Heights for (semi-) synchronous orbits

[Quorthon]

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.

Edited May 21, 2013 by Quorthon

[Lazerman34170]

The orbits also aren't stable if they exit the body's SOI.

ex. Moho's SOI is ~11,000,000 m, and the synchronous orbit is at ~31,000,000 m.

[Quorthon]

The orbits also aren't stable if they exit the body's SOI.

ex. Moho's SOI is ~11,000,000 m, and the synchronous orbit is at ~31,000,000 m.

Thanks. I corrected it.

[xZise]

Hi, I got different values for Moho, Eve an Bop. For example Moho: ((6.674e-11*2.5263617e21*1210000.0^2)/(4*pi^2))^(1/3)-250000=18173165.1 (from Moho's center not surface)

You can see a complete list at http://wiki.kerbalspaceprogram.com/wiki/Stationary_orbit#Altitudes

Fabian

[Tanya Sapien]

I'm currently working on a project which is planned to be the reboot for DRAkTEC and my 'Foxxing Around' youtube series, however I'm needing a few very exact numbers and finding them on my own has been being difficult to no end.

Right now, I'm trying to park Gilly in a geosynchronous and tidally locked orbit around Kerbin using Hyperedit (don't ask.) but I'm having issues getting it exact. Using 2868.75Km causes drift. I punched in the radius of Kerbin thinking Hyperedit was calculating from core instead of surface, but that didn't work either. By playing around with time warp then continually resetting the game timer to zero and punching in narrower and narrower adjustments I managed to fine tune it with a long, arbitrarily complex set of numbers, but then when I tried moving the next planet on my list I came back to it and the tiny bugger was nearly 45 degrees off position. And this is just the orbit, I haven't tried making it tidally locked yet.

Any help would be absolutely invaluable and would get annotation in the videos when they're done.

[shand]

Tanya - be careful, you may be hitting the limitation of accuracy that KSP allows.

[Specialist290]

Another tip: Don't focus too much on getting the orbit exactly circular. The important thing for orbital periods is getting the length of the semi-major axis right. A little eccentricity is tolerable, and in the real world no orbit stays perfectly circular for long anyway.