Question

A satellite in Earth orbit has a mass of 98 kg and is at an altitude of 293 ? 103 km.

(a) What is the potential energy of the Earth-Satellite system?

(b) What is the magnitude of the gravitational force exerted by the Earth on the satellite?

(c) What is the magnitude of the gravitational force exerted by the satellite on the Earth?

Answer 1

a)

m = mass of satellite = 98 kg

M = mass of earth = 5.98 x 10²⁴ kg

R = radius of earth = 6.371 x 10⁶ m

h = altitude = 293 x 10⁶ m

r = orbital radius = R + h = 299.371 x 10⁶ m

Potential energy is given as

U = - GMm/r

U = - (6.67 x 10^-11) (5.98 x 10²⁴) (98)/( 299.371 x 10⁶)

U = - 1.31 x 10⁸ J

b)

magnitude of gravitational force on satellite is given as

F = GMm/r²

F = (6.67 x 10^-11) (5.98 x 10²⁴) (98)/( 299.371 x 10⁶)²

F = 0.44 N

c)

magnitude of gravitational force on earth is given as

F = GMm/r²

F = (6.67 x 10^-11) (5.98 x 10²⁴) (98)/( 299.371 x 10⁶)²

F = 0.44 N