Multistage Rocket Optimization, Geophysics, and the Spacefaring Envelope of Habitable Super-Earths

Abstract

Habitability is typically defined by whether a planet can support life, rather than whether it can support a technological civilization capable of escaping its gravity well. We introduce spacefaring capability as a technological axis of habitability, defined by the ability to place a 1000 kg payload on an escape trajectory using chemical propulsion. We develop a coupled geophysical--atmospheric--astronautical model that maps this ``spacefaring envelope'' as a function of planetary mass and surface pressure. Building on Hippke (2018) and Gonzalez (2020), we optimize multistage chemical rockets by minimizing the reliability-weighted expected launch mass while determining the optimal stage count, first-stage engine number, and mission reliability. Assuming F-1-class first-stage engines, the model reproduces the Saturn V gross lift-off mass to within $\sim\!30\%$ and the F-1 turbopump power to within $\sim\!18\%$. Over $0.1$--$10$~bar, atmospheric pressure changes the required launch mass by up to $\sim\!35\%$ on $0.5\,M_\oplus$ planets, where drag contributes substantially to the ascent $Δv$, but by only a few percent for $M_\oplus \gtrsim 4$. Gravity, rather than atmospheric drag, therefore sets the primary limit on chemical escape from super-Earths. Imposing a post-optimization limit of $\sim\!100$ F-1-class first-stage engines renders escape of the benchmark payload impractical above $\sim\!11.5\,M_\oplus$. This engine-counting constraint independently corroborates the $\sim\!10\,M_\oplus$ limit derived by Hippke (2018) from an engine-independent fuel-ratio argument. These results provide a physically motivated framework for assessing whether rocky exoplanets are capable of supporting technological civilizations that can escape their planetary gravity wells.