Planetary motion and a space station

[serunder]

Homework Statement

A space station is in orbit between the Earth and the moon. The force due to gravity on the space station from the moon is the same as the force due to gravity from the Earth. (FGmoon = FGearth). How far away from the Earth is the space station? How far from the moon is the space station?

Homework Equations

+ attempt at a solution[/B]

I keep getting 0.213 for r(earth) and I have no idea how to solve for the variable, can someone please help me?

 

[haruspex]

Homework Statement

A space station is in orbit between the Earth and the moon. The force due to gravity on the space station from the moon is the same as the force due to gravity from the Earth. (FGmoon = FGearth). How far away from the Earth is the space station? How far from the moon is the space station?

Homework Equations

+ attempt at a solution[/B]

View attachment 206637

I keep getting 0.213 for r(earth) and I have no idea how to solve for the variable, can someone please help me?

It (nearly) all made sense until the final step. You had 3.844.10⁸m-r_moon=9.02 r_moon. How did you proceed from there?

The other small mistake is that in your "given" you defined r_moon and r_earth as the radii of those two bodies, but thereafter used them as the respective distances from their centres to the space station.

 

[serunder]

It (nearly) all made sense until the final step. You had 3.844.10⁸m-r_moon=9.02 r_moon. How did you proceed from there?

The other small mistake is that in your "given" you defined r_moon and r_earth as the radii of those two bodies, but thereafter used them as the respective distances from their centres to the space station.

I figured it out now I think since like you said, it didn't make sense when I tried to use them as their distance, so what I ended up doing was this:

sorry for the crappy formatting but does this seem to be correct?

 

[haruspex]

I figured it out now I think since like you said, it didn't make sense when I tried to use them as their distance, so what I ended up doing was this:

View attachment 206640
sorry for the crappy formatting but does this seem to be correct?

Yes.