http://arxiv.org/abs/1407.5022
It is known that, in the weak-field and slow-motion approximation of general relativity, the stationary component of the gravitational field of a rotating body, proportional to its angular momentum, is able to discriminate between the opposite directions of motion of a pair of counter-orbiting tests particles moving along geometrically identical paths: it is the so-called gravitomagnetic clock effect. In this paper, we show that, to the first post-Newtonian level, there is also a gravitolectric clock effect induced by the static component of the gravitational field of a non-rotating body. Indeed, the difference of the draconitic periods of two test particles moving in opposite directions along identical quasi-circular orbits turns out to be non-vanishing. It depends on the shape, the size and the pericenter location of the orbit, but it is independent of the initial position along it. On the contrary, the gravitoelectric corrections to the anomalistic periods turn out to be the same for both prograde and retrograde orbital motions. For a hypothetical pair of Earth satellites in Supertundra-like orbits, the gravitoelectric draconitic clock effect could be as large as 46 $\mu$s, while a Juno-like orbital configuration around Jupiter would allow to reach about $0.01$ s.
L. Iorio
Mon, 21 Jul 14
33/55
Comments: LaTex2e, 12 pages, no figures, no tables, 15 references
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