How to solve (Gm)/(r-S)^2 = (GM)/r^2 for S

[highc]

I'm working through a problem that was posted here a while ago (https://www.physicsforums.com/showthread.php?t=115170). maltesers posted the equation (Gm)/(r-S)^2 = (GM)/r^2, so far this makes perfect sense, he then goes on to solve for S with S = r - (mr^2)/M, and it is here that he loses me. How did we eliminate the ^2 to go from (r-S)^2 to S = r - ...?

I've been out of the math game a little too long!

 

[neutrino]

That equation is actually incorrect. It should have been

$$\frac{Gm}{(r-S)^2} = \frac{GM}{S^2}$$

 

[George Jones]

That equation is actually incorrect. It should have been

$$\frac{Gm}{(r-S)^2} = \frac{GM}{S^2}$$

This not the only thing wrong.

Look at units. In maltesers' last equation, S is a length, while the last term on the right has units of length squared.

 

[neutrino]

This not the only thing wrong.

Look at units. In maltesers' last equation, S is a length, while the last term on the right has units of length squared.

Now that it's known that the original equation is wrong, why bother about what was derived from it.

Thanks for pointing that out.

 

[highc]

Thanks a lot, I wasted way too much time on this one.