a) At what distance from the center of the earth along a line from the earth to

Question

a) At what distance from the center of the earth along a line from the earth to the moon is there no net force on a 10,000 kg spacecraft? This is the crossover point at which the attraction to the moon becomes larger than the attraction to the earth.

b) The graviational potential energy is the sum of the potential energies with respect to the earth and the moon. Calculate the potential energy of the spacecraft at several points between the surface of the earth and the surface of the moon. Then draw a reasonable graph showing the potential energy from the earth to the moon.

Explanation / Answer

a)

distance between earth and moon,d = 3.84*10^8 m

Let the point be at x meters from earth

Force of attraction due to moon at that point ,

Fm = G*m*Mm/(d-x)^2

where Mm = mass of moon = 7.35*10^22 kg

and force due to earth , Fe = G*m*Me/(x)^2

So, for net force, Fe = Fm

So, G*m*Mm/(d-x)^2 = G*m*Me/(x)^2

So, 7.35*10^22/(3.84*10^8 - x)^2 = 6*10^24/x^2

So, x = 3.45*10^8 m <----------answer

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