[math-fun] "Kepler's Law" for Somsky Planets

"Kepler's Law" for Somsky Planets =========Warren D Smith===Aug 2015===== Probably everybody knew this, but it is worth saying explicitly. If you have a sun of radius S, and antisun (outer ring) of radius R, and their two centers are separated by some fixed distance D, then the locations of all the planet centers lie on an ELLIPSE with foci being the sun and antisun centers. PROOF: For a planet of radius P, the distance from a planet center to sun center is S+P, the distance from planet center to ring center is R-P, hence this distance sum is S+P+R-P=S+R=constant independent of P. That law describes the ellipse. QED -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)