A General Formula for the Maximum Height of Tectonic Mountains on Planetary Bodies

This paper derives a general formula for the maximum height of tectonic mountains on any planetary body with a solid crust and mountain-building processes. Starting from the fundamental strength limit htheory = σ/(ρg) (known since 1932), we introduce a mathematically derived erosion factor E = 1/(1 + α) that accounts for the balance between uplift and erosion. Here α is the ratio of erosion rate to uplift rate, which depends on climate and surface conditions. The complete formula is hreal = σ/[ρg(1 + α)]. Using physically justified values of α for different planetary environments, we predict mountain heights on Earth (8.8 km), Mars (22 km), Venus (11 km), and Triton (6.6 km) — all within 10% of observed values. The formula applies only to bodies with tectonic mountains (not volcanic or impact features) and requires knowledge of rock/ice strength, gravity, density, and the erosion-uplift ratio α. This provides a unified framework for understanding mountain heights across the solar system and for predicting them on exoplanets.