solar system

We study an impact of the cosmological environment on the solar gravitational system by the imbedding formalism of Gautreau. It turns out that the cosmic mean-mass density and the cosmological constant give negligibly small contribution to the gravity potentials. On the other hand, the cosmic acceleration beyond the Robertson-Walker geometry can considerably influence the curvature of spacetime in the solar system. The resulting anomalous constant acceleration towards the Sun is order of magnitude smaller than that measured by Pioneer 10 and 11. However, it is larger than the second order terms of potentials, thus well within the sensitivity of new gravity probes such as the LATOR mission. The general relativity (GR) corrections to Newtonian laws of planetary orbits are small but included in many body dynamical calculations. Due to the great advances in theoretical calculations by numerical codes and permanent technological achievements and improvements, numerous attempts are planned to measure tiny corrections to even higher accuracies as a check of the theory of gravity. In this paper we want to emphasize the importance of including some cosmological corrections to metric potentials and investigating whether they are observable and distinguishable from the higher order parametrized post-Newtonian (PPN) terms. We are faced with a problem of imbedding a Schwarzschild mass (in our case the solar mass) into cosmological fluid. The approach of Einstein and Straus is to cut out a spherical vacuum region and to put therein a Schwarzschild mass, and then to join smoothly two different geometries at the boundary surface. This approach looks quite unnatural because it excludes the expected overlapping of gravity forces. Therefore, we choose a different approach which allows merging of gravity fields, namely, that of Gautreau [1]. He relies on the introduction of geodesic time coordinates, which makes possible defining cosmic fluid sources and imbedding of the Schwarzschild mass. We deal with the so called flat (zero curvature) cosmic spacetime geometry, favoured by current observations. In adition to expansion, we include acceleration into the line element. Small amounts of acceleration or vorticity in cosmological models are allowed by current cosmological data. Moreover, recent claims on the large-scale asymmetry deduced from WMAP 1