  We investigated the influence of dark matter on light propagation in the
solar system. We assumed the spherical symmetry of spacetime 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, $\varrho(t, r) =
\rho(t)(\ell/r)^k$, where $t$ is the coordinate time; $r$, the radius from the
central body; $\ell$, 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 Krasinsky and Brumberg (2004) and found that it
was difficult to provide an explanation for the observed $d{\rm AU}/dt = 15 \pm
4 ~[{\rm m/century}]$.
