Find the velocity of a satellite orbiting above the equator of the earth in geosynchronous orbit (Period=24 hours) in km/hr.

Question

The earth's mass M=5.974x10^(24)kg and radius R=6,731 km.
G=6.673x10^(-11) m^3/(kg*s^2)
Use v=(G*M/R)^(1/2)

I plugged everything in and changed the units,
v=(6.673x10^(-11)*(1/1000)^3*3600^2*5.974x10^(24)/6371)^(1/2)
but I get the answer 28,476.85 and the correct one is 11,060. What am I doing wrong?

Answer 1

You used earth radius for R, but it is the distance of the satellite from earth center that is R. We do not know R in fact yet.

You never used 24 hours
it goes 2 pi R in 24 hours.
so
v also = 2 pi R/(24 *3600)
That is the missing ingredient :)

Answer 2

By the way I bet you did indeed find the velocity of a satellite zipping along between your feet.

Answer 3

Thank you for helping Tyler Mischa. I am tired and going to bed. Hope the above helps.