### Question Description

A satellite has a mass of 106 kg and is located at 2.03 106 m above the surface of Earth. (a) What is the potential energy associated with the satellite at this location? J

(b) What is the magnitude of the gravitational force on the satellite? N

## 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 = 2.3 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 = 106 * 9.8 * 6371000²/(6371000 + 2.3 10^6)²

F = 560.80 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 = - 106 * 9.8 * 6371000 * 2.3 *10^6/(6371000 + 2.3* 10^6)

U = - 1755.48 10^6 J