I have been trying to calculate the time it takes for an object of negligible mass to free fall towards an object with a large mass, taking into account that the gravitational acceleration experienced by the small object increases as it moves closer to the big object.(adsbygoogle = window.adsbygoogle || []).push({});

The first thing I tried was setting up a diffeq:

n''=GM/(h-n)^2

Where G is the gravitational constant, M is the mass of the object, h is the initial height, n is the distance traveled, and ' denotes a derivative. After trying for a few days to solve this equation for n(as a function of t, time), I gave up and tried to solve it using change in kinetic energy, which also didn't work. Any ideas? Thanks.

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# Time for freefall in a varying gravitational field?

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