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I'm trying to automate a landing at a specific spot in Kerbal Space Program and to do that I need to know when the estimated time of impact will be. In short, I'm trying to solve the following question:
Given a planet without an atmosphere with a gravitational parameter $\mu$, radius $r$ and an object with mass $m$, an initial velocity of $v=0$ and a distance $d$ between their centers, what will be the time of impact?
An example: Given a spherical earth without an atmosphere and a brick at an altitude of $100.000$km, how long after release will the brick hit the surface?
I've tried using conservation of energy but that left me with a differential equation I'm unable to solve: http://mathb.in/45230