Question

A satellite in Earth orbit has a mass of 99 kg and is at an altitude of 1.98 X 100 m. (Assume that U = 0 asr →0.) (a) What is the potential energy of the satellite-Earth system? What is the equation for gravitational potential energy when the altitude is comparable to the radius of the Earth? ) (b) What is the magnitude of the gravitational force exerted by the Earth on the satellite? (c) What force, if any, does the satellite exert on the Earth? (Enter the magnitude of the force, if there is no force enter 0.)

Answer 1

given
m = 99 kg
h = 1.98*10^6 m
we know,
Me = 5.98*10^24 kg
Re = 6.37*10^6 m

a) potential energy of the satellite-Earth system = -G*me*m/(Re + h)

= -6.67*10^-11*5.98*10^24*99/(6.37*10^6 + 1.98*10^6)

= -4.73*10^9 J <<<<<<<<-----------Answer

b) The gravitational force exerted by the Earth on the satellite,

F = G*me*m/(re + h)^2

= 6.67*10^-11*5.98*10^24*99/(6.37*10^6 + 1.98*10^6)^2

= 566 N <<<<<<<<-----------Answer

c) The satellite also exert the same amount of force on the Earth.

F = 566 N <<<<<<<<-----------Answer