510 research outputs found
Relativistic Celestial Mechanics with PPN Parameters
Starting from the global parametrized post-Newtonian (PPN) reference system
with two PPN parameters and 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 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 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
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
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
Second post-Newtonian approximation of scalar-tensor theory of gravity
Deep space laser ranging missions like ASTROD I (Single-Spacecraft
Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD,
together with astrometry missions like GAIA and LATOR will be able to test
relativistic gravity to an unprecedented level of accuracy. More precisely,
these missions will enable us to test relativistic gravity to
, and will require 2nd post-Newtonian approximation of
relevant theories of gravity. The first post-Newtonian approximation is valid
to and the second post-Newtonian is valid to in the solar
system. The scalar-tensor theory is widely discussed and used in tests of
relativistic gravity, especially after the interests in inflation, cosmological
constant and dark energy in cosmology. In the Lagrangian, intermediate-range
gravity term has a similar form as cosmological term. Here we present the full
second post-Newtonian approximation of the scalar-tensor theory including
viable examples of intermediate-range gravity. We use Chandrasekhar's approach
to derive the metric coefficients and the equation of the hydrodynamics
governing a perfect fluid in the 2nd post-Newtonian approximation in
scalar-tensor theory; all terms inclusive of are retained
consistently in the equation of motion.Comment: 20 pages, COSPAR2006 H0.1-
A List of References on Spacetime Splitting and Gravitoelectromagnetism
Revised version to be published in the Proceedings of the Encuentros
Relativistas Espa\~noles, September, 2000 [ http://hades.eis.uva.es/EREs2000 ]Comment: 22 pages, LaTeX article style. Please send corrections and additions
to mailto:[email protected]
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