Ratio Problem Dealing with Radius and Centripetal Acceleration

[PeachBanana]

Homework Statement

Two identical satellites orbit the Earth in stable orbits. One satellite orbits with a speed v at a distance r from the center of the earth. The second satellite travels at a speed that is less than v . At what distance from the center of the Earth does the second satellite orbit?

Homework Equations

a = (v)^2/r
F = m/a
F = G (M * m )/ r^2

The Attempt at a Solution

I'm really confused on how to manipulate these equations.

Ultimately, I need to find an equation that relates "r" to "v."
r = a * v^2
So if the second satellite is moving slower doesn't that mean "r" has to be bigger? This makes me think of one of Kepler's Laws.

 

[genericusrnme]

F = m/a

That should read F=ma or a=F/m

What does satellites orbit the Earth in stable orbits tell you about the system?
I'm not sure you understand what you're actually doing when you're working with these equations

 

[PeachBanana]

Wow. That was really careless of me. When it comes to problems like these, I don't understand how to do them well. Stable orbits = equal gravitational force?

 

[genericusrnme]

What should the gravitational force equal?

What does it mean if the orbit is stable?