Question

A satellite of mass 5480 kg orbits the Earth and has a period of 6630 s . Determine the radius of its circular orbit.Determine the magnitude of the Earth's gravitational force on the satellite.Determine the altitude of the satellite.

Answer 1

Mass of the earth, M = 6 x 10^24 kg

Angular velocity, ω = 2π / T

                              = 2π / 6630

                              = 9.47 x 10^-4 rad/s

Mass of the satellite, m = 5480 kg

Radius of earth, R = 6.4 x 10^6 m

(a)

ω^2 = G M / r^3

r^3 = G M / ω^2

       = 6.67 x 10^-11 * 6 x 10^24 / ( 9.47 x 10^-4 )^2

       = 4.462 x 10^20

Radius of the orbit, r = 6.68 x 10^6 m

(b)

Force, F = G M m / r^2

               = 6.67 x 10^-11 * 6 x 10^24 * 5480 / ( 6.68 x 10^6 )^2

               = 4.91 x 10^4 N

(c)

Altitude, h = r - R

                 = ( 6.68 - 6.4 ) x 10^6

                 = 2.8 x 10^5 m