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Abstract In this work we derive the minimum allowed orbital periods of H-rich bodies ranging in mass from Saturn’s mass to 1 M ⊙ , emphasizing gas giants and brown dwarfs (BDs) over the range 0.0003–0.074 M ⊙ . Analytic fitting formulae for as a function of the mass of the body and as a function of the mean density are presented. We assume that the density of the host star is sufficiently high so as not to limit the minimum period. In many instances this implies that the host star is a white dwarf. This work is aimed, in part, toward distinguishing BDs from planets that are found transiting the host white dwarf without recourse to near-infrared or radial velocity measurements. In particular, orbital periods of ≲100 minutes are very likely to be BDs. The overall minimum period over this entire mass range is ≃37 minutes. 

We report the confirmation and mass determination of three hot Jupiters discovered by the Transiting Exoplanet Survey Satellite (TESS) mission: HIP 65Ab (TOI-129, TIC-201248411) is an ultra-short-period Jupiter orbiting a bright ( V = 11.1 mag) K4-dwarf every 0.98 days. It is a massive 3.213 ± 0.078  M J planet in a grazing transit configuration with an impact parameter of b = 1.17 −0.08 +0.10 . As a result the radius is poorly constrained, 2.03 −0.49 +0.61 R J . The planet’s distance to its host star is less than twice the separation at which it would be destroyed by Roche lobe overflow. It is expected to spiral into HIP 65A on a timescale ranging from 80 Myr to a few gigayears, assuming a reduced tidal dissipation quality factor of Q s ′ = 10 7 − 10 9 . We performed a full phase-curve analysis of the TESS data and detected both illumination- and ellipsoidal variations as well as Doppler boosting. HIP 65A is part of a binary stellar system, with HIP 65B separated by 269 AU (3.95 arcsec on sky). TOI-157b (TIC 140691463) is a typical hot Jupiter with a mass of 1.18 ± 0.13  M J and a radius of 1.29 ± 0.02  R J . It has a period of 2.08 days, which corresponds to a separation of just 0.03 AU. This makes TOI-157 an interesting system, as the host star is an evolved G9 sub-giant star ( V = 12.7). TOI-169b (TIC 183120439) is a bloated Jupiter orbiting a V = 12.4 G-type star. It has a mass of 0.79 ±0.06  M J and a radius of 1.09 −0.05 +0.08 R J . Despite having the longest orbital period ( P = 2.26 days) of the three planets, TOI-169b receives the most irradiation and is situated on the edge of the Neptune desert. All three host stars are metal rich with [Fe / H] ranging from 0.18 to0.24.