Classical interpretations of relativistic precessions

Relativists have exposed various precessions and developed ingenious experiments to verify those phenomena with extreme precisions. The Gravity Probe B mission was designed to study the precessions of the gyroscopes rotating round the Earth in a nearly circular near-Earth polar orbit to demonstrate the geodetic effect and the Lense-Thirring effect as predicted by the general relativity theory. In this paper, we show in a very simple and novel analysis that the precession of the perihelion of Mercury, the Thomas precession, and the precession data （on the de Sitter and Lense-Thirring precessions） collected from the Gravity Probe B mission could easily be explained from classical physics, too.

Coupling Between Spin and Gravitational Field and Equation of Motion of Spin

In general relativity, the equation of motion of the spin is given by the equation of parallel transport, which is a result of the space-time geometry. Any result of the space-time geometry cannog be directly applied to gauge theory of gravity. In gauge theory of gravity, based on the viewpoint of the coupling between the spin and gravitational field, an equation of motlon of the spin is deduced. In the post Newtonian approximation, it is proved that this equation gives the same result as that of the equation of parallel transport. So, in the post Newtonian approximation, gauge theory of gravity gives out the same prediction on the precession of orbiting gyroscope as that of general relativity.

Classical Dynamics of Muonic-Electronic Helium and Heliumlike Ions: The Allowance for the Eccentricity of the Muon and Nucleus Orbits

In the previous paper by one of us (hereafter paper I), the author considered Rydberg states of the muonic-electronic helium atom or helium-like ion and used the fact that the muon motion occurs much more rapidly than the electron motion. Assuming that the muon and nucleus orbits are circular, he applied the analytical method based on separating rapid and slow subsystems. He showed that the electron moves in an effective potential that is mathematically equivalent to the potential of a satellite orbiting an oblate planet like the Earth. He also showed that the “unperturbed” elliptical orbit of the electron engages in two precessions simultaneously: the precession of the electron orbit in the plane of the orbit and the precession of the orbital plane of the electron around the axis perpendicular to the plane of the muon and nuclear orbits. The problem remained whether or not the allowance for the ellipticity of the orbit could significantly change the results. In the present paper, we address this problem: we study how the allowance for a relatively low eccentricity ε of the muon and nucleus orbits affects the motion of the electron. We derive an additional, ε-dependent term in the effective potential for the motion of the electron. We show analytically that in the particular case of the planar geometry (where the electron orbit is in the plane of the muon and nucleus orbits), it leads to an additional contribution to the frequency of the precession of the electron orbit. We demonstrate that this additional, ε-depen- dent contribution to the precession frequency of the electron orbit can reach the same order of magnitude as the primary, ε-independent contribution to the precession frequency. Therefore, the results of our paper seem to be important not only qualitatively, but also quantitatively.

Periapsis shift in spherically symmetric spacetimes and effects of electric interactions

The periapsis shift of charged test particles in arbitrary static and spherically symmetric charged spacetimes are studied.Two perturbative methods,the near-circular approximation and post-Newtonian methods,are developed and shown to be very accurate when the results are determined to high orders.The near-circular approximation method is more precise when eccentricity e of the orbit is small,whereas the post-Newtonian method is more effective when orbit semilatus rectum p is large.Results from these two methods are shown to agree when both e is small and p is large.These results are then applied to the Reissner-Nordström spacetime,the Einstein-Maxwell-dilation gravity,and a charged wormhole spacetime.The effects of various parameters on the periapsis shift,particularly that of the electrostatic interaction,are carefully studied.The periapsis shift data of the solar-Mercury are then used to constrain the charges of the Sun and Mercury,and the data of the Sgr A^(*)-S2 periapsis shift are used to determine,for the first time using this method,the constraints of the charges of Sgr A^(*)and S2.