At a certain instant, the earth, the moon, and a stationary 1250kg spacecraft li

Question

At a certain instant, the earth, the moon, and a stationary 1250kg spacecraft lie at the vertices of an equilateral triangle whose sides are 3.84*10^5 km in length.

Find the magnitude of the net gravitational force exerted on the spacecraft by the earth and moon. Answer in Newtons.

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. Answer in degrees

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. Answer in Joules.

Please show all work and answer.

Explanation / Answer

The change in energy = work U = -GMm/a When the satellite is really far away, the kinetic and potential energies = 0 So add the potential between the satellite and the earth, then the satellite and the moon.

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