Asatellite 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.)

(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.

area of focus

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west