The atmosphere’s of the planets and moons vary greatly. To understand why we have to know that every body has a certain speed called the escape velocity at which a particle can escape its gravitational pull and that the speeds of molecules in a gas depend on the gas’s temperature and molecular weight (mass). The escape velocity from a body is given by
$v_{esc} = \sqrt{GM/R} $
where M is the mass of the body, R is its radius and G is Newton’s constant of Universal gravity.
In comparison the speeds of particles in a gas are given by the Maxwell-Boltzmann distribution. In this case the root mean square velocity is given by
$v_{rms} = \sqrt{3k_B T/m} $
where T is the gas’s temperature, m is the particles molecular weight and k_B is a constant called the Boltzman constant.
Basically, if the speeds of the gas particles are even one tenth of the escape speed then the gas will slowly escape the planet or moon. If the speed of the gas particles are much less than the escape velocity the gas will be kept as an atmosphere.
Laboratory Tools
In this lab we will make use of the Gas Retention Simulator designed by the University of Nebraska-Lincoln. This simulator shows how gas escapes from a region depending on its temperature and the escape velocity. The box in the upper left corner, Chamber, is a chamber holds the gas. In the upper right panel the Distribution Plot shows the distribution of velocities for the selected gas and temperature. The box in the lower left, Chamber Properties, allow you to set the chamber properties, that is the temperature of the gas and the escape speed. The panel in the lower right, Gases, allows you to choose up to 3 gasses to put in the chamber. Note you see nothing in the upper two panels if no gas is selected. To start the simulation click the start simulation button in the lower right side. Note you must stop the simulation to make changes.
We will also use the Gas Retention Plot from the University of Nebraska-Lincoln Astronomy Department. Here the upper left panel is the Gas Retention Plot. The upper right panel, Gasses allows you to select which gasses your want on the Gas Retention Plot. The middle right panel, Plot Options, allows you to choose which planets and moons you want displayed on the plot. The bottom panel, Custom Object Properties, allows you to control a red dot on the plot, by varying the temperature and a planets size and density.
Assignment
Let’s start with the Gas Retention Simulation and the case of Earth. Set the temperature at 280 and allow escape from the chamber. Set the escape speed at 1,120 m/s, one tenth the escape speed from Earth. Now choose as the gasses, oxygen, nitrogen and helium and start the simulation. Which gasses stay in Earth’s atmosphere and which escape?
Now let’s change to Earth’s moon, same temperature of 280 but set the escape speed to 238 m/s. Explore other gasses, can any gas remain on the Moon as an atmosphere?
Now let’s change to a situation like on Mars. Set the temperature to 220K and the escape speed to 500 m/s. Set the gasses to oxygen, carbon-dioxide and water. What happens and what does this tell us about the atmosphere on Mars?
Finally let’s look at the giant planets. Use the minimum temperature of the simulator 100K and the maximum escape speed 1900 m/s and set the gasses to helium and hydrogen. This is actually less than one tenth the escape speed from Uranus, but the simulator only goes this high. Why do the giant planets have hydrogen and helium in their atmospheres, but terrestrial planets and moon don’t?
Now let’s turn to the Gas Retention Plot. In the Plot Options panel click on all the planets and moons. Now in gasses click on hydrogen and helium. Notice the difference between the giant planets and everybody else. You can drag the red dot over to Earth’s location. Now move it up so that helium would stay bound to Earth. What would Earth’s radius have to be in that case?
Now click off hydrogen and helium and click on water. What planet can almost hold undo water? Click off water and click on carbon dioxide. What temperature would Mercury have to be to keep carbon dioxide in its atmosphere? Wh temperature would Earth’s Moon need to have?
Questions
- Why is it easier for a planet to have carbon-dioxide than water vapor in its atmosphere?
- How cold would the Earth have to be to keep hydrogen it its atmosphere?
- If you found a new planet and determined it had no atmosphere what are the two possible explanations for why that would be the case?
