Using Gravitational Force Equilibrium to Calculate M2/M1 Ratio

[erykah722]

Homework Statement

Here is the objective: To experiment with the resultant of two gravitational forces. In particular, you will find the equilibrium position for a test mass located on a line between two point masses.

Here are the instructions:
(1) Drag the test mass (red disk) to an arbitrary point on the line and release. Note the value given for x/L, where x is the distance measured from the center of M1 to the center of the test mass.
(2) Repeat (1), but start the test mass farther away from the mass to which it was attracted.
(3) Continue adjusting the starting position of the test mass until you see the message close enough! Think about how to do that in the most efficient way.
(4) From your latest value of x/L, you can compute the mass ratio M2/M1, without needing to know either L or the value of the test mass. You will have to perform a short derivation to get the simple equation you need. (Hint: start by setting the two gravitational forces acting on the test mass equal to one another.)

I got .404L for the equilibrium value.

Homework Equations

F= M*m*G/r²

The Attempt at a Solution

I set the equations up as:

M*m₁*G/0.404² = M*m₂*G/0.596²

I then canceled out the M and G on each equation because they are equal and am left with

m₁/0.163 = m₂/0.355

I'm stuck here. Am I even doing this right?

 

[ojs]

This is just basic algebra, if you have an equation that reads x/a = y/b and you want the ratio of y/x, how would you do that one?

 

[erykah722]

...Wow. I'm sorry, I've been really stressed out. Now I'm embarrassed. Thank you though!