### Question Description

A satellite has a mass of 94 kg and is located at 1.96 106 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?## Explanation & Answer

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b) The acceleration due to gravity at sea level is:

g = G M/R²

R = Earth's radius

At h = 1.96 10^6 m of altitude:

g' = G M/(R+h)²

By dividing the equations:

g'/g = R²/(R+h)²

g' = g R²/(R+h)²

F = m g' = m g R²/(R+h)² = 94 * 9.8 * 6371000²/(6371000 + 1.97 10^6)²

F = 55501.575 N

= = = = = = =

a) U = m g' (R + h) – m g R = m g R²/(R+h) – m g R

U = m g R (R/(R+h) – 1) = - m g R h/(R+h)

U = - 94 * 9.8 * 6371000 * 1.96 10^6/(6371000 + 1.96 10^6)

U = -442,871.24 J

= = = = = = = = = =