Kepler's Laws as Properties of the Kinematic Equations of Motion of a Point Along Second-Order Curves
Abstract
Johannes Kepler empirically established three laws of celestial mechanics. In the scientific literature, Kepler’s laws are usually derived using dynamical variables. This paper shows that Kepler’s laws are consequences of the kinematic equations of an ellipse. The derivation of the formulas is carried out for two variants of the motion of a mathematical point: relative to the focus and relative to the center of the ellipse. Numerical examples are presented.
Fields of Study & Subjects
Historical Geography and Cartography
Experimental and Theoretical Physics Studies
Historical Astronomy and Related Studies
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 4 January 2026
- Document type
- Preprint