Finding the radius of a satellite

1. Oct 1, 2009

Solitary Nut

Just realized how horrible the thread title is. Sorry, I meant the radius of a satellite's *orbit*

1. The problem statement, all variables and given/known data

Two satellites revolve around the Earth. Satellite A has mass m and has an orbit of radius r. Satellite B has mass 6m and an orbit of unknown radius rb. The forces of gravitational attraction between each satellite and the Earth is the same. Find rb.

2. Relevant equations

F=(G(m1m2))/r2

3. The attempt at a solution

F1 = F2, where F1 and F2 are the forces of gravity acting on satellite A and B, respectively.

I equated the formulas for the force of gravity for both satellites because the information given states they are equivalent. I then negated every variable I could - G, m, andmearth, leaving r and rb. It looked like this:

1/r = 6/rb

So I multiplied r and rb into the numerators, getting rb=6r. I don't see what I did wrong here, but clearly it isn't right. Please help set me on the right path, and thanks for at least taking the time to read all of this :)

2. Oct 1, 2009

Andrew Mason

$$GMm_a/r_a^2 = GMm_b/r_b^2$$

does not reduce to 1/ra = 6/rb where mb = 6ma

AM

3. Oct 1, 2009