The molecules that are trapped in a planet’s atmosphere depend on their mass, the planet’s mass, the planet’s radius, and the planet’s temperature. The equation showing the temperature limit is given in Module 5c (the planet must be cooler than this to retain the gas over times on the scale of the lifetime of the Solar System).
(a) On a log-log plot draw the lines showing the temperature limits for molecular hydrogen (H2) and carbon dioxide (CO2) as a function of M/R (where M is the mass in Earth masses [i.e. M = M/MEarth ] , R is the radius in Earth Radii). [Plot log(Temperature) on the y axis and log(M/R) on the x axis.] Show your calculations for one of the molecules.
(b) Then, for all of the planets (not including dwarf planets), make a table showing the data (M, R, M/R, log(M/R), surface temperature, and log (surface temperature) ). Add points on the plot in (a) for the surface temperature of all of the major planets. (You will need to look these up somewhere. You will find that this can be a bit confusing! For example some internet sites confuse average temperature with lowest temperature. Giant planets don’t have a surface but you can find something like this, perhaps called cloud layer temperature.) Your final plot will have two lines (one for each of the molecules) and eight points (one for each planet).
(c) Briefly discuss the results. Which planets are close to a limit and what might that mean for gas retention?
