1. Yes. Gravitational force of earth longer than gravitational force of moon.
2. Expression for gravitational P.
Consider the earth as a uniform sphere of radius R and mass M. Consider a point A at distance ‘r’ from the center of earth. P is another point at a distance ‘x’ from O. Q lies at distance dx from P.
By definition, the gravitational potential energy of the body at point A, is the work done in bringing the body of mass ‘m’ from infinity to that point A The gravitational force on the body at the point P.
is given by F = \(\frac{GMm}{x^2}\).
If the body is displaced from P to Q Work done, dw = F.dx
=\(\frac{GMm}{x^2}\) Therefore, workdone in bringing the body from infinity to the point A,
Since this workdone is stored inside the body as its gravitational potential energy, the gravitational potential energy (U) of a body of mass m at distance r from the center of the earth is given by,
U = \(\frac{-GMm}{r}\)
The gravitational potential energy of a body at a point is defined as the amount of workdone in bringing the body from infinity to that point without acceleration.
3. There is no atmosphere on the moon. Hence we can see the foot steps of Neil Armstrong.
