Gravitational force of the Sun and Earth

[tfugger]

Homework Statement

Earth orbits around the sun at roughly 1.5x10¹¹ m. Mass of Earth is 6x10²⁴ kg. Mass of sun is 1.98892x10³⁰ kg.

There is a point between the sun and the Earth at which the gravitational force by the sun equals that of Earth and the forces cancel each other out. How far is this point from the center of the earth? You will get a quadratic equation.

Homework Equations

I know the force between two bodies is calculated using F=(G*m₁*m₂)/R²

The Attempt at a Solution

Based on the above equation, I thought that this problem would be solved by setting that equation equal to itself. Basically F=F but with the R on the right side as an unknown, then solve for that R. but obviously this results in everything else cancelling out and the R I am left with is equal to the distance between the sun and the Earth (1.5x10¹¹ m).
So I'm confused, I'm not sure what to do...

 

[technician]

This is an exercise in algebra more than anything else.
This magical point is at a distance R from the centre of the Earth and therefore at a distance of 1.5 x 10^11 - R from the centre of the sun.
Stick these in as your r^2 distances in the equation and you will get an equation that can be solved !

 

[tfugger]

thank you very much. so does this mean my equation would be F=(G*m1*m2)/(1.5x10¹¹ - R²) ? or is it [(G*m1*m2)/R²] = [(G*m1*m2)/(1.5x10¹¹ - R²)

i having trouble figuring this out for some reason...