Physics 203
posted by Michael Moskvich .
Mars rotates on its axis once every 24.8 hours.
What is the speed of a geosynchronous satellite orbiting Mars?
What is the altitude of a geosynchronous satellite orbiting Mars?

It is easiest to do the second part of the question first.
You need to use Kepler's Third Law in the form that relates the period (P), the orbital radius measured from the center of the planet (a), and total mass of the system (which in in this case is mainly the mass of Mars) M. You will need to use the Newton gravitational contstant, G.
That law is:
P^2 = 4 pi^2 a^3/(G M)
where G = 6.674*10^11 m^3/(kg s^2)
Look up the mass of Mars, insert P = 24.8 days (converted to seconds) and solve for the distance a. Subtract the radius of Mars to get the altitude.
Once you know P and a, the velocity of the satellite is
V = 2 pi a/P