Relativistic Celestial Mechanics with PPN Parameters

Abstract

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.

71 pages

References in corpus (1)

• Nordtvedt effect in rotational motion

Cited by in corpus (25)

• The IAU 2000 resolutions for astrometry, celestial mechanics and metrology in the relativistic framework: explanatory supplement
• New derivation of the Lagrangian of a perfect fluid with a barotropic equation of state
• Time transfer and frequency shift to the order 1/c^4 in the field of an axisymmetric rotating body
• Physically adequate proper reference system of a test observer and relativistic description of the GAIA attitude
• Testing Theories of Gravity with Planetary Ephemerides
• Second post-Newtonian approximation of scalar-tensor theory of gravity
• Shortcomings of Shapiro delay-based tests of the equivalence principle on cosmological scales
• Scalar-tensor propagation of light in the inner solar system at the millimetric level
• The Relativistic Factor in the Orbital Dynamics of Point Masses
• Extending the first-order post-Newtonian scheme in multiple systems to the second-order contributions to light propagation
• Second post-Newtonian approximation of Einstein-aether theory
• Light propagation in the gravitational field of N arbitrarily moving bodies in 1PN approximation for high-precision astrometry
• Light propagation in the gravitational field of N arbitrarily moving bodies in the 1.5PN approximation for high-precision astrometry
• Covariant Equations of Motion of Extended Bodies with Arbitrary Mass and Spin Multipoles
• Relativistic aspects of rotational motion of celestial bodies
• Constraining massless dilaton theory at Solar system scales with the planetary ephemeris INPOP
• Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity
• Solar System constraints on Renormalization Group extended General Relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect
• The post-linear Schwarzschild solution in harmonic coordinates: elimination of structure-dependent terms
• Collinear and triangular solutions to the coplanar and circular three-body problem in the parametrized post-Newtonian formalism
• Using global positioning systems to test extensions of General Relativity
• Post-Newtonian Reference Frames for Advanced Theory of the Lunar Motion and a New Generation of Lunar Laser Ranging
• Triangular solution to the planar elliptic three-body problem in the parametrized post-Newtonian formalism
• Astronomical relativistic reference systems with multipolar expansion: the global one
• Independent Components of an Indexed Object with Linear Symmetries