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.

在这项工作中，我们推导出了质量范围从土星质量到 1 M _⊙的富氢天体的最小允许轨道周期，强调了 0.0003-0.074 M _⊙范围内的气态巨行星和褐矮星 (BD) 。解析拟合公式为作为身体质量的函数和作为平均密度的函数被呈现。我们假设主星的密度足够高，不会限制最小周期。在许多情况下，这意味着宿主恒星是一颗白矮星。这项工作的部分目的是将 BD 与发现的经过宿主白矮星的行星区分开来，而无需借助近红外或径向速度测量。特别是，≲100 分钟的轨道周期很可能是 BD。在整个质量范围内的总最短时间为 ≃37 分钟。