Where in The Principia...?

Question

I know the planets are round because of gravity. Does anyone know where in The Principia Isaac Newton makes that argument? I have the book and have read through it, but I can't remember. If anyone knows what Book and section, I'd appreciate it. Thanks.

Answer 1

I'm not sure Newton ever made that arguement.... I thought it was in the 1800's... Um... I can't remember his name... Lewis?  Langstrom?  I *think* the theory that a sphere is the least-energetic body of mass was put forth in the 1880's... I'll see if I can find it.

Answer 2

I believe that in the Principia Newton's Keplerian model of the solar system was an idealization that used the assumption that the sun and the planets are uniformly spherical.  I don't think he derived it.