what is the path of a projectile over a flat surface but where the strength of gravity (magically) decreases with height according to the inverse square law? there is some depth, deep underground, which represents absolute zero height. (normally, if the earth is flat, gravity is uniform, unchanging with height.)
is there conservation of energy? if not, what is conserved by Noether's Theorem?
perhaps not too exciting: the path is simply a plot of height versus time in spherically symmetric Newtonian gravitational field for a projectile fired straight up, a degenerate conic section. probably need to solve the Kepler Equation.
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