Estimations of changes of the Sun's mass and the gravitation constant from the modern observations of planets and spacecraft

More than 635 000 positional observations (mostly radiotechnical) of planets and spacecraft (1961-2010), have been used for estimating possible changes of the gravitation constant, the solar mass, and semi-major axes of planets, as well as the value of the astronomical unit, related to them. The analysis of the observations has been performed on the basis of the EPM2010 ephemerides of IAA RAS in post-newtonian approximation. The obtained results indicate on decrease in the heliocentric gravitation constant per year at the level $\dot {GM_{Sun}}/GM_{Sun} = (-5.0 \pm 4.1) 10^{-14} (3\sigma).$ The positive secular changes of semi-major axes $\dot a_i/a_i$ have been obtained simultaneously for the planets Mercury, Venus, Mars, Jupiter, Saturn, as expected if the geliocentric gravitation constant is decreasing in century wise. The change of the mass of the Sun $M_{Sun}$ due to the solar radiation and the solar wind and the matter dropping on the Sun (comets, meteors, asteroids and dust) was estimated. Taking into account the maximal limits of the possible $M_{Sun}$ change, the value $\dot G/G$ falls within the interval $-4.2\cdot10^{-14} < \dot G/G < +7.5\cdot10^{-14}$ in year with the 95% probability. The astronomical unit (au) is only connected with the geliocentric gravitation constant by its definition. In the future, the connection between $GM_{Sun}$ and au should be fixed at the certain time moment, as it is inconvenient highly to have the changing value of the astronomical unit.Comment: 20 pages, 4 tables, accepted for publication in Solar System Research, 2011 (Astronomicheskii vestnik