Calculating circular orbits with particular orbital periods

[Catsceo]

Hey all, I want to be able to calculate orbital periods for circular orbits around every body. For example, a 6 hour circular orbit around Kerbin is at a altitude of 2,868.75 km (kerbosynchronous) How would I calculate a 9 hour circular orbit? Or 12? Or 24? What about around other bodies, like the Mun or Duna?

I've read up about Kepler's 3rd law from searching the forums, but I still don't understand how to calculate an altitude from a known time. Any help guys?

Edited August 3, 2013 by Catsceo

[purpletarget]

You can just take the formula for finding the Time of a given altitude and rearrange it. I don't recall where they listed on the wiki's.

But you can find them in the vid here at about 7:20 or so.

[Rhomphaia]

The orbital period is given by 2À√(a³/μ)

Where a is the semi major axis (for a circular orbit this is the altitude of the orbit plus the radius of the body) and μ is the gravitational parameter of the body. these values can be found on the wiki

Edit: À does not look much like pi on these forums but that is what it is supposed to be

Edited August 2, 2013 by Rhomphaia

[Catsceo]

You can just take the formula for finding the Time of a given altitude and rearrange it. I don't recall where they listed on the wiki's.

But you can find them in the vid here at about 7:20 or so.

The orbital period is given by 2À√(a³/μ)

Where a is the semi major axis (for a circular orbit this is the altitude of the orbit plus the radius of the body) and μ is the gravitational parameter of the body. these values can be found on the wiki

Edit: À does not look much like pi on these forums but that is what it is supposed to be

Thanks guys! I did the math from purple target's video to calculate the semimajor axis of a 9 hour circular orbit around Kerbin and got 3947 km. Launched a ship, put it in orbit, got a (almost) perfect 9 hour orbit!