local noon Solar flux $I_\mathrm{max}$, where $\gamma$ was taken to be $\gamma=0.01$. The system of differential eqns. (\[eqn\_B\_def\]) - (\[eqn\_R\_def\]) dependent on time $t$ and on Solar distance $r$ constitutes a heat conduction problem with periodic excitation (by the planet’s rotation). Thus, the heat balance of the planets is modelled by periodic solutions of the Laplacian heat conduction differential equations. It was solved iteratively by applying Laplace transforms with periodic boundary conditions. The integration over the planet’s surface then yields the radiation flux. In the calculation, we addressed rocky and gaseous planets differently with respect to their thermal properties. Furthermore, the giant gaseous planets are known to have internal sources of heat generation, which also has been taken account of.

The brightest point source in the microwave sky due to the planetary thermal emission is Jupiter, causing an increase in antenna temperature of $T_\mathrm{Jupiter}=93.6$ mK in the $\nu=100$ GHz-channel, followed by Saturn with $T_\mathrm{Saturn}=15.0$ mK. All outer planets apart from Pluto will be visible for [[*Planck*]{}]{}. Estimates show that even Galilean satellites Ganymede, Callisto, Io and Europa and Saturn’s moon Titan are above the detection threshold of [[*Planck*]{}]{}, but they are outshone by the stray-light from Jupiter and Saturn, respectively 