Celestia Forums

I suppose it should be a simple thing, but i can't solve it....

Suppose i'm on the equator of a planet which have a day of X hours.
From there i see a satellite raising each Y hours.
What's the formula to find the satellite orbital period?

- I'm thinking to a simplified, theoretical system, we can think at the satellite orbit as a perfectly circular, equatorial orbit, ecc...
- found that formula, i should put Y<0 for satellites with a period longer than X, right?

My gut feeling says is should look something like P = |Y| + Y/(X-Y)
Where Y is positive when the satellite rotates in the same direction as the planet and negative when it's in a retrograde orbit.

Let's say X = 24 and Y =1 then the result for P = 1 + 1/23 which is a little more than one hour, an expected result: the satellite has to 'catch up' with the viewer.
For Y = -1, we get P = |-1| + -1/25 = 1 - 1/25 which is a little less than one hour. Also as expected.
For Y = 24 (e.g. geostationary), we get no P, because of the division by zero, which is to be expected as well.

Does it work when Y > X. Let's try:

if Y = 72, we get:

P = 72 + 72/-48

No it doesn't Well. Maybe someone else has an idea.