Time's Arrow, Music of the Spheres, December 8, 1994

This is the concert program of the Time's Arrow, Music of the Spheres performance on Thursday, December 8, 1994 at 8:00 p.m., at the Tsai Performance Center, 685 Commonwealth Avenue, Boston, Massachusetts. Works performed were Primo Intermedio by Antonio Archilei and Cristofano Malvezzi, Time Circles by Menachem Zur, Variations for Piano and Woodwind Quintet by Martin Amlin, Celestial Mechanics by Donald Crockett, and Celestial Mechanics, Cosmic Dances for Amplified Piano, Four Hands by George Crumb. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund

Modern Problems of Celestial Mechanics

Survey on celestial mechanics problem

Celestial mechanics in Kerr spacetime

The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy $E$, the axial component of the angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are obtained by solving the Hamilton-Jacobi equation for the dynamical problem of geodesic motion. Employing the action-angle variable formalism, on the other hand, yields a different set of constants of motion, namely, the fundamental frequencies $\omega_{r}$, $\omega_{\theta}$ and $\omega_{\phi}$ associated with the radial, polar and azimuthal components of orbital motion. These frequencies, naturally, determine the time scales of orbital motion and, furthermore, the instantaneous gravitational wave spectrum in the adiabatic approximation. In this article, it is shown that the fundamental frequencies are geometric invariants and explicit formulas in terms of quadratures are derived. The numerical evaluation of these formulas in the case of a rapidly rotating black hole illustrates the behaviour of the fundamental frequencies as orbital parameters such as the semi-latus rectum $p$, the eccentricity $e$ or the inclination parameter $\theta_{-}$ are varied. The limiting cases of circular, equatorial and Keplerian motion are investigated as well and it is shown that known results are recovered from the general formulas.Comment: 25 pages (LaTeX), 5 figures, submitted to Class. Quantum Gra

Application of the methods of celestial mechanics to the rigid body problem Final report, 1 Jul. 1965 - 1 Jun. 1966

Celestial mechanics perturbation methods applied to problem of describing motion of rigid artificial earth satellite about its center of mas

Relativistic Celestial Mechanics with PPN Parameters

Starting from the global parametrized post-Newtonian (PPN) reference system with two PPN parameters $\gamma$ and $\beta$ we consider a space-bounded subsystem of matter and construct a local reference system for that subsystem in which the influence of external masses reduces to tidal effects. Both the metric tensor of the local PPN reference system in the first post-Newtonian approximation as well as the coordinate transformations between the global PPN reference system and the local one are constructed in explicit form. The terms proportional to $\eta=4\beta-\gamma-3$ reflecting a violation of the equivalence principle are discussed in detail. We suggest an empirical definition of multipole moments which are intended to play the same role in PPN celestial mechanics as the Blanchet-Damour moments in General Relativity. Starting with the metric tensor in the local PPN reference system we derive translational equations of motion of a test particle in that system. The translational and rotational equations of motion for center of mass and spin of each of $N$ extended massive bodies possessing arbitrary multipole structure are derived. As an application of the general equations of motion a monopole-spin dipole model is considered and the known PPN equations of motion of mass monopoles with spins are rederived.Comment: 71 page

Interaction between celestial and terrestrial reference frames and some considerations for the next VLBI-based ICRF

In this paper we outline several problems related to the realization of the international celestial and terrestrial reference frames ICRF and ITRF at the millimeter level of accuracy, with emphasis on ICRF issues. The main topics considered are: analysis of the current status of the ICRF, mutual impact of ICRF and ITRF, and some considerations for future ICRF realizations.Comment: Presented at the Journees 2011: Earth rotation, reference systems and celestial mechanics: Synergies of geodesy and astronomy, Vienna, Austria, Sep 19-2

Daemons and DAMA: Their Celestial-Mechanics Interrelations

The assumption of the capture by the Solar System of the electrically charged Planckian DM objects (daemons) from the galactic disk is confirmed not only by the St.Petersburg (SPb) experiments detecting particles with V<30 km/s. Here the daemon approach is analyzed considering the positive model independent result of the DAMA/NaI experiment. We explain the maximum in DAMA signals observed in the May-June period to be associated with the formation behind the Sun of a trail of daemons that the Sun captures into elongated orbits as it moves to the apex. The range of significant 2-6-keV DAMA signals fits well the iodine nuclei elastically knocked out of the NaI(Tl) scintillator by particles falling on the Earth with V=30-50 km/s from strongly elongated heliocentric orbits. The half-year periodicity of the slower daemons observed in SPb originates from the transfer of particles that are deflected through ~90 deg into near-Earth orbits each time the particles cross the outer reaches of the Sun which had captured them. Their multi-loop (cross-like) trajectories traverse many times the Earth's orbit in March and September, which increases the probability for the particles to enter near-Earth orbits during this time. Corroboration of celestial mechanics calculations with observations yields ~1e-19 cm2 for the cross section of daemon interaction with the solar matter.Comment: 12 pages including 5 figure