  We present design considerations for the Transiting Exosatellites, Moons, and
Planets in Orion (TEMPO) Survey with the Nancy Grace Roman Space Telescope.
This proposed 30-day survey is designed to detect a population of transiting
extrasolar satellites, moons, and planets in the Orion Nebula Cluster (ONC).
The young (1-3 Myr), densely-populated ONC harbors about a thousand bright
brown dwarfs (BDs) and free-floating planetary-mass objects (FFPs). TEMPO
offers sufficient photometric precision to monitor FFPs with ${\rm M}\geq1{\rm
M}_{\rm J}$ for transiting satellites. The survey is also capable of detecting
FFPs down to sub-Saturn masses via direct imaging, although follow-up
confirmation will be challenging. TEMPO yield estimates include 14 (3-22)
exomoons/satellites transiting FFPs and 54 (8-100) satellites transiting BDs.
Of this population, approximately $50\%$ of companions would be "super-Titans"
(Titan to Earth mass). Yield estimates also include approximately $150$
exoplanets transiting young Orion stars, of which $>50\%$ will orbit
mid-to-late M dwarfs and approximately ten will be proto-habitable zone,
terrestrial ($0.1{\rm M}_{\oplus} - 5{\rm M}_{\oplus}$) exoplanets. TEMPO would
provide the first census demographics of small exosatellites orbiting FFPs and
BDs, while simultaneously offering insights into exoplanet evolution at the
earliest stages. This detected exosatellite population is likely to be markedly
different from the current census of exoplanets with similar masses (e.g.,
Earth-mass exosatellites that still possess H/He envelopes). Although our yield
estimates are highly uncertain, as there are no known exoplanets or exomoons
analogous to these satellites, the TEMPO survey would test the prevailing
theories of exosatellite formation and evolution, which limit the certainty
surrounding detection yields.
