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Statement of a problem № 3303

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Two bodies of mass m and M are initially at rest in an inertial reference frame at a great distance apart. They start moving towards each other under gravitational attraction. Show that as they approach a distance d apart (d << r), their relative velocity of approach will be sqrt(2G(M+m)/d)constant, where G is the gravitational constant.

Solution:
Two bodies of mass m and M are initially at rest in an inertial reference frame

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