Unizor - Physics4Teens - Energy - Gravitational Field - Problems
Channel: Zor Shekhtman on UNIZOR Education
Date: 17/09/2019

Unizor - Physics through a Looking Glass of Mathematician

Problems on Gravitational Energy

Problem 1
Gravitational potential of a spherical gravitational field around a point-mass M at a distance r from it is defined as the work performed by gravity to bring a probe object of a unit mass from infinity to this point and is expressed as
Vr = −G·M /r
Why is this formula independent of trajectory of a probe object or its exact final position relative to the point-mass M, but only on a distance itself from the source of gravity?

Problem 2
Given two point-masses of mass M each, fixed at a distance 2R from each other.
Prove that the gravitational potential of a gravitational field produced by both of them at each point on a perpendicular bisector between them equals to a sum of individual gravitational potentials of these point-masses at this point, as if they were the only source of gravitation. In other words, prove that gravitational potential is additive in this case.

Problem 3
Express mass M of a spherical planet in terms of its radius R and a free fall acceleration g on its surface.

Problem 4
Express gravitational potential VR of a spherical planet on its surface in terms of its radius R and a free fall acceleration g on its surface.