Question

4. -110 points SerCP10 7 P034 A satellite has a mass of 406 kg and is located at 2.03 x 106 m above the surface of Earth. (a) What is the potential energy associated with the satellite at this location? (b) What is the magnitude of the gravitational force on the satellite?

Answer 1

mass m = 406 kg

height above the surface of the earth is h = 2.03 * 10^6 m

the radius of the earth is R = 6.371 * 10^6 m

mass of earth M = 5.972 * 10^24 kg

a) The potential energy associated with the satellite is

U = - G * M * m / (R+h)

U = - (6.67 * 10^-11 * 5.972 * 10^24 * 406) / ((6.371 * 10^6) + (2.03 * 10^6))

U = - 1.925 * 10^10 J

b)

Gravitational force F = G * M * m / (R+h)^2

F= (6.67 * 10^-11 * 5.972 * 10^24 * 406) / ((6.371 * 10^6) + (2.03 * 10^6))^2

F = 2.291 kN