TITLE:
A Hysteretic Description of Non-Kepler’s Orbit in Two-Body Celestial Mechanics
AUTHORS:
Tardad Ulaanbaatar
KEYWORDS:
Celestial Mechanics, Orbital Mechanics, Kepler’s Laws, Wave Function, Planetary Motion
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
13,
2025
ABSTRACT: Tycho Brahe was known for his comprehensive and remarkably accurate astronomical observations, and was considered one of the greatest astronomers before the invention of the telescope. However, Johannes Kepler, using conic sections, formulated three laws of planetary motion based on Tycho’s observations. The formulas for circles and ellipses thus derived, and the traditional formula for ellipses based on a single focus of an elliptical orbit, were impractical and led to large and small errors. Because astronomy at that time was based on observations and mathematical formulas derived from them, these laws are still considered valid today. Unfortunately, Kepler’s laws are not really “laws” of the laws of physics, but rather trends that Kepler noticed and calculated using astronomical observations of the planets. This paper describes the eccentricity, amplitude, phase shift, angular momentum, polarization, radial path, and orbital energy of two-body orbital mechanics simultaneously, and then presents a wave function formula that avoids the above-mentioned difficulties. The results are in good agreement with the observational data. This paper contains 26 new equations and 11 figures, and it is hoped that the findings and results will contribute to the progress of the theory of celestial mechanics.