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Thermal Escape of Atmospheres The temperature of a planetary atmosphere is an indication of the average kinetic energy of its molecules. If some molecules in an atmosphere have too much kinetic energy, they may be able to escape the gravitational pull of a planet and float away into space. For a given temperature, most molecules in an atmosphere will zoom around at speeds near the peak thermal speed. (A small percentage of molecules will zoom around much more quickly.) = 3 vth (measured in m/s) is the peak thermal speed. kB is the Boltzmann constant: 1.38 x 1023 m 2 kg1 s 2 K 1 . T (measured in K) is the temperature. m (measured in kg) is the mass of the atmospheric molecule The escape speed from a planets surface depends on the strength of its gravitational field. = 2 v (measured in m/s) is the escape speed. G is the gravitational constant: 6.67 x 1011 m 3 kg1 s 2 . M (measured in kg) is the mass of the object you want to escape. r (measured in m) is the distance from the center of the object you want to escape. In the distant past, liquid water was widespread across the surface of Mars. Today, most of that water is long gone. In part, this is because Mars does not have a protective ozone layer to shield it from the Suns UV radiation, which is energetic enough to dissociate water molecules into separate hydrogen and oxygen components. A planet will typically retain a gas in its atmosphere only if the escape speed is at least 6 times larger than the peak thermal speed of the gas. Can Mars hold on to a molecular hydrogen atmosphere? What about a molecular oxygen atmosphere? Given your answer above, how does this explain the red color of the Martian crust?

Added by Encarnacion H.

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