A rocket with mass 7.00×103 kg is in a circular orbit of radius 7.50×106 m aroun

Question

A rocket with mass 7.00×103 kg is in a circular orbit of radius 7.50×106 m around the earth. The rocket's engines fire for a period of time to increase that radius to 8.80×106 m , with the orbit again circular. Part A: What is the change in the rocket's kinetic energy? Does the kinetic energy increase or decrease? Part B: What is the change in the rocket's gravitational potential energy? Does the potential energy increase or decrease? Part C: How much work is done by the rocket engines in changing the orbital radius?

Explanation / Answer

m = mass of rocket = 7000 kg

M = mass of earth = 5.98 x 1024 kg

ri = initial radius = 7.5 x 106 m

rf = final radius = 8.8 x 106 m

Using conservation of energy

initial PE + KEi = final PE + KEf

- GMm / ri + KEi = - GMm / rf + KEf

- (6.67 x 10-11) (5.98 x 1024) (7000) / (7.5 x 106) + KEi = - (6.67 x 10-11) (5.98 x 1024) (7000) / (8.8 x 106) + KEf

change in KE = - 5.49 x 1010 J

since final KE < initial KE . hence the KE decreases

change in PE = - change in KE = 5.49 x 1010 J

since final PE > initial PE , hence PE increases

c)

work done = change in KE = 5.49 x 1010 J

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