Question

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?

Answer 1

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.

Answer 2

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)

Answer 3

a=-.0107r
b=.0107*6.16*10^15=6.59*10^13