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*The web address of the paper is gr-qc/ 0403068

Parameterized post-Newtonian theory of reference frames, multipolar expansions, and equations of motion in the N-body problem* Sergei Kopeikin and Igor Vlasov, University of Missouri-Columbia. *The web address of the paper is gr-qc/ 0403068. Scalar-tensor theory. Field equations.

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*The web address of the paper is gr-qc/ 0403068

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  1. Parameterized post-Newtonian theory of reference frames, multipolar expansions, and equations of motion in the N-body problem*Sergei Kopeikin and Igor Vlasov,University of Missouri-Columbia *The web address of the paper is gr-qc/ 0403068

  2. Scalar-tensor theory Field equations 1 PN approximation Gauge and boundary conditions Global frame (BCRF) (t, x) Coordinate transformation (t, x) (u, w) Local frame (GCRF) (u, w) Pointwise matching of scalar field and metric Laws of conservation Translational and rotational equations of motion Multipolar decomposition

  3. Barycentric RS { t, xi } Geocentric RS { u, wi }

  4. Geocentric coordinates span the space-time inside the world tube bounded by external matter Barycentric coordinates span the whole space-time point of matching of the two coordinate systems

  5. Center of mass of a finite size massive body doesn’t move along a geodesic. This effect exists even in the Newtonian approximation. The center of mass moves with the acceleration Qi with respect to the geodesic passing through its initial position For the Earth this acceleration amounts to 3.10-11 m/s2 The geodetic acceleration is about 6.10-3 m/s2 so the effect is of order 5.10-9 S world line of the center of mass geodesic in the global RS

  6. 4 1 3 2 Spherical symmetry of a moving body is not well-defined in the global frame:

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