Gravitational potential The gravitational force between two point masses M and m is
where G is the gravitational constant.
a. Verify that this force field is conservative on any region excluding the origin.
b. Find a potential function φ for this force field such that F = –▿φ.
c. Suppose the object with mass m is moved from a point A to a point B, where A is a distance r1 from M and B is a distance r2, from M. Show that the work done in moving the object is
d. Does the work depend on the path between A and B? Explain.
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