Carbon Dioxide in the Martian Atmosphere

Spectroscopic studies of Mars, made over a period of more than 80 years, had produced no conclusive evidence concerning the nature of the atmospheric gases. All that could be said was that if certain gases were present, then their abundances must be less than various specified amounts. But there was no positive proof that these gases were present at all.

Although it was quite certain that Mars had an atmosphere, and approximate estimates had been made of its pressure, nothing was definitely known about its composition until near the end of 1947. On October 7 of that year, G. H. Kuiper, then at the McDonald Observatory, Texas, compared the infrared spectrum of Mars with that of the Moon obtained at the same time. The purpose of this comparison was to allow for spectral absorp tion in Earth's atmosphere. Since the Moon has no atmosphere, any difference in the spectra of Mars and the Moon could then be attributed to gases present in the Martian atmosphere.

The spectra obtained in this manner are reproduced in figure 5.1. The spectrum of Mars shows two small dips at wavelengths of 1.57 and 1.60 ¡x, with indications of others at 1.96, 2.01, and 2.06 /¿, which are not present in the spectrum of the Moon.2 These absorption wavelengths are characteristic of carbon dioxide, so Kuiper concluded that this gas is present in the Martian atmosphere. Confirmation was obtained by a more detailed observation of the spectrum made in February 1948 when Mars was closer to Earth. The three absorption bands in the wavelength region of 2 /x were more pronounced than in the original spectrum in figure 5.1. From the extent of the spectral absorption, Kuiper estimated the mass of carbon dioxide over unit area of the surface of Mars to be about twice the average over Earth's surface.

On Earth, atmospheric (barometric) pressures are commonly stated in terms of millimeters or centimeters, or inches, of mercury. A standard atmosphere at sea level on Earth, for example, is 760 millimeters of mercury. But 760 millimeters of mercury on Mars would not be the same pressure as a standard atmosphere on Earth because of the difference in the gravitational forces on the two planets. Consequently, other units are used to express pressures both on Earth and on the planets so that they can be compared with one another.

One such unit in common use is the bar, defined as a pressure of 1 million dynes per square centimeter (dyn/cm2). (The dyne

2 The symbol /x stands for 1 micron, which is one-millionth part of a meter. It is a convenient unit for expressing wavelengths in the infrared region of the spectrum.

FIGURE 5.1. Infrared spectra of Mars and the Moon. (Spectra by G. P. Kuiper; courtesy University of Chicago Press.)

is a unit of force and pressure is force per unit area.) It happens that the standard atmosphere of 760 millimeters of mercury is equivalent to 1.013 million dyn/cm2, or 1.013 bars. When making rough comparisons, 1 bar may be taken as approximately equivalent to the atmospheric pressure at Earth's surface. When it is required to indicate pressures of a smaller order of magnitude, it is convenient to employ the millibar, which is a one-thousandth part of a bar, as the unit. Thus, the standard atmospheric pressure on Earth is roughly 1000 (actually 1013) millibars.

Another way of stating the pressures or, rather, the abundances of particular atmospheric gases is in terms of their effective depth or reduced thickness. The reduced thickness of a particular gas is equal to its hypothetical thickness at a uniform density. This quantity of gas is taken to be that which would, at normal (terrestrial) atmospheric temperature and pressure, exert the same force on the surface as the actual gas in the planet's atmosphere. The unit commonly used is the meter-atmosphere, and for carbon dioxide (molecular weight 44) on the surface of Mars, the reduced thickness can be related to the pressure by

1 meter-atmosphere = 0.074 millibar

The abundance of carbon dioxide in the terrestrial atmosphere is equivalent to a reduced thickness of roughly 2 meter-atmospheres. Hence, according to Kuiper's estimate given above, the reduced thickness of the gas in the Martian atmosphere would be about 4 meter-atmospheres. A recalculation of the data, made by J. Grandjean and R. M. Goody in 1955, indicated that the quantity of carbon dioxide on Mars was more than six times greater than Kuiper had thought. This would make the reduced thickness about 27 meter-atmospheres, and the contribution of carbon dioxide to the pressure at the surface of Mars, that is, the partial pressure of this gas, would be roughly 2 millibars.

At the time these estimates were made, the total atmospheric (or barometric) pressure on Mars was considered to be in the vicinity of 80 millibars, and it appeared that carbon dioxide gas would constitute only a few percent of the atmosphere. The other major constituents would then presumably be gases that could not be identified because they did not produce detectable spectral absorption lines (or bands). Two such gases are nitrogen and argon which have absorption lines (or bands) in the short-wavelength (ultraviolet) region that cannot pass through Earth's atmosphere.

As mentioned earlier, nitrogen, presumably released from Earth's outer layers, is the chief constituent of the terrestrial atmosphere. Because it is relatively inert chemically and has a moderately high molecular weight (28), it seemed reasonable to suppose that, in spite of the smaller gravitational attraction, nitrogen would also be found in the Martian atmosphere. Furthermore, argon, which is even more inert chemically and has a higher molecular weight (40) than nitrogen, might well be expected to be present, also. As on Earth, the argon would be produced by radioactive decay of potassium-40 in the outer layers of Mars.

In 1961 a typical estimate of the proportions of the major constituents of the Martian atmosphere was the following: 93 molecular percent of nitrogen, 5 to 6 percent of argon, and 1 to 2 percent of carbon dioxide. There would undoubtedly be some minor (trace) constituents, as in the terrestrial atmosphere. Among these, water vapor was considered to be a possibility, partly because of the existence of the polar caps. It was not until 1963 that the presence of water vapor in the Martian atmosphere was definitely established.

A dramatic change in the views concerning the composition of the atmosphere of Mars resulted from a study of the infrared spectrum made during the opposition in the early part of 1963. It appeared that the abundance of carbon dioxide was greater than had been accepted previously, about 55 meter-atmospheres, corresponding to a partial pressure of roughly 4.2 millibars at the surface. At the same time, the total atmospheric pressure on Mars was estimated to be in the vicinity of 25 millibars, rather than 80 millibars or so.

From these results the conclusion drawn was that the Martian atmosphere contains something like (4.2/25) X 100, or about 17 percent of carbon dioxide. Subsequent spectral investigations have indicated that the reduced thickness of this gas on Mars may approach 100 meter-atmospheres; its partial pressure would then be approximately 7.5 millibars. At the same time, the estimates of the total pressure have been reduced some what, and values ranging from about 7 to around 20 millibars have been suggested.

The current view is that the atmosphere of Mars contains at least 50 percent of carbon dioxide. On the basis of the lower value of the atmospheric pressure given, some scientists have, in fact, suggested that the Martian atmosphere consists almost entirely of carbon dioxide. It may be significant, too, that a reconsideration of the computations made by Grandjean and Goody, based on Kuiper's approximate data of 1948, but using more recent values of the total atmospheric pressure, leads to the conclusion that carbon dioxide constitutes from 50 to 100 percent of the Martian atmosphere.

Water Vapor in the Martian Atmosphere

In addition to carbon dioxide, water vapor has been definitely identified in the atmosphere of Mars. This substance is of special interest because of its connection with the development of life on the planet. That water vapor is present has been assumed for many years. The brilliant white polar caps of Mars have long been thought to consist, at least in part, of small ice (or hoarfrost) crystals. Because one cap increases in size during the local autumn and winter in its hemisphere while the other is decreasing during the local spring and summer in the other hemisphere, it appears that there is a transfer of water vapor from one hemisphere to the other. If this is the case, there should always be some water vapor in the atmosphere of Mars.

During the early years of this century, observers claimed to have detected some of the characteristic infrared bands of water vapor in the Martian spectrum. Later work cast doubt on the validity of the results, and for some time the matter remained uncertain. Estimates of the amount of water vapor in the atmosphere were made on the basis of various meteorological phenomena, such as the disappearance of morning haze, the change in size of the polar caps, etc., but there was no really positive evidence that there was any water in the atmosphere.

In 1963, however, L. D. Kaplan, G. Munch, and H. Spinrad, of the California Institute of Technology and the Jet Propulsion Laboratory, obtained definite spectroscopic proof that there is water vapor in the atmosphere of Mars. The positive detection was made possible by observation of the Dop-pler shift of the lines in the Martian spectrum. It is a familiar fact that the pitch (frequency) of a train whistle or automobile horn appears first to increase and then to decrease as the vehicle passes by a stationary observer. The change in frequency (wavelength), as a result of the relative motion of the source and the observer, applies to light as well as to sound.

The general phenomenon was first described by the Austrian physicist C. J. Dop-pler in 1842 and is called the Doppler effect. As a result of this effect, the wavelengths of all lines in the spectrum of Mars, as measured on Earth, are increased when the two planets are moving away from each other. At, or close to, eastern quadrature (fig. 3.9), Mars appears to be receding from Earth at its maximum speed of about 15 km/sec (24 mps). The conditions should then be optimum for observing the Doppler effect on the lines in the spectrum of Mars, and this could be used as an aid to identifying their source.

The spectrum of Mars, taken at the Mount Wilson Observatory on the night of April 12-13, 1963, when the planet was at eastern quadrature, after the opposition of February 4, 1963, showed the presence of a band in the wavelength vicinity of 8200 A.3 This band was caused by absorption by water vapor in Earth's atmosphere, but alongside each of the lines in the band was a weaker absorption line, shifted in wavelength by a mean value of 0.42 A. The wavelength shift Ad, caused by the Doppler effect, can be readily calculated from the expression where A is the unshifted wavelength, v is the velocity with which Mars appears to be receding from Earth, and c is the velocity of light. In the present case, A is 8200 A, v is 15 km/sec , and c is 3.0X105 km/sec. Therefore, XD should be 0.41 A.

FIGURE 5.2. Doppler shift in the spectrum of water vapor near 8200 A. (After L. D. Kaplan, G. Miinch, and H. Spinrad.)

The shape of the spectral absorption curve, averaged over four lines of different wavelengths in the vicinity of 8200 A, is seen in figure 5.2. The vertical line indicates the wavelength in the normal spectrum of water vapor, and which probably arises from absorption in Earth's atmosphere. The arrow

3 The symbol  represents the angstrom unit, equal to 10"8 centimeters, which is commonly used to express wavelengths of spectral lines.

shows where the Doppler-shifted line in the Martian spectrum should appear according to the calculation made above. The slight dip in the curve, located very close to the position of the arrow, is thus evidently caused by absorption by water vapor in the atmosphere of Mars.

It is the general practice to express the water vapor abundance on Mars in terms of the precipitable water. This is the hypothetical average (and uniform) depth of liquid water that would be formed over the whole planet if all the water vapor in the atmosphere were condensed into liquid water.

The quantity of water on Mars was calculated from the spectroscopic measurements (fig. 5.2) to be 1.4±0.7 mg/cm2. Because liquid water has a density of 1 g/cm3, a mass of 1 mg/cm2 corresponds to a depth of 10~3 c< "itirneter of liquid water. The estimated precipitable water in the atmosphere of Mars is thus (1.4±0.7) X10"3 centimeter. Such small amounts are often stated in microns; as defined in the footnote on page 76, 1 micron is 10~6 meter, or 10"4 centimeter. Hence, the average amount of precipitable water on Mars was found to be 14±7 microns.

For comparison, it may be noted that the amount of precipitable water is around 1000 microns over desert areas on Earth and it is up to 10 times as large where the humidity is high. As the average over the whole Earth is about 2000 microns, the Martian atmosphere is extremely dry from the terrestrial point of view.

The observations on the 8200-A band described above were repeated and confirmed at the McDonald and Lick Observatories during the Martian apparition in the winter of 1964-65. Separate spectrograms were taken of the northern and southern hemispheres of the planet, and a definite connection was found between the estimated quantities of water vapor in the atmosphere and the changes in size of the polar caps. Detectable amounts of water vapor, approximately 15 microns of precipitable water, began to appear in the northern hemisphere in the late Martian spring when the dimensions of the north polar cap started to decrease rapidly. When the rate of shrinkage had leveled off, in late spring, water vapor was found to be distributed almost equally (10 microns) over both northern and southern hemispheres. At this time, water vapor was beginning to concentrate over the southern hemisphere, and by early summer in the northern hemisphere (early winter in the southern hemisphere) most of the water vapor (25 microns) was in the atmosphere over the southern hemisphere of Mars. These results suggest that water is transferred as vapor back and forth from one polar cap to the other according to the season.

The period during which reliable spectroscopic observations can be made for any given Martian apparition is very limited. Consequently, a series of studies of this kind at several opportunities will be required to determine how the water vapor in the atmosphere in the two hemispheres varies throughout the whole Martian 5 ear. It may be mentioned that on Earth there is relatively little transfer of water vapor between the Northern and Southern Hemispheres. For one thing, the changes in the polar caps of Earth are much less drastic than on Mars, and for another, there is a great deal more water available in each Hemisphere.

An alternative procedure for eliminating or reducing the effect of Earth's atmospheric water vapor is to make spectroscopic measurements at high altitudes. The radiations reaching the instruments have then passed through only a small part of the atmosphere, for which allowance can be made. Observations of the infrared spectrum of Mars, at a wavelength of 1.4^, were carried out in January 1963 from a balloon at an altitude of 14 kilometers

(45 000 feet) over France and also from the Jungfrau Scientific Station, Switzerland, at an elevation of 3.5 kilometers (11 200 feet). The results, according to A. Dollfus, indicated that the precipitable water on Mars was about 150 microns. This value, however, is thought to be too high.

In March 1963, the unmanned balloon Stratoscope II, carrying a 36-inch reflecting telescope and an infrared spectrometer, was launched from Palestine, Tex., and reached an altitude of some 80 000 feet. The absorption in the spectrum in the wavelength region of 2.1 ¡l was in best agreement with 10 microns of precipitable water in the atmosphere of Mars, but uncertainties in the reduction of the data did not permit a more precise conclusion than that the quantity of water was less than 40 microns.

Other Gases in the Martian Atmosphere

It is expected that there are small quantities of carbon monoxide and of oxygen (atoms and molecules), particularly in the upper layers of the Martian atmosphere, produced by the decomposition of carbon dioxide, viz

by the ultraviolet radiation of wavelength shorter than 1600 A in sunlight. As in Earth's atmosphere, some of the oxygen atoms (O) and molecules (O.) would probably combine to form ozone (03).

During 1968, an unpublished (oral) report from the Jet Propulsion Laboratory implied that spectroscopic evidence had been obtained for the presence of carbon monoxide in the atmosphere of Mars. Although this result has not yet been confirmed, there is little reason to doubt its accuracy. If there is indeed some carbon monoxide in the atmosphere of Mars, then traces of oxygen and ozone are probably also present. So far, however, they have not been identified.

Spectral observations of Mars are made at all possible opportunities with the object of detecting constituents of the atmosphere, in addition to those mentioned above. So far, negative results have been reported for methane (CH4), ammonia (NH3), nitrogen dioxide (N02), hydrogen sulfide (H2S), formaldehyde (HCHO), and acetaldehyde (CH3CHO).

A preliminary report, published in 1966, indicated that there might be traces of certain hydrocarbons, that is, compounds of hydrogen and carbon, known as substituted methanes, in the Martian atmosphere. If this had been correct, it would have had considerable significance in connection with the problem of the occurrence of life on the planet, but a careful review of the spectroscopic data showed that the results were probably caused by instrumental factors.

Among the gases which have been sought but not yet detected in the Martian atmosphere, special interest attaches to nitrogen dioxide. In 1963, C. G. Kiess and his associates in the United States claimed to have observed some of the characteristic lines of this molecule in the spectrum of Mars. On the assumption that significant amounts of nitrogen dioxide are present, they had previously (1960) developed novel interpretations of several Martian phenomena, including the nature of the polar caps and the yellow clouds and the cause of the so-called blue haze.

Because of its importance in these respects, several scientists have searched for the lines of nitrogen dioxide in the spectrum of Mars, but without success. It has been estimated, in fact, that the upper limit of the abundance of nitrogen dioxide in the Martian atmosphere is about 0.01 millimeter-atmosphere. This is much less than that normally found over the city of Los Angeles. Because nitrogen dioxide is decomposed by the ultraviolet radiation in sunlight, it is not surprising that the amount, if any, in the atmosphere of Mars is very small.

Composition of the Martian Atmosphere

In reviewing what is known about the composition of the atmosphere of Mars, all that can be said is that carbon dioxide is probably the major constituent. There are very small quantities of water vapor and possibly also some carbon monoxide. If the latter is present, then traces of oxygen and ozone are to be expected, but they have not yet been detected.

If the atmosphere of Mars was produced by the liberation of gases from the outer layers (crust) of the planet, in a manner similar to that which apparently occurred on Earth, some nitrogen should be present. Estimates of the composition of the gases exhaled by Earth's crust indicate that they contain roughly 5 to 10 molecules of carbon dioxide to one of nitrogen. On Earth, most of the carbon dioxide has been removed by processes requiring the presence of liquid water. It is doubtful, in view of the small amount of water now available, that any of these processes could have taken place to a substantial extent on Mars.

Furthermore, because molecular nitrogen is a relatively inert gas with a moderately high molecular weight, the loss of this gas, by chemical reaction or by escape into space, should be small. It would seem, therefore, that the ratio of carbon dioxide to nitrogen in the present atmosphere of Mars should not be greatly different from that of the gases released from the crust. If this is the same as on Earth, then the Martian atmosphere may have some 10 to 20 molecular percent of nitrogen. From the available data on the abundance of carbon dioxide and the total atmos pheric pressure on Mars, it would appear that this is possible but not certain.

It has long been assumed that the Martian atmosphere also contains some argon, perhaps a little over 1 percent of the quantity of nitrogen, as in Earth's atmosphere. Because there are undoubtedly potassium compounds near the surface of Mars, there will probably be some argon in the atmosphere produced by radioactive decay of potassium-40. On Earth, the differentiation processes, described in chapter IV, which have taken place in the interior have resulted in a concentration of potassium near the surface. If there has been no differentiation in the interior of Mars, then the proportion of potassium in the crust may be lower than on Earth, and then so also would be the abundance of argon in the atmosphere.

The foregoing discussion has been based on the assumption that the present Martian atmosphere has originated entirely from the interior of the planet. Some scientists, however, have suggested the possibility that part, at least, may have come from external sources, such as impacting meteorites and, especially, comets. According to one widely held theory, comets contain substantial quantities of solidified carbon dioxide, methane, ammonia, and water. Upon impact with a planet, these substances would vaporize and so contribute to the atmosphere. Because the mass of a large comet approaches that of the Martian atmosphere, which is about 3X1016 kilograms, the impact of such a comet could have a significant influence on the atmospheric composition.

Possibility of Permafrost on Mars

The small amount of water vapor in the Martian atmosphere presents an interesting problem. In terrestrial volcanic gases, water vapor is by far the most common constituent, and the condensation of this vapor has led to the formation of the oceans. The interior of Mars probably contains chemically bound water in the form of hydrates and there is some evidence that such hydrated compounds are present on the surface of the planet. For example, as will be seen in the next chapter, the reddish-yellow color of Mars is generally ascribed to a hydrated oxide of (ferric) iron. Furthermore, according to a report published in 1967 by W. M. Sinton of the Lowell Observatory, Flagstaff, Ariz., a strong emission band at a wavelength of around 3.1 /x in the Martian spectrum, from both light and dark areas, is produced by hydrated minerals.

As a result of heating in the interior of the planet, the water present in these hydrates should be liberated as vapor from the crust of Mars, just as it is on Earth. If the carbon dioxide and nitrogen in the Martian atmosphere have also been released from the interior, then they should have been accompanied by substantial amounts of water vapor. What, then, has happened to this water? Some has probably been decomposed into hydrogen and oxygen by ultraviolet radiation from sunlight. The hydrogen, being a very light gas, has escaped. The very small, so far undetected, quantity of oxygen in the Martian atmosphere suggests either that there has been very little decomposition of water, or more probably, that the oxygen has reacted chemically with materials on the surface. The apparent presence of highly oxidized (ferric) iron compounds (ch. VI) indicates that this may have occurred.

The intriguing suggestion has been made that water vapor from the interior of Mars is retained just beneath the surface in the form of permafrost. In regions of high latitude on Earth, in the vicinity of the poles, the temperature of the ground below a shallow depth is always less than 0° C. Water is then perma nently frozen into the soil and becomes an essentially integral part of it. This is the permafrost which is estimated to occur under about a fourth of Earth's land areas. In some places, such as northern Alaska and Siberia, it has a depth of almost 1000 feet.

There are reasons for believing that, on Mars, the temperature a very short distance under the surface is always well below 0° C over almost the whole of the planet (ch. VI). The conditions are thus everywhere suitable for the trapping as permafrost of any water vapor released from the crust. In these circumstances, and because there are no bodies of water on Mars, the abundance of water vapor in the atmosphere would inevitably be low. Nevertheless, the total quantity of water just below the ground might be considerable. Some laboratory evidence for the formation of permafrost under Martian conditions is described in chapter X. As will be seen there, the matter has important implications in connection with the possibility of the existence of life on the planet.

The Atmospheric Pressure on Mars:

Early Estimates

Prior to 1963, two main methods were used to estimate the (barometric) pressure of the atmosphere at the surface of Mars. One of these, called the photometric (light-measuring) method, depends on observations of the variation of the brightness of the planet at different wavelengths and phase angles (p. 43). The apparent brightness arises from the scattering, or random reflection (as distinguished from specular or mirrorlike reflection), of sunlight both by the surface material and by the atmosphere (fig. 5.3). From the observations mentioned above, the relative contributions of these two sources can be calculated. The amount of scattering from the atmosphere can thus be estimated. Then, by

FIGURE 5.3. Scattering and specular reflection.

the use of established formulas relating the pressure of a gas to the brightness caused by scattering, the pressure of the Martian atmosphere can be evaluated.

One of the first, if not the first, attempt to use light-scattering data to estimate the barometric pressure on Mars was made in 1908 by Percival Lowell. He took the visual albedo (p. 65) of Mars to be 0.27, and from this he somewhat arbitrarily subtracted 0.10 for the surface, leaving 0.17 for the albedo of the atmosphere. Then, he estimated the albedo of Earth's atmosphere to be 0.75. The albedo values used by Lowell are now known to be too high, but his approach to the problem is nevertheless of interest.

The amount of scattering of light by a gas is roughly proportional to its mass per unit area. Because the albedo is a measure of the scattering, Lowell estimated that the total mass of the atmosphere per unit area of Mars is 0.17/0.75 = 0.23 of the mass per unit area of the terrestrial atmosphere. The force of gravity on Mars is about 0.38 times that on Earth, so the atmospheric pressure on Mars should be 0.23X0.38 = 0.087 of Earth's barometric pressure. As seen earlier, the Earth's barometric pressure is about 1 bar, which means the pressure on Mars should be roughly 0.087 bar, or 87 millibars.

In 1926, D. H. Menzel in the United States used a more refined treatment of the albedo of Mars at different wavelengths to show that the ratio of the Mars/Earth atmospheric masses per unit area is about 0.18. The barometric pressure on Mars would then be approximately 68 millibars.

An important advance in the use of light-scattering measurements to determine the Martian atmospheric pressure was reported in 1934 by the Russian astronomers N. Bara-bashov and B. Semejkin. They used red, blue, and yellow filters to obtain photographic data on the scattering of light from bright areas on Mars at three different wavelengths. From the results the atmospheric pressure was estimated to be some 50 millibars. Later work by Barabashov and other Russian scientists, however, gave significantly higher pressures, over 100 millibars, using the same technique.

From visual estimates of the brightness of different surface areas, made in France during the Martian apparition of 1939, G. de Vau-couleurs developed simple procedures for determining the relative brightness of the surface and atmosphere of the planet. In this way, the atmospheric pressure was calculated to lie between about 80 and 90 millibars.

The second of the older techniques for determining the surface pressure on Mars is called the polarimetric method. It is considered to be capable of yielding more accurate results than the methods depending on light scattering. To understand its essential principle, it is necessary to say something about the polarization of light. Incidentally, polarization measurements have been frequently used in studies of the surface and atmosphere of Mars. Relevance of this technique to surface studies is discussed in chapter VI.

Light (and similar electromagnetic radiations) can be regarded as consisting of electric and magnetic waves combined in such a manner that the electric and magnetic field directions are always at right angles. For the present purpose, it is sufficient to consider only the electric wave. Suppose that a plane is placed at right angles to the direction of propagation of the light. The electric wave will then intersect this plane at a line, as indicated by the arrow in figure 5.4. This intersection, which has both magnitude and direction, is called the electric vector of the wave.

FIGURE 5.4. Electromagnetic wave and electric vector.

FIGURE 5.4. Electromagnetic wave and electric vector.

In unpolarized light, the electric vectors of successive waves are completely random and point in all directions, as shown in figure 5.5. In polarized light, however, there is a certain degree of order in the orientations of the electric vectors. Specifically, in plane polarized light, the electric vectors always lie in the same plane. By the use of suitable materials, such as tourmaline or calcite crystals or Polaroid sheet, the light which is polarized in a particular plane can be distinguished from that polarized in another plane. For the present purpose, it is important to note that scattered light is always polarized to some extent.

FIGURE 5.5. Directions of electric vector in unpolarized and plane polarized light.

Like the brightness of the planet, the polarization of the reflected scattered light from Mars is due in part to light scattered by the surface and in part to scattering by the atmosphere. The total polarization is expressed numerically by a quantity P which is defined by

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