You are asked to design a planet of mass M and uniform density p such that it has the maximum possible acceleration due to gravity g at a point on its surface.

Find the shape of this planet, and then find g.

Take G as the universal gravitational constant.

I was not able to solve this myself. While I recalled that the "calculus of variations", e.g., the use of Lagrange Multipliers, is often used for such optimizations, I had forgotten how they worked. That is given here. 

Edited on January 10, 2019, 1:28 am

Posted by Steven Lord on 2019-01-04 21:46:05