  Rubble piles are a common feature of solar system bodies. They are composed
of monolithic elements of ice or rock bound by gravity. Voids occupy a
significant fraction of the volume of a rubble pile. They can exist up to
pressure $P\approx \epsy\mu$, where $\epsy$ is the monolithic material's yield
strain and $\mu$ its rigidity. At low $P$, contacts between neighboring
elements are confined to a small fraction of their surface areas. As a result,
the effective thermal conductivity of a rubble pile, $\kcon\approx
k(P/(\epsy\mu))^{1/2}$, can be orders of magnitude smaller than, $k$, the
thermal conductivity of its monolithic elements. In a fluid-free environment,
only radiation can transfer energy across voids. It contributes an additional
component, $\krad=16\ell\sigma T^3/3$, to the total effective conductivity,
$\keff=\kcon +\krad$. Here $\ell$, the inverse of the opacity per unit volume,
is of order the size of the elements and voids. An important distinction
between $\kcon$ and $\krad$ is that the former is independent of the size of
the elements whereas the latter is proportional to it. Our expression for
$\keff$ provides a good fit to the depth dependence of thermal conductivity in
the top $140\,\mathrm{cm}$ of the lunar regolith. It also offers a good
starting point for detailed modeling of thermal inertias for asteroids and
satellites. Measurement of the response of surface temperature to variable
insolation is a valuable diagnostic of a regolith. There is an opportunity for
careful experiments under controlled laboratory conditions to test models of
thermal conductivity such as the one we outline.
