Consider the earth's radius to be 6.40x103km, its mass to be 6.00x1024kg, the Moon's mass to be 7.36x1022kg, and the Moon's radius to be 1.74x103km. The average value for the Earth-Moon distance is 3.84x105kg. Neglect friction and rotation.
a. Sketch the potential energy as a function of the position on a line between the Earth's centre and the Moon's centre, for positions between the surfaces of the two bodies (ignore positions inside the bodies).
b. Find the position where the potential has an extremum (maximum or minimum) between the Earth and the Moon. Find the gravitational force on a test particle of mass m at that location.
c. Calculate the minimum work required to transport a mass of 1.0kg from the surface of the Earth to the surface of the moon, ignoring air resistance.
The Attempt at a Solution
I'm not sure on how to start with this problem. I don't know how i should graph the potential energy as a function of the position on a line (firstly, how can we find the potential energy in a point between two masses? Calculate both potential energies with respect to the Moon and Earth at that point?). As well, how can we calculate the work required to transport the mass? I tried finding the difference in potential energy between a point in the surface to a point in the Moon, but it doesn't work (answer is 58.7 MJ).
Thank you in advance.