Question

Two satellites revolve around a planet in coplanar circular orbits in the same direction with periods of revolution 1 hour and 8 hour respectively. The radius of the satellite A is 10^4 km then find the angular speed of B with respect to A.

As R^3 is directly proportional to T^2 for planetary orbits, I found that the radius of orbit is 4x10^4 km for B.

Also, as T=2 * pi/ angular speed; I just subtracted angular speed of A From B.... This gives -7*pi/4 rad/hour. The correct answer is supposed to be pi/3 rad/hour..... I'm missing something, maybe I should consider gravity between them?

Answer 1

What is it then?

Answer 2

For the sake a argument say the two satellites have the same angular velocity w one is at a radius R1 and the other at radius R2. Given this situation I would say the relative angular velocity is zero. The proposed solution given by @Catch.me would give the relative angular velocity of w. This makes no sense. There is no relative motion.

Answer 3

@gleem
Yea you are right
I just wanted to get the answer given :(
accept my apologize

Answer 4

this is a great question. please can you post the methodology as and when you get it.

i think you need to look at the relative rotation of B about A as they both move in space. i just don't see how π features in the answer on that basis. it is really a function of the angle between the satellites, and that will be a function of time, albeit periodic.

Answer 5

I honestly think no headway is being made here. I'm closing the question because I need to ask another.