Atmospheric Escape

The online version of this lab below is in the form of a canvas quiz though I can see running this in a variety of different ways online (group discussion based, short answer, etc). I recommend running this with an accompanying discussion forum so the students can discuss with their peers the activity, questions and workout problems together as they would in an in-person lab. You and your TAs can monitor the forum and jump in to help, if necessary.

Introduction

The ability of a planet to retain or hold an atmosphere depends predominantly on two factors: Temperature and Gravity. The temperature of a planet is important because it is really just a measure of how fast, on average, the molecules of gas in the atmosphere are moving. 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. Please note, the calculations in this quiz will not appear on the midterm exam. You are however responsible for understanding the concepts, in particular how temperature and pressure dictate which molecules are found and their retention in an atmosphere.

Goals

You will use the following data tables and equations to compute the escape velocity, mass and temperatures of planets given various atmospheric molecules to answer the questions.

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. Table 1 above lists the escape velocities and distances for a few worlds in our solar system.

The temperature of a planet is determined mainly by its distance from the Sun. Table 2 below shows the temperature a planet would have at various distances from the Sun.

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 mass of a molecule is measured in atomic mass units (amu). You can find the periodic table in Wikipedia where you can look up the atomic mass of different elements which molecules are comprised of. The mass of each element is given as the number at the bottom of each box. To find the mass of a molecule, just add up the masses of each element times the number of each element in the molecule which is given by the subscripts. A few molecules and their masses are given in Table 3 below.

The speed of a molecule of gas (in m/s) can be determined from the equation:

v g a s = 157 ( T e m p e r a t u r e m o l e c u l a r m a s s )

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:

v g a s < 1 6 v e s c

For example, the escape velocity of earth is 11,200 m/s. To calculate the speed molecules have to reach to achieve Earth's escape velocity we write