Find the radius R of the orbit of a geosynchronous satellite that circles the earth. (Note that R is measured from the center of the earth, not the surface.) You may use the following constants:

The universal gravitational constant G is 6.67ร10โ11Nโm2/kg2

The mass of the earth is 5.98ร1024kg

The radius of the earth is 6.38ร106m.

Answer: 4.225 * 10^7m

Explanation:

Remember, there exists only one force acting on earth's satellite system

F = GMm/R²

Where F = magnitude of force that acts on the satellite

G = universal gravitational constant

M = mass of the earth

m = mass of the satellite

R = radius of the earth

It is worthy if note that the gravitational force on the satellite, will provide a kind of centripetal acceleration that pulls the satellite inward, holding it still in a circular orbit.

w = 2π/T

w = angular velocity

T = period, which happens to be 24hrs

w = 2π/24*60*60

w = 7.27 * 10^-5 rad/s

R = [GM/w²]^⅓

R = [ (5.98*10^24) * (6.67*10^-11) / (7.27 * 10^-5) ²]^⅓

R = 4.225 * 10^7m