GPE Between the Moon and the Earth?

[isukatphysics69]

Homework Statement

How to determine GPE between moon and earth?

Homework Equations

mgh

The Attempt at a Solution

I know that gpe near Earth's surface is mgh, but at larger distances is there a specific way to calculate?

 

[Orodruin]

You can only use mgh when your gravitational field can be well approximated by a homogeneous one. This is not the case for the Earth-Moon system. You need to use Newton’s expression for the gravitational potential.

 

[isukatphysics69]

You can only use mgh when your gravitational field can be well approximated by a homogeneous one. This is not the case for the Earth-Moon system. You need to use Newton’s expression for the gravitational potential.

so -(GMm/R^2) = Gravitational energy
so i will need the R to be sqrt(x^2+y^2) with the Earth centered at 0,0
Energy mechaninc will be the kinetic from the moon plus the gravitational energy at each time dt
also the velocity will be sqrt(x^2+y^2)

 

[isukatphysics69]

That's a lot of energy

I have my Earth at 0,0 so the kinetic energy from Earth is 0, kinetic energy of moon is .5mv^2 and potential energy is -GMm/R^2 and that is all of the energies i can think of. do those energy values look about right? id love to go to sleep so tired

 

[gneill]

so -(GMm/R^2) = Gravitational energy

No, you don't square the R in the denominator when calculating gravitational PE. When you do square it you're calculating the gravitational force instead (Newton's Law of Universal Gravitation).