# Analysis of Earth, Moon and Spacecraft system (gravity)

At a certain instant, the earth, the moon, and a stationary 1470 kg spacecraft lie at the vertices of an equilateral triangle whose sides are 3.84 x 10^5 km in length.

a) Find the magnitude of the net gravitational force exerted on the spacecraft by the earth and moon. Find in N.

b) Find the direction of the net gravitational force exerted on the spacecraft by the earth and moon. State the direction as an angle measured from a line connecting the earth and the spacecraft. (in degrees)

c) What is the minimum amount of work that you would have to do to move the spacecraft to a point far from the earth and moon? You can ignore any gravitational effects due to the other planets or the sun. (in J)

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#### Solution Preview

See attached file.

First draw a diagram of the physical situation

Change distance R to be in metres so R = 3.84 x 108 m

Work out the gravitational pull of the Earth on the spacecraft

Earth Mass ME = 5.96 x 1024 Kg

Mass of spacecraft m = 1470 Kg

Gravitational force exerted by Earth on spacecraft is given by

FS-E = G.MEm/R^2

G = 6.674 x 10^-11 N(M/Kg)2

FS-E = 6.674 x 10^-11 x 5.96 x 10^24 x 1.47 x 10^3 /{3.84 x 10^8}^2 N

FS-E = 3.9654 N directed from S TO E

Moon Mass MM = 7.35 x 10^22 Kg

Gravitational force exerted by the Moon on the ...

#### Solution Summary

A 3 point system is analysed consisting of the Earth, Moon and Spacecraft and the gravitational forces (magnitude & direction) experienced on the spacecraft due to the Moon and the Earth are determined from the geometry. The amount of work required to move the spacecraft an infinite distance away from the Earth/Moon system is then determined