Two satellite S, and S, revolve around a planet in
coplanar circular orbits in the opposite sense. The
period of revolutions are T and 8T respectively.
Find the linear speed of S, as observed by an
astronaut in S, when, then angular separation is
as shown in figure
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Angular speed of satelite s2 w.r.t. s1 when they are closest to each other is given by,
w = |v1-v2| / |r1-r2|
But for planetary motion,
v1 = 2πr1/T1
v2 = 2πr2/T2
w = 2π× |(r1/T1 - r2/T2 ) ÷ (r1-r2)|
w = 2π× |(r1T2 - r2T1)/T1T2| ÷ |r1-r2|
w = 2π× | [r1T2- r2T1] / [T1T2/(r1-r2)] |
This is formula for angular speed of satelite s2 w.r.t. s1.
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