Axis Stability: Earth is at a fairly constant 23.5 degree axis tilt (varies between 23 and 26 degrees) and that stability is due to our moon. For example, Mars, without any massive moons, has an axis tilt that varies between 15 and 35 degrees.
Your first moon will have twice the gravitational potential energy as the moon, and the next moon will have about 1/125 of the PE. This is negligible compared to the first moon, so your planet would have much more consistent weather and seasonal patterns than earth, so everything is fine here.

Slowdown: The Earth used to have days that lasted about 6 hours, but the moon changed that. It slowed the Earth down considerably, to about 25% of its original rotational velocity. Your first moon would initially slow down your planet twice as much as the moon, meaning that if that moon was captured on earth instead of our moon, days would be 48 hours. (As long as the capture process was the same.)

• Nice answer Louis, welcome to the site. Jan 8, 2016 at 19:40
• You could verify that you software is set up correctly: drop in numbers for other multibody systems. E.g Mars, and it's moons. Our moon is anomalous in other ways. Terra-Luna should be considered a double planet. Luna's path around the sun is concave solarly everywhere. And the sun has to be a perturbing force too, so it's a 4 body problem. I suspect that the moon is too massive for much else to be stable. In general: Jan 9, 2016 at 22:04

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.

• I appreciate the difficulty of the 3 body problem, and one way to check this would be to run a simulation. However, my suspicion is that the has been extensive work done in orbital dynamics -- people who have run a million simulations and have found one of the following: A: No system with 2 moons where the mass of one is larger than X% of the central body is stable. B: No system is stable where the smaller moon is larger than X. C: No system is stable where the ratio of orbital radii is smaller than X. etc. Dec 6, 2015 at 14:54
• First order tides are easy to calculate as superposition of appropriate sine waves. Reality, of course, is far messier. E.g. Lunar tides on an isolated island in the middle of the ocean are only a few feet. But in the Georgia Strait between Vancouver Island and the mainland they are 20-30 feet. (Landing on an ocean trip at low tide requires a good walk across kelp covered rocks to reach camp.) Dec 6, 2015 at 14:54
• I don't see why a deeper gravity well would support more moons. Jupiter and Saturn can have many moons because the moon is small compared to the central body -- the correction terms for moon-moon interaction are tiny compared to the main force. Jan 12, 2016 at 19:18
• @SherwoodBotsford You could be right. My answer was based on my understanding of the Hill Sphere, which is the area where an object orbits around another object. If you were inside our moons hill sphere, youd be orbiting the moon. leave it, and now you're orbiting the earth. Leave the earths hill sphere, and youre orbiting the sun. The planets with larger mass have larger hill spheres. Being far away from the sun helps too. Larger the sphere, the more room for moons to orbit. Jan 12, 2016 at 19:33