Post-Keplerian perturbations of the hyperbolic motion in the field of a rotating massive object. Analysis in terms of osculating and nonosculating (contact) elements

Abstract

The perturbations of the hyperbolic motion of a test particle due to the general relativistic gravitoelectromagnetic Schwarzschild and Lense-Thirring components of the gravitational field of a rotating massive body are analytically worked out to the first post-Newtonian level in terms of the osculating Keplerian orbital elements. To the Newtonian order, the impact of the quadrupole mass moment of the source is calculated as well. The resulting analytical expressions are valid for a generic orientation in space of both the orbital plane of the probe and the spin axis of the primary, and for arbitrary values of the eccentricity. They are applied to 'Oumuamua, an interstellar asteroid which recently visited our solar system along an unbound heliocentric orbit, and to the Near Earth Asteroid Rendezvous (NEAR) spacecraft during its flyby of the Earth. The calculational approach developed can be straightforwardly extended to any alternative models of gravity as well.

LaTex2e, 22 pages, 5 tables, no figures. Accepted for publication in The Astrophysical Journal. Typo corrected in Equation (34)

References in corpus (10)

• An Update on Monitoring Stellar Orbits in the Galactic Center
• Initial characterization of interstellar comet 2I/Borisov
• Kinematics of the old stellar population at the Galactic Center
• The Energy Transfer Process in Planetary Flybys
• Geodesic motion in Euclidean Schwarzschild geometry
• Acceleration of 1I/`Oumuamua from radiolytically produced H${}_2$ in H${}_2$O ice
• Gravitational Radiation from hyperbolic encounters in the presence of dark matter
• A complete characterisation of the orbital shapes of the non-circular Kerr geodesic solutions with circular orbit constants of motion
• Updated values of solar gravitational moments $J_{2n}$ using HMI helioseismic inference of internal rotation
• Analysis of the PPN Two-Body Problem Using Non-Osculating Orbital Elements

Cited by in corpus (1)

• Estimating the strength of Lorentzian distribution in non-commutative geometry by solar system tests