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Q.

Two Earth’s satellites move in a common plane along circular orbits. The orbital radius of one
satellite is r while that of the other satellite is rΔr (HereΔr<r)

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a

Time interval separates the periodic approaches of the satellites to each other over the minimum
distance is 4πr5/23(GM)1/2Δr.

b

Angular velocity of approach between two satellites is 3(GM)1/2Δr2r5/2

c

Time interval separates the periodic approaches of the satellites to each other over the minimum
distance is 2πr5/23(GM)1/2Δr.

d

Angular velocity of approach between two satellites is 3(GM)1/2Δrr5/2.

answer is A, D.

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Detailed Solution

ω1=(GM)1/2(rΔr)3/2;ω2=(GM)1/2r3/2

Question Image

r2=r;r1=rΔr

Angular velocity of approach =ω1ω2

=(GM)1/2[r3/2(rΔr)3/2r3/2(rΔr)3/2]

(GM)1/2×[1(13Δr2r)]r3/2(1Δrr)3/2=3(GM)1/2Δr2r5/2

Time period of approach

2πω1ω2=4πr5/23(GM)1/2Δr

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