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?
(b) What is the magnitude of the gravitational force on the satellite?
Thank you for the opportunity to help you with your question!
g = G M/R²
R = Earth's radius
At h = 2.03 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 + 2.03*10^6)²
F = 597.43 N <---ANSWER
Working on part b NOW! :)
Sorry that is part B (the coffee is getting to me ;) ) . Part A will be posted shortly
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 * 2.03*10^6)/(6371000 + 2.03 *10^6)
U = - 1.59 * 109 J <---ANSWER FOR POTENTIAL ENERGY (PART A)
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