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Changes in the Sun's mass and gravitational constant estimated using modern observations of planets and spacecraft

E. V. Pitjeva, N. P. Pitjev

Solar System Research, 46(1), 78-87 (2012)

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More than 635 thousand positional observations of planets and spacecraft of various types (mostly radiotechnical ones, 1961–2010) were used to estimate possible changes in the gravitational constant, Sun’s mass, and semi-major axes of planetary orbits, as well as the associated value of the astronomical unit. The observations were analyzed based on the EPM2010 ephemerides constructed at the Institute of Applied Astronomy (Russian Academy of Sciences) in a post-Newtonian approximation as a result of simultanious numerical integration of the equations of motion of nine major planets, the Sun, the Moon, asteroids, and trans-Neptunian objects. The heliocentric gravitational constant GM ⊙ was found to vary with a rate of (GṀ ⊙/GM ⊙ = (−5.0 ± 4.1)) × 10−14 per year (at the 3σ level). The positive secular changes in the semimajor axes ȧ i /a i were found for Mercury, Venus, Mars, Jupiter, and Saturn provided by high-precision observations. These changes also correspond to the decrease in the heliocentric gravitational constant. The changing of GM ⊙, itself is probably caused by the loss of the mass M ⊙ of the Sun due to its radiation and solar wind; these effects are partly compensated by the material falling onto the Sun. Allowing for the maximum bounds on the possible change in the Sun’s mass M ⊙, it has been found from the change obtained in GM ⊙ that the annual change Ġ/G of the gravitational constant G falls within the interval −4.2 × 10−14 < ȧ/G < +7.5 × 10−14 with a 95% probability. The astronomical unit (AU) is connected by its definition only with the heliocentric gravitational constant. The decrease of GM ⊙ obtained in this paper should correspond to a secular decrease in the AU. It is shown, however, that the modern level of accuracy does not allow us to determine a change in the AU. The attained posibility of determining changes in GM ⊙ using high-accuracy observations encourages us to have a relation between GM ⊙ and the AU fixed for a certain moment in time, since it is inconvenient to have a time-dependent length for the AU.