# Homework Help: Orbital Energy Problem

1. Feb 19, 2008

### linnus

1. The problem statement, all variables and given/known data
100 ton rocks are "thrown" from the moon to the earth.

(a) Calculate the location of the point, between the Earth and the Moon, where the gravitational field strength is zero. Give your answer in km, from the center of the Earth.
(b) What is the difference in PE between the surface of the Moon (at the point closest to Earth) and the “balance point” you found in part a? (HINT: be sure to take into account the change in PE due to the Moon’s gravity, and the change due to Earth’s.)

mass of earth=5.97*10^24 Kg
mass of moon=7.37*10^22 Kg
radius of Moon's orbit= 384,000 Km

I got the first one to be 341,333 Km
I don't know how to do the 2nd one
2. Relevant equations
I got the first one to be

-GMm/r

3. The attempt at a solution
So, for part B i did
change in PE= PE at object of surface of moon- PE at the balance point
change in PE= ((-GM(moon)m/radius of moon)+(GM(earth)m/(distance from earth to surface of moon))-((GM(moon)m/distance from the moon to to balance point )+(GM(earth)m/distance from the earth to the balance point)
is that right?
I got PE= 7.88 x 10^11 joules...

Last edited: Feb 19, 2008