> We assume the hole is small compared to the size of the earth, and the package
light compared to the mass of the earth, so we can neglect h and m.<p>If you're going to write a paper that builds intuition, you should write one on this problem. Physicists always make magical simplifying assumptions that drive me absolutely bananas. And wow! Things get so much simpler but are still correct to an order of magnitude.<p>The same thing they do when gathering / discarding possible factors.<p>I actually suspect this is revisionist. Most folks would probably start with various factors / powers and guess-and-check until some of those factors have zero power and the dimensions work out.<p>Relevant XKCD:
<a href="https://www.explainxkcd.com/wiki/index.php/793:_Physicists" rel="nofollow">https://www.explainxkcd.com/wiki/index.php/793:_Physicists</a>