Barometric pressure profiles · Greenhouse warming · Jeans escape · Earth vs Mars vs Venus vs Titan
This simulation compares the atmospheres of Earth, Mars, Venus, Titan and the Moon across three linked panels: a logarithmic pressure-versus-altitude profile, a radiative energy balance, and a surface-temperature bar chart. Pressure follows the barometric formula, P = P₀·exp(−h/H), with each world’s real scale height H. Surface temperature is built from the radiative equilibrium temperature plus a greenhouse increment, and a Jeans escape parameter λ gauges how tightly each atmosphere is bound.
How atmospheric pressure thins exponentially with altitude (scale height H ranges from 8.5 km on Earth to 21 km on Titan), how incoming sunlight S = S₀/d² is partly reflected by albedo α and balanced against thermal emission σT⁴, and how the greenhouse increment and Jeans parameter λ = v_esc²·m/(2k_B T) determine surface warmth and whether gas is retained.
Pick a world with the five planet buttons (Earth, Mars, Venus, Titan, Moon). Then drag the three sliders: CO₂ percentage changes the greenhouse warming (it scales logarithmically), cloud albedo α sets how much sunlight is reflected, and solar luminosity scales the incident flux from 0.1 to 2 S₀. The Stats panel updates surface temperature, scale height, pressure, escape velocity and λ live.
Venus and Earth are nearly twins in size, yet Venus has a 92-atmosphere CO₂ blanket that traps roughly 430 K of greenhouse warming, baking its surface to about 735 K — hotter than Mercury despite being further from the Sun.
Scale height H is the vertical distance over which atmospheric pressure falls by a factor of e (about 37 per cent). It equals k_B·T divided by the mean molecular mass times gravity, so warmer, lighter, low-gravity atmospheres are puffier. That is why cold but low-gravity Titan has H near 21 km while Earth’s is about 8.5 km.
It first finds the radiative equilibrium temperature from the absorbed sunlight, T_eq = (S(1−α)/4σ)^¼, where S is the solar flux scaled by distance and luminosity. It then adds a greenhouse increment that grows logarithmically with CO₂, calibrated to give Earth its +33 K boost. The surface temperature shown is T_eq plus that increment.
λ compares a gas molecule’s gravitational binding energy to its thermal energy: λ = v_esc²·m/(2k_B·T). A large λ (roughly above 15–30) means the atmosphere is well retained, while a small value means light molecules can readily escape to space. This is a key reason low-gravity Mars and the Moon struggle to hold onto their gas.
Mars has a low escape velocity of about 5 km/s and lacks a strong global magnetic field, so over billions of years thermal escape and stripping by the solar wind removed most of its air. Today its surface pressure is only about 0.006 atmospheres, around 0.6 per cent of Earth’s, which the pressure profile makes visible at a glance.
The framework is correct in form — the barometric law, radiative equilibrium, Stefan-Boltzmann emission and the Jeans parameter are all real physics. The numbers are simplified, however: scale height is treated as constant with altitude, the greenhouse term is a single calibrated logarithmic fit rather than a full radiative-transfer calculation, and clouds are reduced to one albedo value. It is an educational comparison, not a research climate model.