  The study of planets and small bodies within our Solar System is fundamental
for understanding the formation and evolution the Earth and other planets.
Compositional and meteorological studies of the giant planets provide a
foundation for understanding the nature of the most commonly observed
exoplanets, while spectroscopic observations of the atmospheres of terrestrial
planets, moons, and comets provide insights into the past and present-day
habitability of planetary environments, and the availability of the chemical
ingredients for life. While prior and existing (sub)millimeter observations
have led to major advances in these areas, progress is hindered by limitations
in the dynamic range, spatial and temporal coverage, as well as sensitivity of
existing telescopes and interferometers. Here, we summarize some of the key
planetary science use cases that factor into the design of the Atacama Large
Aperture Submillimeter Telescope (AtLAST), a proposed 50-m class single dish
facility: (1) to more fully characterize planetary wind fields and atmospheric
thermal structures, (2) to measure the compositions of icy moon atmospheres and
plumes, (3) to obtain detections of new, astrobiologically relevant gases and
perform isotopic surveys of comets, and (4) to perform synergistic,
temporally-resolved measurements in support of dedicated interplanetary space
missions. The improved spatial coverage (several arcminutes), resolution
($\sim1.2''-12''$), bandwidth (several tens of GHz), dynamic range ($\sim10^5$)
and sensitivity ($\sim1$ mK km s$^{-1}$) required by these science cases would
enable new insights into the chemistry and physics of planetary environments,
the origins of prebiotic molecules and the habitability of planetary systems in
general.
