| [Activity] |
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Atmospheric Escape |
Objective
Working with the escape velocities of the Earth and Moon, with the velocity of a gas molecule, and with the temperatures of the solar system as a function of the distance from the Sun, the student willIntroduction
The ability of a planet to hold on to an atmosphere depends mainly on two factors: temperature and gravity. The temperature of a planet is important because it is really just a measure of how fast the molecules of gas in the atmosphere are moving around. The higher the temperature the faster the molecules are moving. The gravity of a planet is important because it determines the escape velocity of a planet. Any object with a velocity greater than the escape velocity will escape the gravitational pull of the planet.The gravity of a planet is determined by its mass and radius. A planet with a stronger gravitational pull will have a higher escape velocity. The following table lists the escape velocities for our Earth and the Moon:
| Body | Vescape (m/s) |
|---|---|
| Earth | 11,200 |
| Moon | 2,300 |
The temperature of a planet is determined mainly by its distance from the Sun. The following table shows the temperature a planet would have at various distances from the Sun:
| Distance (AU) | 0.5 | 1.0 | 2.0 | 4.0 | 6.0 | 8.0 |
|---|---|---|---|---|---|---|
| Temperature (K) | 566 | 400 | 283 | 200 | 163 | 141 |
Finally, the speed of a molecule of gas in an atmosphere depends on its temperature and on its mass. A heavier molecule moves slower than a light molecule at the same temperature. The velocity of a molecule of gas can be determined from the equation:
A table of a few molecules and their masses follows:
| Molecule | Symbol | Mass |
|---|---|---|
| hydrogen | H2 | 2 |
| water | H2O | 18 |
| nitrogen | N2 | 28 |
A "rule of thumb" in planetary science is that a planet can hold onto a gas for the age of the solar system if the velocity of the gas is less than one-sixth the escape velocity of the planet. The equation from this is:
