WSEAS Transactions on Applied and Theoretical Mechanics
Print ISSN: 1991-8747, E-ISSN: 2224-3429
Volume 20, 2025
When the Future Perfectly Reflects the Past in Celestial Mechanics
Authors: , ,
Abstract: Newton’s equations of celestial mechanics for the N-body problem possess a continuum of solutions
in which the future trajectories are a perfect reflection of their past. These solutions evolve from zero initial
velocities of the N bodies. Consequently, the future gravitational forces acting on the N bodies are also a perfect
reflection of their past. The proof is carried out via Taylor series expansions.