3-Body Problems, Hidden Constants, Trojans and WIMPs
We present a new celestial mechanics for wimps in gravitational systems as well as new results for classical problems.
This work includes two new results-principally two new constants of motionfor 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 systemslike that of the trojans.
The latter result uses a generalisation of our semi-classical mechanics for schr\"odinger 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.