 Isothermal pressure-level transit radius

Let $R_p$ be a reference radius at pressure $P_0$ in an isothermal atmosphere. It can be a reference isobar on a gas giant, rather than a solid surface. Assume constant temperature $T$, constant mean molecular weight $\mu$ in units of hydrogen mass $m_H$, and approximately constant gravitational acceleration $g$. The ideal gas law and hydrostatic equilibrium giveIntegrating from the reference isobar yieldsReducing the pressure by a factor $e$ therefore increases the pressure-level radius by one atmospheric scale height. Constant gravity is a thin-atmosphere approximation over the height range being modeled.

A pressure-level radius is not automatically the observed transit radius. Transmission depends on the line-of-sight optical depth, which also requires composition and opacity. Different reference pressures or cloud assumptions can therefore assign different pressure levels to the same observed exoplanet transmission spectrum.^[ref]