Gravitational Forces Question Tricky

[XcKyle93]

Homework Statement

Two planets have masses M and m, and the ratio M/m=25. The distance between the planets is R. The Point P, is between the planets as shown (there is no picture though), and the distance between M and P is x. At P, the gravitational forces on an object due to M and m are equal in magnitude. What is x?

Homework Equations

F = (G*M*m)/R^2

The Attempt at a Solution

I am stumped. Can you really figure this out with the info given? I ended up with some quadratic equation: 0 = 25R^2 - 50Rx + 24x^2

 

[berkeman]

Homework Statement

Two planets have masses M and m, and the ratio M/m=25. The distance between the planets is R. The Point P, is between the planets as shown (there is no picture though), and the distance between M and P is x. At P, the gravitational forces on an object due to M and m are equal in magnitude. What is x?

Homework Equations

F = (G*M*m)/R

The Attempt at a Solution

I am stumped. Can you really figure this out with the info given? I ended up with some quadratic equation: 0 = 25R^2 - 50Rx + 24x^2

Two things -- your equation that you list is not quite right. And the 2nd "m" in the equation is meant to be the mass of an object a distance R away from a mass M. You will need to have three masses listed in your initial equations (the object's mass will cancel out).

 

[Doc Al]

I am stumped. Can you really figure this out with the info given? I ended up with some quadratic equation: 0 = 25R^2 - 50Rx + 24x^2

Stumped? Looks to me like you figured it out just fine. Now just solve the quadratic!

 

[XcKyle93]

I accidentally type the inverse square law incorrectly, but I edited my initial post to fix that. Why would I need three masses if the mass of the object cancels out?

 

[XcKyle93]

Stumped? Looks to me like you figured it out just fine. Now just solve the quadratic!

Alright, awesome, I was just unsure of myself. Thanks!

 

[berkeman]

I accidentally type the inverse square law incorrectly, but I edited my initial post to fix that. Why would I need three masses if the mass of the object cancels out?

My point was that M and m are listed in the problem as the masses of the two planets. That doesn't fit the equation that you wrote.

 

[XcKyle93]

Perhaps I should have used slightly different variables for the equation that I wrote down; it was meant to be a general formula.