11 research outputs found
Conservation laws for systems of extended bodies in the first post-Newtonian approximation.
The general form of the global conservation laws for -body systems in the
first post-Newtonian approximation of general relativity is considered. Our
approach applies to the motion of an isolated system of arbitrarily
composed and shaped, weakly self-gravitating, rotating, deformable bodies and
uses a framework recently introduced by Damour, Soffel and Xu (DSX). We succeed
in showing that seven of the first integrals of the system (total mass-energy,
total dipole mass moment and total linear momentum) can be broken up into a sum
of contributions which can be entirely expressed in terms of the basic
quantities entering the DSX framework: namely, the relativistic individual
multipole moments of the bodies, the relativistic tidal moments experienced by
each body, and the positions and orientations with respect to the global
coordinate system of the local reference frames attached to each body. On the
other hand, the total angular momentum of the system does not seem to be
expressible in such a form due to the unavoidable presence of irreducible
nonlinear gravitational effects.Comment: 18 pages, Revte
The Relativistic Factor in the Orbital Dynamics of Point Masses
There is a growing population of relativistically relevant minor bodies in
the Solar System and a growing population of massive extrasolar planets with
orbits very close to the central star where relativistic effects should have
some signature. Our purpose is to review how general relativity affects the
orbital dynamics of the planetary systems and to define a suitable relativistic
correction for Solar System orbital studies when only point masses are
considered. Using relativistic formulae for the N body problem suited for a
planetary system given in the literature we present a series of numerical
orbital integrations designed to test the relevance of the effects due to the
general theory of relativity in the case of our Solar System. Comparison
between different algorithms for accounting for the relativistic corrections
are performed. Relativistic effects generated by the Sun or by the central star
are the most relevant ones and produce evident modifications in the secular
dynamics of the inner Solar System. The Kozai mechanism, for example, is
modified due to the relativistic effects on the argument of the perihelion.
Relativistic effects generated by planets instead are of very low relevance but
detectable in numerical simulations
Phenomenology of the Lense-Thirring effect in the Solar System
Recent years have seen increasing efforts to directly measure some aspects of
the general relativistic gravitomagnetic interaction in several astronomical
scenarios in the solar system. After briefly overviewing the concept of
gravitomagnetism from a theoretical point of view, we review the performed or
proposed attempts to detect the Lense-Thirring effect affecting the orbital
motions of natural and artificial bodies in the gravitational fields of the
Sun, Earth, Mars and Jupiter. In particular, we will focus on the evaluation of
the impact of several sources of systematic uncertainties of dynamical origin
to realistically elucidate the present and future perspectives in directly
measuring such an elusive relativistic effect.Comment: LaTex, 51 pages, 14 figures, 22 tables. Invited review, to appear in
Astrophysics and Space Science (ApSS). Some uncited references in the text
now correctly quoted. One reference added. A footnote adde