Two identical spacecraft A and B are in circular orbits about Earth, with B at h

Question

Two identical spacecraft A and B are in circular orbits about Earth, with B at higher altitude. For the following statements, decide whether they are true. You only need to check answers; you do not need to justify your answers. However, for each question I have provided blank space for any calculations (not graded) you may need to do to answer the question. B has smaller potential energy. True. False. Not enough information. B has smaller total (mechanical) energy. True. False. Not enough information. B has the larger ratio of potential energy to total energy (i.e.. a larger proportion of B's total energy is potential energy, compared to the proportion for spacecraft A). True. False. Not enough information.

Explanation / Answer

(A) PE = - G Me m / r

G, Me and m are same for A and B.

r is greater for B.

hence G Me m / r will be smaller for B.

but PE is negative of G Me m / r

hence PE will be greater for B.

False

(B) total energy = PE + KE

= - G Me m / r + m v^2 / 2

= - G Me m / r + ( G Me m / 2 r)

= - G Me m / 2 r

hence A will have smaller energy.

False

(C) PE / total energy = 2

it is same for both

False

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