A rocket with mass 6.00×103 kg is in a circular orbit of radius 7.50×106 m aroun

Question

A rocket with mass 6.00×103 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 8.70×106 m , with the orbit again circular.

A) What is the change in the rocket's kinetic energy? Does the kinetic energy increase or decrease?

Express your answer with the appropriate units. Enter positive value if the kinetic energy increases and negative value if the kinetic energy decreases.

B)What is the change in the rocket's gravitational potential energy? Does the potential energy increase or decrease?

CHow much work is done by the rocket engines in changing the orbital radius?

Explanation / Answer

orbital speed v = sqrt(GM/r)

kinetic energy in the orbit K = 0.5*m*v^2 = 0.5*G*M*m/r

dKE = K2 - K1

DKE = 0.5*G*M*m*(1/r2 - 1/r1)

dKE = 0.5*6.67*10^-11*5.97*10^24*6*10^3*( (1/(8.7*10^6)) -(1/(7.5*10^6)))

W = -21969600000 J

decreases

B)

potential energy U = -GMm/r

dU = GMm*(1/r1 - 1/r2)

dU = 6.67*10^-11*5.97*10^24*6*10^3*( (1/(7.5*10^6)) -(1/(8.7*10^6)))

dU = 43939200000

increases

part c)

W = du + dk = 43939200000-21969600000 = 21969600000 J

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