# Calculate Low/High/Geo orbits for other planets? - math lite - gamedev

I have a situation where I have proceduraly generated planets and moons in a solar system. These bodies have varying mass and radius.

Now what I want to do is be able to define a circular orbital path around each (Planet and Moons) that would be conceptually equivalent to Low Earth Orbit, High Earth Orbit, and Geosynchronous Earth Orbit.

I don't want to get into high math calculating things exactly, and like I stated previously these orbits are circular not elliptical anyway. What I do need is really just a way to fake it so it seems somewhat logical and semi-believable.

Does anyone have any idea on how I might best go about this? I would guess that the main, or maybe only necessary, variable in the equation would be the mass of the planet or moon?

Also as a side but semi-related question would there be something similar I should take into account when placing moons around a planet to keep it semi logical?

Thanks for any help!

• For a bit more clarity, this is a 2D game and I will be drawing a circle around the planets to represent the orbits. All I really need to do is just calculate the altitude of the three orbit types. – jwvanderbeck Nov 14 '15 at 22:29

## 1 Answer

For low/high orbit, you could just make them proportional to the diameter of the planet -- low orbit 250km for Earth, 125km for one half Earth's diameter, and so on -- the lower bound is dependent on atmosphere.

For synchronous orbit, you can use the equations derived here or here; keep in mind the difference between altitude (above the surface of the body) and radius (from the center of the body). It's dependent on the rotational speed of the body, though, which is widely variable. Planets close to the star might be tidally locked or in an stellar-orbital resonance (like Mercury) in which case their synchronous orbit altitude would be outside their sphere of influence.

For placement of moons, a lower bound would be the Roche limit; an upper bound would be the planet's Hill sphere. Moon-to-moon interaction would be dependent on the moons' Hill spheres. In reality the moons would have complicated resonant interactions like those of Jupiter's, but those are more complicated than I'm willing to deal with in my space game. ;)

• Bodies actually don't rotate or orbit actually so it (I think) simplifies things a great deal. It is basically a static snapshot of a solar system. As for "Just make them proportional", I guess I could go that route but thought it would make more sense if higher mass/higher gravity planets were different from lower mass ones, even if they were the same size. Then again I may be over complicating it there - this is supposed to be simple and easy to absorb by a player. – jwvanderbeck Nov 14 '15 at 22:52
• I assume you mean roughly half the Hill sphere size, for stability. – Nathan Tuggy Nov 14 '15 at 23:27
• @jwvanderbeck: If the bodies don't rotate then synchronous orbits would be impossible. Planet's rotation speed would need to be between orbital period at planet's Hill sphere and it's Low Orbit period (realistically, considerably less or the planet would break apart). You can believably fake the moons' interactions by setting their orbits such that their orbital periods are ratios of natural numbers, 2/3, 4/5, 1/8 etc. (e.g. if one moon's period is 20 days, make another to have a 30-day period. – SF. Nov 14 '15 at 23:30
• No sorry I probably made it more confusing than I should of. They don't rotate during gameplay would be a better way to put it. Think of a snapshot in time of a working planetary system. – jwvanderbeck Nov 15 '15 at 0:02