Papers by Bahram Mashhoon
The Pioneer 10 and 11 spacecraft yielded the most precise navigation in deep space to date. These... more The Pioneer 10 and 11 spacecraft yielded the most precise navigation in deep space to date. These spacecraft had exceptional acceleration sensitivity. However, analysis of their radio-metric tracking data has consistently indicated that at heliocentric distances of ∼20-70 astronomical units, the orbit determinations indicated the presence of a small, anomalous, Doppler frequency drift. The drift is a blue-shift, uniformly changing with a rate of ∼ (5.99 ± 0.01) × 10 −9 Hz/s, which can be interpreted as a constant sunward acceleration of each particular spacecraft of a P = (8.74 ± 1.33) × 10 −
We define the general Hill system and briefly analyze its dynamical behavior. A particular Hill s... more We define the general Hill system and briefly analyze its dynamical behavior. A particular Hill system representing the interaction of a Keplerian binary system with a normally incident circularly polarized gravitational wave is discussed in detail. In this case, we compute the Poincaré-Melnikov function explicitly and determine its zeros. Moreover, we provide numerical evidence in favor of chaos in this system. The partially averaged equations for the Hill system are used to predict the regular behavior of the Keplerian orbit at resonance with the external radiation.
Journal of Physics A: Mathematical and General, 2000
The general phenomena associated with sustained resonance are studied in this paper in connection... more The general phenomena associated with sustained resonance are studied in this paper in connection with relativistic binary pulsars. We represent such a system by two point masses in a Keplerian binary system that evolves via gravitational radiation damping as well as an external tidal perturbation. For further simplification, we assume that the external tidal perturbation is caused by a normally incident circularly polarized monochromatic gravitational wave. In this case, the second-order partially averaged equations are studied and a theorem of C. Robinson is employed to prove that for certain values of the physical parameters resonance capture followed by sustained resonance is possible in the averaged system. We conjecture that sustained resonance can occur in the physical system when the perturbing influences nearly balance each other.
Classical and Quantum Gravity, 1997
The long term nonlinear dynamics of a Keplerian binary system under the combined influences of gr... more The long term nonlinear dynamics of a Keplerian binary system under the combined influences of gravitational radiation damping and external tidal perturbations is analyzed. Gravitational radiation reaction leads the binary system towards eventual collapse, while the external periodic perturbations could lead to the ionization of the system via Arnold diffusion. When these two opposing tendencies nearly balance each other, interesting chaotic behavior occurs that is briefly studied in this paper. It is possible to show that periodic orbits can exist in this system for sufficiently small damping. Moreover, we employ the method of averaging to investigate the phenomenon of capture into resonance.
Classical and Quantum Gravity, 1999
The long-term dynamical evolution of a Keplerian binary orbit due to the emission and absorption ... more The long-term dynamical evolution of a Keplerian binary orbit due to the emission and absorption of gravitational radiation is investigated. This work extends our previous results on transient chaos in the planar case to the three dimensional Kepler system. Specifically, we consider the nonlinear evolution of the relative orbit due to gravitational radiation damping as well as external gravitational radiation that is obliquely incident on the initial orbital plane. The variation of orbital inclination, especially during resonance capture, turns out to be very sensitive to the initial conditions. Moreover, we discuss the novel phenomenon of chaotic transition.
Classical and Quantum Gravity, 1997
The method of averaging is used to investigate the phenomenon of capture into resonance for a mod... more The method of averaging is used to investigate the phenomenon of capture into resonance for a model that describes a Keplerian binary system influenced by radiation damping and external normally incident periodic gravitational radiation. The dynamical evolution of the binary orbit while trapped in resonance is elucidated using the second order partially averaged system. This method provides a theoretical framework that can be used to explain the main evolutionary dynamics of a physical system that has been trapped in resonance.
The long term perturbation of a Newtonian binary system by an incident gravitational wave is disc... more The long term perturbation of a Newtonian binary system by an incident gravitational wave is discussed in connection with the issue of gravitational ionization. The periodic orbits of the planar tidal equation are investigated and the conditions for their existence are presented. The possibility of ionization of a Keplerian orbit via gravitational radiation is discussed.
Journal of Mathematical Physics, 1996
The gravitational ionization of a Keplerian binary system via normally incident periodic gravitat... more The gravitational ionization of a Keplerian binary system via normally incident periodic gravitational radiation of definite helicity is discussed. The periodic orbits of the planar tidal equation are investigated on the basis of degenerate continuation theory. The relevance of the Kolmogorov-Arnold-Moser theory to the question of gravitational ionization is elucidated, and it is conjectured that the process of ionization is closely related to the Arnold diffusion of the perturbed system. 04.20.Cv, 04.30.+x, 95.10.Ce
The implications of the recent classical nonlocal generalization of Einstein's theory of gravitat... more The implications of the recent classical nonlocal generalization of Einstein's theory of gravitation for gravitational physics in the Solar System are investigated. In this theory, the nonlocal character of gravity simulates dark matter. Nonlocal gravity in the Newtonian regime involves a reciprocal kernel with three spatial parameters, of which two have already been determined from the rotation curves of spiral galaxies and the internal dynamics of clusters of galaxies. However, the short-range parameter a 0 remains to be determined. In this connection, the nonlocal contribution to the perihelion precession of a planetary orbit is estimated and a preliminary lower limit on a 0 is determined.
The general relativistic gravitomagnetic clock effect involves a coupling between the orbital mot... more The general relativistic gravitomagnetic clock effect involves a coupling between the orbital motion of a test particle and the rotation of the central mass and results in a difference in the proper periods of two counter-revolving satellites. It is shown that at (c-2) this effect has a simple analogue in the electromagnetic case. Moreover, in view of a possible measurement of the clock effect in the gravitational field of the Earth, we investigate the influence of some classical perturbing forces of the terrestrial space environment on the orbital motion of test bodies along opposite trajectories.
General Relativity and Gravitation, 1998
Using a novel coordinate system, we rederive the field equations and equa tions of motion for 5-d... more Using a novel coordinate system, we rederive the field equations and equa tions of motion for 5-dimensional relativity in the general case where the metric can depend on all 5 coordinates (ie, Kaluza-Klein theory without the cylinder restriction). We show that in ...
Physical Review Letters - PHYS REV LETT, 1982
Physics Letters A, 1987
ABSTRACT
The basic role of the hypothesis of locality in the theory of relativity is discussed. A conseque... more The basic role of the hypothesis of locality in the theory of relativity is discussed. A consequence of this assumption is the accelerated clock hypothesis (ACH). The limitations of ACH are investigated and compared with experimental data.. The possibility of using highly accurate clocks to test various aspects of general relativity is emphasized.
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Papers by Bahram Mashhoon