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'Sweeping Satellite' printed from https://nrich.maths.org/
Hint 1: Gravitational potential energy is the integral of the
gravitational force, and evaluates to a negative number,
theoretically being zero when infinitely far away.
Hint 2: In the Newtonian gravitational field equation, it can be
shown that $GM = gR^2$. That assumes a spherical body of
course.