What is the altitude of a geosynchronous satellite orbiting Mars, it rotated once every 24.8 hrs?

Answer 1

It figures out to be 10600 miles altitude. Mars has only about 1/10 the mass of the Earth so the altitude for marsosynchronous orbit is much smaller than on Earth's geosynchronous where it is 22200 mi. Since I went this far, I asked the computer for the other planets too:

Mercury 149000
Venus 90300
Earth 22200
Mars 10600
Jupiter 54800
Saturn 32110
Uranus 35500
Neptune 38500
Pluto 11100

Answer 2

I read somewhere that it would be roughly half way between the orbits of Phobos and Diemos. You could calculate it yourself using Kepler's laws if you know the altitude and period of one of Mars' satellites, such as Diemos.