The TEMPO Survey II: Science Cases Leveraged from a Proposed 30-Day Time Domain Survey of the Orion Nebula with the Nancy Grace Roman Space Telescope

The TEMPO (Transiting Exosatellites, Moons, and Planets in Orion) Survey is a proposed 30-day observational campaign using the Nancy Grace Roman Space Telescope. By providing deep, high-resolution, short-cadence infrared photometry of a dynamic star-forming region, TEMPO will investigate the demographics of exosatellites orbiting free-floating planets and brown dwarfs -- a largely unexplored discovery space. Here, we present the simulated detection yields of three populations: extrasolar moon analogs orbiting free-floating planets, exosatellites orbiting brown dwarfs, and exoplanets orbiting young stars. Additionally, we outline a comprehensive range of anticipated scientific outcomes accompanying such a survey. These science drivers include: obtaining observational constraints to test prevailing theories of moon, planet, and star formation; directly detecting widely separated exoplanets orbiting young stars; investigating the variability of young stars and brown dwarfs; constraining the low-mass end of the stellar initial mass function; constructing the distribution of dust in the Orion Nebula and mapping evolution in the near-infrared extinction law; mapping emission features that trace the shocked gas in the region; constructing a dynamical map of Orion members using proper motions; and searching for extragalactic sources and transients via deep extragalactic observations reaching a limiting magnitude of $m_{AB}=29.7$\,mag (F146 filter).