Calculating the speed of a satellite

[Kartoffelkuchen]

Hello guys, I have a question:

I want to calculate the speed of a satellite which is in a circular orbit around Kerbin. Or Earth, the formula should be the same. I have looked on the internet and found some formulas for exactly this, but the problem is that when I tried to calculate the formulas I always got results like 4.83318...x10^14. And that can't be true at all. Would you guys be so kind to help me? I would really want to calculate that, but I can't come to a correct result. And I am not really skilled in maths at all, so don't be angry with me when I don't understand something directly!

Thanks in advance,

Kartoffelkuchen

[Nikolai]

If the satellite is far smaller than the planet it's orbiting, the velocity is approximately sqrt(G*M/r), where G is the gravitational constant, M is the mass of the planet, and r is the radius of the orbit (not the altitude!). Ensure that G is in the same units as M and r, and you should be good to go. For example, G in the MKS (meters-kilograms-seconds) system is 6.67384*10^-11 m^3 kg^-1 s^-2, the mass of Earth is about 5.972*10^24 kg, and the radius of Earth is 6,378,140 m; if you plug-and-chug for a satellite 200 km up, you should get a velocity of about 7,784 m/s.

Edited May 21, 2015 by Nikolai

[Jonboy]

Here's the simplest way in your situation:

V=R*sqrt(G/(R+h))

R is the radius of the planet, which for Kerbin is 600,000 meters. G is the acceleration due to gravity on the surface, which on Kerbin is 9.807 m/s^2 (the same as on Earth). "h" is your height above Kerbin. So using a 100 km orbit as an example:

v = 600,000 m * sqrt( 9.807 m/s^2 / ( 600,000 m + 100,000 m ) = 2,245.8 m/s

(Just keep in mind that this assumes a perfectly circular orbit, and a satellite of negligible mass compared to the planet.)

Edited May 21, 2015 by Jonboy