Question

A 31500-kg spaceship is halfway between the Earth and the Moon. Find the net gravitational force (in Newtons) of attraction exerted on the ship by the Earth and the Moon. (Given: Earth-moon distance = 3.84 x 108 m)
Moon
mass (kg): 7.36 x 10^22
radius (m): 1.74 x 10^6
Earth
mass (kg): 5.98 x 10^24
radius (m): 6.38 x 10^6

Answer 1

The magnitude of the net gravitational force will be the force exerted by the earth minus that exerted by the moon. The formula for the gravitational force is:
\[F=\frac{ GMm }{ r ^{2} }\] where G is the gravitational constant (6.67×10^-11 N·(m/kg)^2), M is the mass of the earth or moon depending on which force you are calculating, m is the mass of the spaceship, and r is the distance from the spaceship to the center of the body (mass or earth) that you are looking at.

Answer 2

Thanks for your response, I do appreciate it very much. However, the area in which I am finding trouble is not in the formula, it is in the calculation of the Net force from the pull of the two planets.

Answer 3

The force from the moon is "positive" and uses the moon mass and the spaceship mass. The force from the earth is "negative" and uses the spaceship mass and the earth's mass. The net force is the difference between these two, once you have calculated them individually.

Answer 4

The two forces actually lie along the same line in this problem; the force of the moon's gravity pulls the ship towards the moon, and the force of the Earth's gravity pulls the space ship towards the Earth. Since they're exactly opposite in direction you can just add them together ( like @douglaswinlowcooper said), knowing that (in this picture) the force of the moon points in the negative direction and the force of the earth pulls in the positive direction

So with normal direction conventions
\[\sum F = F_{g \ E}-F_{g \ M}=F_{Net}\]

So in this instance, if the net force is positive, the space ship is being pulled towards the Earth, and if it's negative the spaceship is being pulled towards the moon.