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.

Moho____[30,993,821]_____19,656,592

Eve______10,958,472______6,877,502

Gilly_________42,138_________21,734

Kerbin_____2,868,750______1,585,176

Mun______[2,970,563]_____1,797,329

Minmus______357,940_______203,286

Duna_____[2,879,999]_____1,695,873

Ike_______[1,133,895]_______666204

Dres________732,244_______410,219

Laythe____[4,686,318]_____2,767,176

Vall_______[3,593,201]_____2,152,563

Tylo_____[14,157,877]_____8,696,880

Bop_______[2,618,169]____[1,606,391]

Pol_________2,415,079_____1,505,122

Eeloo________683,690_______352,989

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.