Influence of dark matter on light propagation in solar system

We investigated the influence of dark matter on light propagation in the solar system We assumed the spherical symmetry of space-time and derived the approximate solution of the Einstein equation, which consists of the gravitational attractions caused by the central celestial body, i.e the Sun, and the dark matter surrounding it We expressed the dark matter density in the solar system in the following simple power-law form, q(t, r) = rho(t)(l/r)(k), where t is the coordinate time; r, the radius from the central body; l, the normalizing factor, k, the exponent characterizing r-dependence of dark matter density; and rho(t), the arbitrary function of time t. On the basis of the derived approximate solution, we focused on light propagation and obtained the additional corrections of the gravitational time delay and the relative frequency shift caused by the dark matter As an application of our results, we considered the secular increase in the astronomical unit reported by Krasmsky and Brumberg (2004) and found that it was difficult to provide an explanation for the observed dAU/dt = 15 +/- 4 m/century. (C) 2009 COSPAR Published by Elsevier Ltd. All rights reserved