Relativity Science Calculator - Proof: Kepler's 3rd ( Harmonic ) Law

Proof: Kepler's 3rd ( Harmonic ) Law

( Or, how to derive Kepler's 3rd Law from the 2nd? )

"Geometry, which before the origin of things was coeternal with the divine mind and is God himself (for what could there be in God which would not be God himself?), supplied God with patterns for the creation of the world, and passed over to Man along with the image of God." - Johannes Kepler ( 1571 - 1630 )

relativity approximations

circular planetary orbital motion

universal planetary constant by Henry Cavendish in 1797centripetal acceleration for circular planetary orbital motion

circular planetary orbital motion - again

elliptical planetary orbital motion

semi-minor axis of planetary elliptical motionKepler's 2nd Law: Equal Areas in Equal Timessemi-major axis, semi-minor axis of the ellipseconstant angular momentum, semi-major axis of the ellipse

§ References:

  1. "Kepler's Laws - The equation of motion", Horst Knörrer, ETH Zürich - Eidgenössische Technische Hochschule Zürich ( Swiss Federal Institute of Technology Zürich ), Department of Mathematics