Recently, on Reddit (of course), someone posted a video talking about how long it would take to fall straight through the center of the earth to the other side. One of the nice parts of the video is that it shows you what the time would be when we account for the actual, non-uniform density of the earth. The video just showed an Excel sheet, though.
I recommend you watch the linked video so you have a good visual of the problem. Once you’ve done that, come on back! In this post I’m going to show you how to solve the problem using Python and a numerical integrator from SciPy.