Physics Question?

Question

A satellite is in a circular orbit about the earth (ME = 5.98 1024 kg). The period of the satellite is 1.10 104 s. What is the speed at which the satellite travels?

I am studying for a physics final and this is one homework question that I got wrong. I can't seem to find the right combination of equations for this problem. The correct answer is 6110 m/s. Any help would be greatly appreciated.

I mainly need help on arriving at the correct answer that I gave in my post above.

Answer 1

If we are to assume a circular orbit then the centripetal force must be equal to the force of gravity

mv^2/r=GMm/r^2
where
m - mass of the satellite
v - velocity of the satellite in the orbit
r-distance of the satellite from the center of the Earth
M- mass of the earth
G - universal gravitational constant

then v^2=GM/r
also v=2(Pi r)/t r=vt/(2 Pi)
then v^3=2 Pi GM/t

v= (2 pi GM / t) ^1/3=

since GM=3.986005x10^14 m^3/s^2 we have
v= (2 (3.14...) 3.986005x10^14 m^3/s^2/ (1.1 10 ^4))^1/3=
v=6106m/s (very close)

I hope that helps