help

Orbital Characteristics of a Two-Moon System Orbiting a Planet

-- Reigna | January 29, 2023

Radio image of the protoplanetary disk around young star HL Tau.

Question:

Hello, I am worldbuilding for a story and I need a bit of help. So, there is a planet with a radius of 1050.5km. It has two moons orbiting it (they are in the same trajectory), the one closer to the planet has a radius of 65.65625km and the other one has a radius of 131.3125km. Those two moons eclipse each other twice every year (a year is the same as on Earth). I am trying to find their speed of orbit and their distance between one another and the planet so that they are somewhat realistic. The planet, in most other aspects, is like our Earth. Thank you for the help!

-- Reigna

Answer:

I think that you can derive the information you are looking for by noting that:

(1) Since the moons eclipse each other twice per year, the orbital period of the outer moon must be equal to three times the orbital period of the inner moon (for two moons orbiting in the same plane)

(2) Applying Kepler’s Third Law, which states that for an object in orbital motion about another object that the orbital period of that object is proportional to the cube of its semi-major axis. Combining this law with what you know from (1) above, you can say that the ratio of the semi-major axes of the inner moon to the outer moon is (1/3)^(2/3), or about 0.48

From this point I believe that you should be able to derive the orbital speeds and distances from each other.

-- Jeff Mangum

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