What was the magnitude of the net gravitational force (in N) on Apollo 11 (mass 3.01 ✕ 104 kg) when it was halfway in its journey between Earth and the Moon?

Question

Take the distance between Earth and the Moon as 3.84 ✕ 105 km.

Consider that the shuttle is moving in the direction from Earth to the Moon.

Answer 1

M₁ = mass of earth (look it up in your physics book)

M₂ = mass of moon (look it up in your physics book)

m = mass of vehicle (given)

r = distance from earth to vehicle = distance from moon to vehicle = (1/2)(3.84 ✕ 10⁵ km) = (1/2)(3.84 ✕ 10⁸ m)

G = constant of universal gravitation (look it up in your physics book)

 

The magnitude of the net gravitational force is

 

F_net = GM₁m/r² - GM₂m/r² = (Gm/r²)(M₁ - M₂)

 

It points toward the earth.  The direction of travel does not matter in this problem; the force is determined by position only.  Plug in the numbers and get your answer.