PHYSICS OF THE SPACE ENVIRONMENT

 

PHYS/EATS 3280

 

 

Notes Set 3

 

 

The Neutral Upper Atmosphere

 

The structure of the upper atmosphere is governed by the basic physical laws of Gravitation, the Ideal Gas Law and Hydrostatic Equilibrium.  This leads to a pressure and density variation with altitude of the form shown in Figure 3.1   How can we explain these strong variations in temperature, pressure and density?  And how can we predict the temperatures, pressure and air densities at typical spacecraft altitudes ?

Figure 3.1 : The variation of some key atmospheric properties with height.

 

These questions can be answered by considering first the fundamental law of hydrostatic balance or equilibrium.

 

Hydrostatic equilibrium is the balance between the weight of a gas column and the pressure of the gas.  Consider a gas column with density r and of cross-sectional area A as shown in Fig. 3.2.

 

Fig 3.2

 

Since pressure is force per unit area the difference in pressure between the top and bottom of the column is given by

 

            P-(P+dP) =grdz

           

which can be rearranged to give

 

            dP = -rgdz

 

the equation of hydrostatic balance.  By using the ideal gas equation P = rRT/M  [where R = 8.314 J mole-1 K-1 is the Universal Gas Constant, r is the density of air in kg m-3, M is mean molecular weight – nominally 0.0289 kg mole-1 - and T is the temperature] we can substitute for  r= PM/RT  to obtain

 

            dP/P  = (-Mg/RT)dz

 

            d lnP  = (-Mg/RT)dz

 

            lnP  = (-Mg/RT)z + const

 

or        lnP  = (-Mg/RT)z + ln P0

 

or         P(z)  = P0 exp(-z/H) where H = RT/Mg

H is known as the scale height of the atmosphere and can be locally defined for regions where the temperature is fairly constant. The scale height basically defines how rapidly atmospheric pressure decreases with altitude.  It has a value of about 7 km in the very lowest parts of the atmosphere; around 5 km in the middle atmosphere where, as we will see the temperature is very low; but has much larger values towards the top of the atmosphere  where the temperatures are very high ~ 55 km at 300 km above the surface.

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Given that the scale height in the lower atmosphere is only about 7 km, only a small fraction of the total mass of the atmosphere is above about 15 km. 

 

This tenuous gaseous medium that constitutes the upper atmosphere exhibits a considerable range of different characteristics each of which may be used to divide the atmosphere into different regions.  These different divisions are summarized in Figure 3.3.

 

 

Figure 3.3  The division of the atmosphere in to regions based on various properties

 

 

Temperature Regimes - Division based on temperature structure

 

The traditional division of the atmosphere is based on its temperature structure with various 'spheres' where the temperature gradient is either positive or negative separated by 'pauses'.  On the average the temperature decreases in the troposphere by about 7 ºC/km up to 10-12 km height where there is a fairly well defined tropopause.  The lower stratosphere is at first isothermal but then the temperature increases as a result of the absorption of solar ultra violet radiation by ozone.  The maximum heating occurs at about 50 km height and defines the stratopause.  Above this the temperature again decreases to the mesopause which is often rather ill-defined but can be considered as a region between 80 and 100 km where the coldest temperatures in the atmosphere occur.  Mesopause temperatures during summer at high latitudes can be as low as 110 K.  Above this, in the thermosphere,  the temperature again rises as a result of solar heating at first rapidly but then more slowly toward the so called exospheric temperature which, depending on the degree of activity on the sun, can be anywhere between 800 K at solar minimum and  2500 K at solar maximum.  In the thermosphere the heating is mainly due to photo-dissociation of molecular oxygen and photo-ionization of atomic oxygen by extreme UV radiation.

                   

Chemical Composition Regimes - Division based on composition.

 

Below about 100 km the composition of the atmosphere can be regarded as constant with the proportions of the main gases being as in Table 3.1

Table 3.1: Composition of the atmosphere at the ground.

Molecule                      Mass number                Volume %        Concentration (cm-3)

Nitrogen                       28.02                           78.1                 2.1 x 1019

Oxygen                        32.00                           20.9                 5.6 x 1018

Argon                           39.96                           0.9                   2.5 x 1017

Carbon Dioxide            44.02                           0.03                 8.9 x 1015

Neon                            20.17                           0.002               4.9 x 1014

Helium                          4.00                             0.0005             1.4 x 1014

Water                           18.02                           variable          

 

The relatively constant composition is maintained by turbulent mixing and as a result the region can be designated the turbosphere or homosphere.  Above this the mean distance between the air molecules is larger than the scale of the eddy motions that mix the homosphere and these can no longer be maintained.  Accordingly, the individual component gases separate according to their molecular weights with the heaviest gravitating towards the bottom and the lightest, as we will see, literally escaping out the top.  As a result, the composition and the mean molecular weight of the atmosphere varies with height as illustrated by Figure 3.

 

In the homosphere the scale height for all of the main component gases is the same, H=RT/gMav where Mav is the mean molecular weight, while in the heterosphere the concentration of each gas decreases with height in accordance to its own scale height given by H=RT/gMi where Mi is the molecular weight of the individual component in question.  The atmosphere is then said to be in diffusive equilibrium with the individual gases establishing their own height variations as defined by there masses and the local temperature.  This is of great importance at spacecraft altitudes and is illustrated in Figs. 3.4 and 3.5

 

Fig 3.4. : The variation of atmospheric composition with height.

 

Fig 3.5. : More on the variation of atmospheric composition with height.

 

Variations in thermospheric composition

 

In the thermosphere the effects of molecular diffusion and the lack of turbulent mixing determine the variation of composition with altitude.  Molecular diffusion becomes rapid because of the increased mean free path between collisions and the component gases attain their own vertical distributions in accordance with the hydrostatic law as described above.  The action of solar UV radiation to dissociate molecular oxygen leads to an atmosphere rich in atomic oxygen.  The greater mass of the nitrogen molecule causes the atmosphere to be nearly pure atomic oxygen at around 300 km altitude.  At even greater altitudes ( >1000 km) the next lightest atom, helium, takes over and we are in the heliosphere [N.B. there are two uses of this term – see later].  Above 3000 km hydrogen begins to become the dominant species and the region is sometimes designated the protonosphere.  The actual transition heights is dependent on the thermospheric temperature profile since this controls the scale heights of the components.   If the exospheric temperature is increased the heavier components are able to stretch up to higher altitudes as their scale heights increase and so, at a given altitude, the number density of a component increases.  A notable exception to this is hydrogen since at higher exosphere temperatures the loss rate to space increases and since the source in the lower atmosphere is more or less constant the concentration must decrease if the flux out the top is to balance the flux in at the bottom.  This is illustrated in Fig. 3.6.

Fig. 3.6 : The effect of temperature on exospheric composition.  Geopotential heights are given on the left of the diagrams, geometric heights on the right.

 

 

Division based on gaseous escape

 

Due to the decreasing density of the atmosphere the mean distance between collisions increases with height and above about 500 km this distance is so great that a molecule or atom with sufficient energy can leave the Earth's gravitational field and therefore leave the atmosphere completely.  This height is known as the exobase.  In order to leave the earth's gravitational field the particle must have sufficient energy to overcome gravity, i.e., its kinetic energy mv2/2 > mg(h)(Re+h) where the right hand side of the equation is the work required to move a particle with mass m at altitude h to infinity.  At the surface of the earth the required escape velocity  is 11.2 km s-1 regardless of the mass of  the particle.  According to the Maxwell-Boltzmann velocity distribution only the very lightest molecules and atoms are likely to have sufficient velocity to leave the atmosphere at typical exospheric temperatures.  The velocity distribution for hydrogen atoms is illustrated in Fig. 3.7.

 

 

Fig. 3.7.

 

 

Since hydrostatic equilibrium depends on the gas law and thereby the assumption of a Maxwell-Boltzmann velocity distribution  it cannot apply where there is significant gas loss from the atmosphere since the high velocity end of the distribution is being eaten away.  Hydrostatic equilibrium should therefore not be assumed above the exobase but the equation is usually used (for want of a better one) to describe the variation of pressure and density with height up to 2000 km.