Affording a Planet With Geometry

Which planet shape maximizes gravity at a given point? A guide for purchasing a personal Earth. 🌍 I first heard this puzzle from Drake Thomas at an interview for the Atlas fellowship. It also appears in the following: • ~kantor/QUIZ/02/. • For a continuation, consider the optimal shape in other dimensions! I suggest starting in 2D. 00:00 - Backstory 01:57 - The task ahead 03:08 - “Underneathness“ 04:01 - A long list 06:26 - Sweet symmetry 07:29 - Newton to the rescue 08:36 - Grand finale 10:15 - Hang on!