  While the data analysis of $\gamma$-ray telescopes has now become more
robust, some signals may be misinterpretations of a time-variable foreground
emission from the Solar System, induced by low-energy cosmic-ray interactions
with asteroids. Our goal is to provide emission templates for this
time-variable diffuse $\gamma$-ray foreground by considering the populations of
Main Belt Asteroids, Jovian and Neptunian Trojans, Kuiper Belt Objects, and the
Oort Cloud. We model the spatial distribution of all known asteroids by
performing 3D-fits to determine their density profiles and calculate their
appearances by line-of-sight integrations. Because Earth and the asteroids are
moving with respect to each other, we obtain diffuse emission templates varying
on timescales of days to decades. We find that the temporal variability can
lead to flux enhancements which may mimic emission features unless properly
taken into account. This variation is further enhanced by the Solar cycle as
the cosmic-ray spectrum is attenuated by the Solar modulation potential,
leading to a relative flux increase of the outer asteroids. The cumulative
effect of the time-dependent emission is illustrated for the case of the 511
keV OSSE fountain, and for emission features near the Galactic Centre, both
being possible misinterpretations of the Solar System albedo. We recommend that
$\gamma$-ray data analyses should always take into account the possibility of a
time-variable foreground. Due to the ecliptic overlap with the Galactic plane,
the Galactic emission is expected to be weaker by 0.1-20%, depending on time
(relative planetary motion), energy, and Solar cycle, which has immense
consequences for the interpretation of dark matter annihilation cross sections,
cosmic-ray spectra and amplitudes, as well as nucleosynthesis yields and
related parameters.
