2022/09/21 by Aubrey Truman, Truman, Aubrey, Richard Durran +1
Physics and Astronomy · #70F07 70F05 70F15 35Q40 #Astrophysics of Galaxies (astro-ph.GA) #Cosmology and Gravitation Theories #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Pulsars and Gravitational Waves Research
paper · pdf · doi:10.48550/arxiv.2209.10600
openalex publication_date 2022/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work includes two new results - principally two new constants of motion for the linearised restricted 3-body problem (e.g. for the Trojan asteroids) and an important isosceles triangle generalisation of Lagrange's equilateral triangle solution of the restricted case leading to hidden constants for Hildans as well as Trojans. Both of these results are classical, but we also have included new results on Newtonian quantum gravity emanating from the asymptotics relevant for WIMPish particles, explaining the origin of systems like that of the Trojans. The latter result uses a generalisation of our semi-classical mechanics for Schrödinger equations involving vector as well as scalar potentials, presented here for the first time, thereby providing an acid test of our ideas in predicting the quantum curvature and torsion of WIMPish trajectories for our astronomical elliptic states. The combined effect is to give a new celestial mechanics for WIMPs in gravitational systems as well as new results for classical problems. As we shall explain, we believe these results could help to see how spiral galaxies evolve into elliptical ones. A simple classical consequence of our isosceles triangle result gives a Keplerian type 4^\textrmth Law for 3-body problems. This is confined to the Appendix.