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.)
(c) At what speed must a barge leave the rail gun in order to just barely reach the “balance point”?
(d) If the rail gun can accelerate the barges at 100 m/sec2, how long does the rail gun have to be?
by the way:
mass of earth=5.97*10^24 Kg
mass of moon=7.37*10^22 Kg
radius of moon= 1738 Km
radius of earth= 6378 Km
radius of Moon's orbit= 384,000 Km
I got part a to be 341,333 km, but I don't know how to do b,c and d.