Question

A satellite of mass 5520 kg orbits the Earth and has a period of 6700 s . A) Determine the radius of its circular orbit. B) Determine the magnitude of the Earth's gravitational force on the satellite. C) Determine the altitude of the satellite.

Answer 1

In an orbit

gravitational force provides necessary centripetal force

Fg = Fc

G*Mm/r^2 = mv^2/r

v = sqrt(GM/r)

timeperiod T= 2*pi*r/v

T = 2*pi*r/sqrt(GM/r)

T = 2*pi*r^(3/2)/sqrt(GM)

r = orbital radis

M = mass of earth = 5.97*10^-24 kg

6700 = 2*pi*r^(3/2)/sqrt(6.67*10^-11*5.97*10^24)

orbital radius r = 7.68*10^6 m

(B)

Fc = GMm/r^2 = 6.67*10^-11*5.97*10^24*5520/(7.68*10^6)^2

Fc = 37266.34 N   <<<===========ANSWER

(C)

r = R + h

R = radius of earth = 6.37*10^6 m

h = r - R

h = (7.68*10^6) - (6.37*10^6) = 1.28*10^6 m <<<<===========ANSWER