# Could my moons-planet system be stable?

In my fictional world I have selected all parameters to maximize the Hills Sphere of my planet. The planet has three times Earth's mass and it is located in 2 AU from its star that's 1.4 times more massive than our Sun.

I want to have three moons on a 1:2:4 resonance. I also want:

• the first one to be as large as our moon to the sky
• the second 1.5 times larger
• and the third, half our moon's size.

To achieve this I have assumed:

• the first moon having 1.1 lunar radius,
• the second 2.3
• and the third 1.1.

Their orbits are 18, 36, 72 days.

I don't really care about their density and I assumed that their masses are

• 1 lunar mass (probably rocky)
• 3 lunar mass (water or ice world)
• 0.3 lunar mass (probably ice world)

This is my effort to achieve the stability of the system, what parameters should I reconsider to make it more stable? I am willing to change almost everything even the resonance, but I want them to be visible from my planet in the way moon is to Earth.

So any ideas?

This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

• Wouldn't this be better to ask over at astronomy? astronomy.stackexchange.com – Martine Votvik Jun 20 '16 at 19:15
• I am new here and i wasn't sure.If its more suited there I can do it. – teorf Jun 20 '16 at 19:17
• @MartineVotvik Questions about the stability of planetary systems are fine here; we've had loads of them. They can be hard to answer, but in general, they're fine. – HDE 226868 Jun 20 '16 at 19:21
• @HDE226868 ah, fair enough. It's a but tricky to learn which questions should be directed elsewhere or not. I can see how it would be directed back here as well. – Martine Votvik Jun 20 '16 at 19:37
• Thanks for reminding me about Universe Sandbox. And by "thanks" I mean I won't get to sleep tonight. 4 teraflops CUDA card, 3 monitors, on my "work" computer. – JDługosz Jun 21 '16 at 8:24

## 1 Answer

You propose a fairly simple system.

On the other hand, you said nothing about inclination and eccentricity! Maybe the orbits intersect and will crash on the 3rd lap!

If everything is circular, in the same plane, in the same direction, and indeed you don’t have any other planets, than I suppose it would be stable.

The rather large moon will make the central mass of the planetary system lumpy, but being in perfect resonance will mean that everything repeats each time around, so if it works at all with those times it will be stable.

Still, ask an astrophysicist or use a numeric simulation to check.