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Question:

The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R1 to another of radius R2 (R2 > R1) is

2GmM(1/R1 - 1/R2)

GmM(1/R1 - 1/R2)

GmM(1/R2 - 1/R1)

1/2GmM(1/R1 - 1/R2)

Solution:

We know that, KE = (-GMm/2R)
The kinetic energy of the satellite in the orbit of radius R1 is KE1 = -GMm/2R1
The kinetic energy of the satellite in the orbit of radius R2 is KE2 = -GMm/2R2
The additional kinetic energy to be provided to the satellite is
ΔKE = KE2 - KE1 = (-GMm/2R2) - (-GMm/2R1) = GMm(1/2R1 - 1/2R2) = 1/2 GMm(1/R1 - 1/R2)