Planetary atmospheres

3.4 Planetary atmospheres

This section will discuss the formation and evolution of planetary atmospheres. In every case the planet’s original atmosphere will have come from the solar neb- ula out of which the Sun and planets formed. Its composition will thus have been similar to that of the Sun so that it will have been largely composed of the light elements hydrogen and helium. This was the only source of the atmospheres of the outer planets but may not have contributed very much to the terrestrial plan- ets as, by the time they had formed, the solar wind of the young star would have ejected much of the solar nebula outwards beyond the inner planets. In addition, as will be seen below, an atmosphere of light gases could not have been kept by these relatively small planets due to their relatively high surface temperatures and low gravity.

Consider an atmosphere made up of a number of different gases, some of light molecules, such as hydrogen and helium, and some of heavier molecules, such as carbon dioxide, ammonia and methane. The law of Equipartition of Energy states that all species of molecules in the atmosphere will have roughly equal kinetic

energies (½mv 2 ). This means that for a given temperature, lighter molecules with smaller masses, will have higher velocities than heavier molecules. The average kinetic energies of the gas molecules will depend on the temperature of the atmo- sphere so, in hotter atmospheres, the molecules will be moving faster.

The average kinetic energy of motion of a molecule is related to the absolute temperature, T, by:

1/2mv 2

m 2 kg s K .

Our Solar System 2 – The Planets

Giving:

For a given temperature (and hence kinetic energy), the velocity of a given mol- ecule will be inversely proportional to the square root of its molecular mass, so molecules of hydrogen (molecular mass 2) will move on average four times faster than those of oxygen (molecular mass 32). If a molecule in the upper part of an atmosphere happens to be moving upwards at a suffi ciently high velocity, then it could exceed the escape velocity of the planet and so escape into space. The escape velocity depends on the mass of the planet so it should be apparent that hot, light planets might well lose all the lighter molecules that they might have once have had in their atmospheres whilst cooler, more massive planets will be able to hold on to even the lightest molecules within their atmospheres.

Let us calculate the average velocity for nitrogen molecules which have a mass

kg: v

So, for nitrogen (molecular mass 28) and oxygen (molecular mass 32) in the Earth’s atmosphere at a temperature of ∼300 K, the typical molecular speeds are

0.52 and 0.48 km s , respectively. This is far smaller than the escape velocity of the Earth which is 11.2 km s so we would not expect these gases to escape from our atmosphere. In fact, it is not quite as simple as that. Due to collisions between them, molecules do not all move at the same speed; some are faster and some slower than the average. The relative numbers of molecules at speeds around the average is given by the Maxwell–Boltzmann distribution .

A very small fraction of the molecules in a gas have speeds considerably greater than average, with one molecule in 2 million moving faster than three times the average speed, and one

in 10 16 exceeding the average by more than a factor of 5. Consequently, a very few molecules may be moving fast enough to escape, even when the average molec- ular speed is much less than the escape velocity. Calculations show that if the escape velocity of a planet exceeds the average speed of a given type of molecule by a factor of 6 or more, then these molecules will not have escaped in signifi cant amounts during the lifetime of the Solar System.

In the Earth’s atmosphere, the mean molecular speeds of oxygen and nitrogen are well below one-sixth of the escape speed. Now consider the Moon: its escape velocity is 2.4 km s and, assuming that any atmosphere it might have had would

have been at the same temperature as our own, the mean molecular speeds of

86 Introduction to Astronomy and Cosmology

nitrogen and oxygen would be only about fi ve times less than the Moon’s escape velocity so it is not surprising that it has no atmosphere! If Mercury had an atmo- sphere it would have a temperature of ∼700 K, giving nitrogen or oxygen an aver- age molecular speed of about 0.8 km s , signifi cantly more than one-sixth of Mercury’s escape velocity of 4.2 km s . There has thus been ample time for these molecules to escape.

These arguments allow us to see why our own atmosphere contains very little hydrogen. Hydrogen molecules move, on average, at about 2 km s , which is just more than one-sixth of the Earth’s escape velocity. Hydrogen will thus have been able to escape and now makes up only 0.000055% of the atmosphere! In contrast, consider Jupiter: its escape velocity is 60 km s and it has a surface temperature of only 100 K. In the Jovian atmosphere, the speed of the hydrogen molecules is only about 1 km s , 60 times less than the escape velocity, and so Jupiter has been able to keep the hydrogen as the largest constituent in its atmosphere.

Summary

• Mercury, the Moon and all satellites except for Titan and Triton have effec-

tively no atmospheres, though Mercury has an extremely thin ‘transient’ atmosphere of hydrogen and helium temporarily captured from the solar wind. • The other terrestrial planets cannot hold on to hydrogen or helium, so will

have lost all the initial atmospheres derived from the solar nebula. • The outer planets are both massive and cold and so have been able to keep all of the light gases acquired from the solar nebula. Though similar in mass to the Moon, Titan and Triton are suffi ciently cold to have kept atmospheres, largely made up of nitrogen.

• The dwarf planets Pluto and Eris are so cold that any nitrogen or other gases would be frozen and form part of the surface.

3.4.1 Secondary atmospheres

Later in their lives, the planets Venus, Earth and Mars gained further atmospheres which were the result of out-gassing from volcanoes. It is thought that only 1% of the current Earth’s atmosphere remains from its primeval atmosphere. Volca- nic eruptions produce varying amounts of gases which arise from the melting of the planet’s crust at great depth. All eruptions differ but, in general, release gases such as water vapour, carbon dioxide, sulphur dioxide, hydrogen sulphide, ammonia, nitrogen and nitrous oxide. It is thought that ultraviolet light falling on water vapour in the upper atmospheres of Venus and Mars would have split it into hydrogen and hydroxyl (OH). The hydrogen molecules would then have escaped

Our Solar System 2 – The Planets

3.4.2 The evolution of the earth’s atmosphere

We have seen how the primeval atmosphere of the Earth, largely made up of hydro- gen and helium would have been lost and replaced by a secondary atmosphere which was the result of volcanic out-gassing. It was primarily made up of carbon dioxide and water vapour, with some nitrogen but virtually no oxygen and con- tained perhaps 100 times as much gas as at present. As the Earth cooled, much of the carbon dioxide dissolved into the oceans and precipitated out as carbonates.

A major change began some 3.3 billion years ago when the fi rst oxygen pro- ducing bacteria arose on Earth and which, in the following billion years, gave us much of the oxygen in our atmosphere. Oxygen and bacteria could then react with the ammonia released by out-gassing to form additional nitrogen. More nitrogen was formed by the action of ultraviolet radiation on ammonia in a pro- cess call photolysis.

As the vegetation increased, the level of oxygen in the atmosphere increased signifi cantly and an ozone layer appeared. This gave protection to emerging life forms from ultraviolet light and enabled them to exist on land as well as in the oceans. By about 200 million years ago about 35% of the atmosphere was oxy- gen. The remainder of the atmosphere was largely nitrogen as, alone of all the gases present in the secondary atmosphere, it does not readily dissolve in water.

Volcanic activity recycles and replenishes the molecules of the atmosphere and has, in particular, recycled the greenhouse gas carbon dioxide – necessary for the Earth’s surface temperature to have remained suffi ciently warm for the existence of life. The carbonates, formed as carbon dioxide dissolves in the oceans, and shells of calcium carbonate produced by marine life, fall to the ocean beds. Thus, over time, one might expect the amount of carbon dioxide in the atmosphere to reduce, tending to make the Earth colder. However, movements of the oceanic plates of the Earth’s crust bring them up against the continental plates. As the oceanic plates are denser, they pass under the continental plates – a process known as

subduction – and volcanic activity releases the carbon dioxide back into the atmosphere.