Research Article | Open Access
Lorenzo Iorio, "The Effect of General Relativity on Hyperbolic Orbits and Its Application to the Flyby Anomaly", Scholarly Research Exchange, vol. 2009, Article ID 807695, 8 pages, 2009. https://doi.org/10.3814/2009/807695
The Effect of General Relativity on Hyperbolic Orbits and Its Application to the Flyby Anomaly
We investigate the impact of the general relativistic gravitoelectromagnetic forces on hyperbolic orbits around a massive spinning body. The gravitomagnetic field, causing 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 gravitoelectric 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 , radial and transverse components and of the velocity, and speed 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 of mm ; while the gravitoelectric force was modeled in the software used to process the NEAR data, this was not done for the gravitomagnetic one. The range rate and the speed are affected by general relativistic gravitoelectromagnetism at (gravitoelectric) to (gravitomagnetic) mm levels. The changes in the range are of the order of (gravitomagnetic) to (gravitoelectric) mm.
- B. Mashhoon, “Gravitoelectromagnetism: a brief review,” in The Measurement of Gravitomagnetism: A Challenging Enterprise, L. Iorio, Ed., pp. 29–39, NOVA, Hauppauge, NY, USA, 2007.
- J. D. Anderson, J. K. Campbell, and M. M. Nieto, “The energy transfer process in planetary flybys,” New Astronomy, vol. 12, no. 5, pp. 383–397, 2007.
- J. D. Anderson, J. K. Campbell, J. E. Ekelund, J. Ellis, and J. F. Jordan, “Anomalous orbital-energy changes observed during spacecraft flybys of earth,” Physical Review Letters, vol. 100, no. 9, Article ID 091102, 4 pages, 2008.
- A. E. Roy, Orbital Motion, Institute of Physics, Bristol, UK, 4th edition, 2005.
- H. I. M. Lichtenegger and L. Iorio, “Post-Newtonian orbital perturbations,” in The Measurement of Gravitomagnetism: A Challenging Enterprise, L. Iorio, Ed., pp. 87–100, NOVA, Hauppauge, NY, USA, 2007.
- J. Lense and H. Thirring, “Über den Einfluss der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie,” Physikalische Zeitschrift, vol. 19, pp. 156–163, 1918.
- B. Mashhoon, F. W. Hehl, and D. S. Theiss, “On the gravitational effects of rotating masses: the Thirring-Lense papers,” General Relativity and Gravitation, vol. 16, no. 8, pp. 711–750, 1984.
- B. Mashhoon, F. W. Hehl, and D. S. Theiss, “On the gravitational effects of rotating masses: the Thirring-Lense papers,” in Nonlinear Gravitodynamics, R. J. Ruffini and C. Sigismondi, Eds., pp. 349–388, World Scientific, Singapore, 2003.
- L. Iorio, Ed., The Measurement of Gravitomagnetism: A Challenging Enterprise, L. Iorio, Ed., NOVA, Hauppauge, NY, USA, 2007.
- M. Soffel, Relativity in Astrometry, Celestial Mechanics and Geodesy, Springer, Berlin, Germany, 1989.
- G. A. Flandro, “Fast reconnaissance missions to the outer solar system utilizing energy derived from the gravitational field of Jupiter,” Astronautica Acta, vol. 12, no. 4, pp. 329–337, 1966.
- J. A. van Allen, “Gravitational assist in celestial mechanics—a tutorial,” American Journal of Physics, vol. 71, no. 5, pp. 448–451, 2003.
- C. Lämmerzahl, O. Preuss, and H. Dittus, “Is the physics within the solar system really understood?,” in Lasers, Clocks and Drag Free Control: Exploration of Relativistic Gravity in Space, H. Dittus, C. Lämmerzahl, and S. G. Turyshev, Eds., pp. 75–104, Springer, Berlin, Germany, 2008.
- J. P. Mbelek, “Special relativity may account for the spacecraft flyby anomalies,” http://arxiv.org/abs/0809.1888.
- M. E. McCulloch, “Modelling the flyby anomalies using a modification of inertia,” Monthly Notices of the Royal Astronomical Society: Letters, vol. 389, no. 1, pp. L57–L60, 2008.
Copyright © 2009 Lorenzo Iorio. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.