Several weeks back I calculated the heights for synchronous and semi-synchronous orbits for all the celestial bodies in KSP.
I want to share these numbers here with you.
What does "synchronous and semi-synchronous orbit" mean?
A scapeship in a synchronous, equatorial orbit allways stays over the same spot of the surface.
This spaceship's orbital period is matched with the revolution of the planet.
A spaceship in a synchronous, non-equatorial orbit seems to shift north and south at a constant longitude.
A spaceship in a semi-synchronous orbit makes exactly two orbits while the planet makes one revolution.
For the numbers I'd like to make some kind of chart: the first column lists the celestial bodies by their name. The second column shows the height of the synchronous orbit and the third column shows the height of the semi-synchronous orbit.
All heights are in meters.
Orbits that are not stable because they intersect with another sphere of incfluence are put in brackets.
Have fun with these numbers! I hope you find them useful.
How can I calculate this myself?
You need four "ingrediences":
- the sidereal rotation period in seconds
- the half sidereal rotation period
- the gravitational parameter of the body in m^3/s^2 (the gravitational parameter is the product of the gravitational constant and the mass of the body)
- the equatorial radius of the body in meters
Insert these numbers into this equation:
h = ((µ * t^2) / (4 * pi^2)) ^(1/3) - R_p
h is the height for the (semi-)synchronous orbit
µ is the gravitational parameter
t is the (half)sidereal rotation period
R_p is the equatorial radius
This gives you the desired height for your orbit.