An atmospheric molecule has an average thermal velocity, Vth, that may be estimated from the Maxwell velocity distribution:
The probability that a molecule will escape from any given atmosphere depends on the relationship between Vesc and Vth: a molecule escapes more easily the lighter it is (which really goes without saying), the smaller the planet, and the higher its temperature. This explains the absence of a permanent atmosphere on Mercury, as well as the atmospheric composition of the giant planets, which is dominated by hydrogen and helium: their gravitational field is such that even hydrogen has not been able to escape over the whole lifetime of the Solar System. In contrast, the gravitational fields of the terrestrial planets are insufficient to retain hydrogen and helium: their chemical composition is dominated by the elements C, N, and O (as CO2, N2, H2O, and O2).
In what form did the carbon, nitrogen and oxygen occur in the protosolar nebula? Assuming thermodynamic equilibrium, the abundance of molecules containing C and N is governed by the following reactions:
which tend to form CH4 and NH3 at low temperatures and high pressures, and CO and N2 at high temperatures (a few hundred K) and low pressures. When CO and N2 predominate, CO reacts with H2O to form CO2:
Based on thermodynamic equilibrium, therefore, to a first approximation we may expect to find an atmosphere rich in CH4 and NH3 in the giant planets, and one that is dominated by CO, CO2, and N2 (following the escape of hydrogen) in the terrestrial planets. Overall, this model agrees with observations. It does not, however, explain the atmospheres of Titan, Triton, and Pluto, which are rich in N2 and CH4. Lewis and Prinn (1984) have suggested that CO and N2 that formed in the pro-tosolar nebula at its beginning, when the temperature was sufficiently high, could have been trapped when the disk cooled, if this took place sufficiently quickly. In the case of Titan, it is possible that nitrogen was present originally in the form of ammonia, NH3, which was subsequently altered into N2 through photolysis in the atmosphere.
220.127.116.11 The Thermal Structure of the Planetary Atmospheres
An atmosphere is the gaseous envelope that separates the body from its external environment (interplanetary medium, solar wind, or magnetosphere). The processes that take place there arise partly through this interaction with the outer environment (photolysis of neutral molecules, dissociation and ionization, interaction with the solar wind and, where appropriate, with the magnetic field), and partly its interaction with the surface (volcanism, tectonics, and greenhouse effect), or with the deeper layers (internal dynamics). The same mechanisms are likely to be present in the atmospheres of exoplanets (see Chap. 7).
Let us remind ourselves of the general nomenclature (Fig. 4.12): the lower region of an atmosphere, where all the non-condensable components are uniformly mixed, is the homosphere. Above this, and separated from it by the homopause, is the heterosphere where gases diffuse independently of one another as a function of the atomic or molecular mass. The homosphere is divided into several regions, depending on the dominant energy-transfer process within each. The lowest layer of an atmosphere is the troposphere. In the terrestrial planets, this layer is in direct contact with the surface. Within it the temperature decreases as altitude increases. Above the troposphere (at an altitude of approximately 12 km for the Earth), lies the stratosphere. The temperature increases as altitude increases, because of the absorption of solar radiation by the molecules and aerosols in the atmosphere as a function of the photochemical reactions that take place. (In the case of the Earth, this is the region where the ozone layer forms though photochemical changes to oxygen; in the giant planets, methane photochemistry dominates within this layer.)
In general terms, the parameters of an atmosphere (temperature, pressure, and density) are linked by the following equations:
• the hydrostatic equilibrium law, which is an exact balance between the pressure-gradient force and the gravitational force:
where P is the pressure, p the density, z the altitude, and g gravity;
t Atomic oxygen
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