Daniel O. answered • 12/26/12

Math and Physics Tutor, with a math and physics degree

First convert period T into seconds.

T = 24hrs = 24*60*60 = 86400 seconds.

Then equate gravitational force between the satellite and earth, and centripetal force on the satellite, since the forces are equal. Use v = 2*pi*r/T in place of velocity in the centripetal force formula. I won't show the derivation (unless you'd like me to, then say so) but you'll get to:

r^{3} = T^{2}GM_{E}/(4*pi^{2})

which you can solve for r. G is the gravitational constant, M_{E} is the mass of the earth. Note that r is the distance from the center of the earth, subtract the earth's radius from that if you want altitude above the earth's surface.