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Secular increase of astronomical unit from analysis of the major planet motions, and its interpretation

G. A. Krasinsky, V. A. Brumberg

Celestial Mechanics and Dynamical Astronomy, 90(3), 267-288 (2004)

Keywords: cosmology ephemerides, relativity, astronomical unit

About the paper Full text


From the analysis of all available radiometric measurements of distances between the Earth and the major planets (including observations of martian landers and orbiters over 1971–2003 with the errors of few meters) the positive secular trend in the Astronomical Unit AU is estimated as d/dt AU=15±4m/cy . The given uncertainty is the 10 times enlarged formal error of the least-squares estimate and so accounts for possible systematic errors of measurements and deficiencies of the mathematical model. The reliability of this estimate as well as its physical meaning are discussed. A priori most plausible attribution of this effect to the cosmological expansion of the Universe turns out inadequate. A model of the observables developed in the frame of the relativistic background metric of the uniform isotropic Universe shows that the corresponding dynamical perturbations in the major planet motions are completely canceled out by the Einstein effect of dependence of the rate of the observer’s clock (that keeps the proper time) on the gravitational field, though separately values of these two effects are quite large and attainable with the accuracy achieved. Another tentative source of the secular rate of AU is the loss of the solar mass due to the solar wind and electromagnetic radiation but it amounts in d/dt AU only to 0.3 m/cy. Excluding other explanations that seem exotic (such as secular decrease of the gravitational constant) at present there is no satisfactory explanation of the detected secular increase of AU, at least in the frame of the considered uniform models of the Universe.