Ultra-hot Jupiters (UHJs) have recently been the focus of several atmospheric studies due to their extreme properties. While molecular hydrogen (H2) plays a key role in UHJ atmospheres, it has not been directly detected on an exoplanet. To determine the feasibility of H2 detection via transmission spectroscopy of the Lyman and Werner bands, we modeled UHJ atmospheres with H2 rotational temperatures varying from 2000 to 4000 K orbiting A-type stars ranging from
T; eff = 8500 K to T; eff = 10,300 K. We present simulated transmission spectra for each planet-star temperature combination while adding Poisson noise varying in magnitude from 0.5% to 2.0%. Finally, we cross-correlated the spectra with expected atmospheric H2 absorption templates for each temperature combination. Our results suggest that H2 detection with current facilities, namely the Hubble Space Telescope, is not possible. However, direct atmospheric transmission spectroscopy of H2 may be viable with future UV-capable flagship missions.