Akarsh Simha
An elementary proof of Kepler's first law, i.e. that bounded planetary orbits are elliptical, is derived without the use of calculus. The proof is similar in spirit to previous derivations, in that conservation laws are used to obtain an expression for the planetary orbit, which is then compared against an equation for the ellipse. However, we derive the equation that we match against, using trigonometry, from two well-known properties of the ellipse. Calculus is avoided altogether.
Comments: 7 pages, 2 figures
Journal reference: American Journal of Physics 89.11 (2021): 1009-1011
Comment on "An algebra and trigonometry-based proof of Kepler's first law" by Akarsh Simha: https://arxiv.org/abs/2111.11938
Manfred Bucher
The recent non-calculus proof of Kepler's first law succeeds because of an obscure, but valid property of the ellipse.
Comments: 3 pages
Поход по ссылкам показал, что этим баловался даже сам Унру:
Kepler's laws without calculus: https://arxiv.org/abs/1803.06770
William G Unruh
Kepler's laws are derived from the inverse square law without the use of calculus and are simplified over previous such derivations.
Comments: 11pages 3 figures --second version adds polygonal solution to equations. Third version cleans up the derivation of the polygonal ellipse
Впрочем, это я уже постил:)) По теме см. также тут.
И еще на ту же тему, но здесь, скорее, передирание Ландафшица без ссылок:
Elementary Solution of Kepler Problem (and a few other problems): https://arxiv.org/abs/2112.09064
M. Moriconi
We present a simple method to obtain the solution of a few orbital problems: the Kepler problem, the modified Kepler problem by the addition of an inverse square potential and linear force.
Comments: To appear in Revista Braileira de Ensino de Física