The effect of general relativity on hyperbolic orbits and its application to the flyby anomaly

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

Scientific paper

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LaTex2e, 23 pages, 15 figures, 1 table, 15 references. To appear in Scholarly Research Exchange (SYREXE). I thank the referees

Scientific paper

10.3814/2009/807695

We investigate qualitatively and quantitatively the impact of the general relativistic gravito-electromagnetic forces on hyperbolic orbits around a massive spinning body. The gravito-magnetic field, which is the cause of the well known Lense-Thirring precessions of elliptic orbits, is generated by the spin S of the central body. It deflects and displaces the trajectories differently according to the mutual orientation of S and the orbital angular momentum L of the test particle. The gravito-electric force, which induces the Einstein precession of the perihelion of the orbit of Mercury, always deflects the trajectories inward irrespective of the L-S orientation. We numerically compute their effect on the range r, radial and transverse components v_r and v_\tau of the velocity and speed v of the NEAR spacecraft at its closest approach with the Earth in January 1998 when it experienced an anomalous increase of its asymptotic outgoing velocity v_\infty o of 13.46 +/- 0.01 mm sec^-1; while the gravito-electric force was modeled in the software used to process the NEAR data, this was not done for the gravito-magnetic one. The range-rate and the speed are affected by general relativistic gravito-electromagnetism at 10^-2 (gravito-electric)-10^-5 (gravito-magnetic) mm sec^-1 level. The changes in the range are of the order of 10^-2 (gravito-magnetic)-10^1 (gravito-electric) mm.

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