Consider the Earth and the Moon as a two-particle system.

(a) Find the gravitational field of this two-particle system at the point that is exactly halfway between the Earth and the Moon. (Assume a radial direction r̂ from the Earth to the Moon. Express your answer in vector form.)
g =
N/kg


(b) An asteroid of mass 6.16 ✕ 1015 kg is at the point exactly halfway between the Earth and the Moon. What is the magnitude of the gravitational force on it?

3 answers

exactly half way? zero, there is no net force either. Remember E is a vector, and is pointing in the direction of the mass. for halfway between, the E's add to zero.

b. hmmmm, just answered.
Because earth is far more massive than moon, net force would be toward earth.
if d = distance to earth and distance to moon (in other words d = distance between/2)
ME = mass earth and MM = mass moon
F/m = G(ME/d^2 - MM/d^2) = (G/d^2)(ME-MM)
a=-.0107r
b=.0107*6.16*10^15=6.59*10^13