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

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 $\sim \text{\hspace{0.17em}⁣}30\mathrm{\%}$ and the F-1 turbopump power to within $\sim \text{\hspace{0.17em}⁣}18\mathrm{\%}$. Over $0.1$–$10$~bar, atmospheric pressure changes the required launch mass by up to $\sim \text{\hspace{0.17em}⁣}35\mathrm{\%}$ on $0.5M_{\oplus }$ planets, where drag contributes substantially to the ascent $\mathrm{\Delta }v$, 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 $\sim \text{\hspace{0.17em}⁣}100$ F-1-class first-stage engines renders escape of the benchmark payload impractical above $\sim \text{\hspace{0.17em}⁣}11.5M_{\oplus }$. This engine-counting constraint independently corroborates the $\sim \text{\hspace{0.17em}⁣}10M_{\oplus }$ 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.