|M||Mass of the planet (kg)|
|r||Planetary radius (m)|
|h||Height of the exobase, use h = 0 if unknown (m)|
|L||Luminosity of the star, sol: 3.86 x1026 (W)|
|Ro||For a planet: Minimum orbital radius of the planet (m)|
|For a moon: Minimum orbital radius of the planet - Maximum orbital radius of the moon (m)|
This equation reveals a minimum value. Below this value, Hydrogen will escape from the atmosphere into space. Without Hydrogen there is no water, and without liquid water the planet cannot support life as we know it. Hydrogen escapes from an atmosphere slowly at first. As Hydrogen is lost gravity decreases slightly, increasing the rate of loss. On a gas giant, atmosphere is lost until a balance is reached with heavier gases. On a wet terrestrial planet, the increasing Oxygen concentration will determine what happens next. If there is enough Carbon then CO2 will increase atmospheric temperature, increasing the rate of loss. This will produce a runaway greenhouse effect, like Venus. If there is not enough Carbon then the planet will cool. If it cools enough then the atmosphere could collapse, like Mars. A collapsing atmosphere will also increase the rate of loss.
This equation can also be used for other gases using different k values. The k value is inversely proportional to the mass of the gas. Hydrogen, being the lightest gas, will escape the fastest.
Earth can only just hold Hydrogen, it's right near the crossover point in the equation. The amount of Hydrogen it retains is stable over geological timescales, so it will not turn into a gas giant.