How Do Orbital Dynamics Affect Satellites with Different Masses and Distances?

[bcjochim07]

Homework Statement

Three satellites orbit a planet of radius R. Satellites s1 and s3 have mass m. Satellite s2 has a mass of 2m. Satellites s1 & s2 have orbits 2R from the center of the planet. Satellite s3 has an orbit of 3R from the center of the planet. Satellite s1 orbits in 250 minutes and the force on s1 is 10,000 N

a)What are the periods of s2 and s3?
b)What are the forces on s2 and s3

Homework Equations

T= [(4pi)^2/GM]*r^3

The Attempt at a Solution

As I'm starting this problem, I'm wondering: Do I have to consider the forces between the satellites as well? And if I do, how will I know the distances between them? Or is the force on s1 only the force from the gravity of the planet? Can I get some suggestions on how to start this?

 

[bcjochim07]

Is this going to end up being an expression or a number?

 

[bcjochim07]

Ok, I just had some thoughts, according to Kepler's third law it seems to me that satellite 2 would also have a period of 250 minutes. Then by reasoning, increasing the radius by a factor of 1.5 would increase the period by a factor of 1.5^3 so the period of s3 would be 250* (1.5)^3. Is this correct?

 

[bcjochim07]

F= GMm/r^2 So Then likewise, the force on s2 would be 20,000N & s3 would be 10000/(1.5^2)