Finding the radius of a satellite

[Solitary Nut]

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

Homework Statement

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 r_b. The forces of gravitational attraction between each satellite and the Earth is the same. Find r_b.
Express your answer in terms of r.

Homework Equations

F=(G(m₁m₂))/r²

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, andm_earth, leaving r and r_b. It looked like this:

1/r = 6/r_b

So I multiplied r and rb into the numerators, getting r_b=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 :)

 

[Andrew Mason]

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, andm_earth, leaving r and r_b. It looked like this:

1/r = 6/r_b

So I multiplied r and rb into the numerators, getting r_b=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 :)

Check your algebra:

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

does not reduce to 1/r_a = 6/r_b where m_b = 6m_a

AM

 

[Solitary Nut]

Gah, I see. Radical(6)r

Thanks a lot for your help