Question

A satellite in earth orbit has a mass of 99 kg and is at an altitude of 2.02 106 m. (assume that u = 0 as r â â.) (a) what is the potential energy of the satelliteâearth system? j (b) what is the magnitude of the gravitational force exerted by the earth on the satellite? n (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

(a)          What is the potential energy: PE = -G * M * m/r

 

Where: M is the mass of the earth which is 5.98 * 10^24 kg.

m is the mass of the satellite.

r is the space from the center of the earth to the satellite

 

To conclude this distance add the radius of the earth to the altitude. Radius of the earth is 6.38 * 10^6 meters.

 

 

r = 6.38 * 10^6 + 2.02 * 10^6 = 8.38 * 10^6

PE = 6.67 * 10^-11 * 5.98 * 10^24 * 99/8.38 * 10^6 = 4.71240095 * 10^9 J

 

 

(b) magnitude of the gravitational force exerted by the Earth

 

Fg = G * M * m/r^2

Fg = 6.67 * 10^-11 * 5.98 * 10^24 * 99/(8.38 * 10^6)^2 = 562.3078873 N

 

 

(c) There are no other forces that the satellite exert on the Earth. So therefore, it is 0.