What distance is the magnitude of gravity equal between earth and moon?

[zakh4527]

Homework Statement

At a point between the Earth and moon, the magnitude of the Earth's gravitational acceleration equals the magnitude of the moons gravitational acceleration. What is the distance of that point from the center of the earth? The distance from the center of the Earth to the center of the moon is 383000km and the radius of the Earth is 6370km. The radius of the moon is 1738km and the acceleration of gravity at it's surface is 1.62m/s^2.

Homework Equations

none given to work with.

The Attempt at a Solution

I really have no idea how to start this. What I tried was...

F=ma F=mMG/R^2 => a=GM/R^2

GMe/R^2 = GMm/(3.83E^8-R^2)

MmR^2=Me(3.83E^8-R^2)

R^2= Me(3.83E^8)/(Mm+Me)

where Mm= Mass of moon and Me = mass of earth.

The problem is I don't even know if I can use the masses of the Earth and moon because they were not given in the problem. Is there a way to do this without using mass?

Thanks for all the help in advance!

 

[LowlyPion]

Welcome to PF.

You must use the masses. If not given then they expect you to look them up.

Otherwise your method is almost OK.

However,

GMe/R^2 = GMm/(3.83E^8-R^2)

Should be

GM_e/R² = GM_m/(3.383*10⁸- R)²

Edit: Note I see in looking again they maybe expect you to calculate based on the radius and values of g on Earth and moon.

 

[LowlyPion]

Note as I realize on second reflection, you can figure the G*M of Earth and moon from the additional information they supply.

a = GM/r²

a*r² = GM

Where r is the radius at the surface that a is measured.

 

[zakh4527]

Thanks! Yeah, actually I was leaning towards the idea of solving fro GM. Thanks for pointing out the (3.383*108- R)^2