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2:29:10 2:29:50 2:30:30 2:31:10 Greenwich mean time

FIGURE 5.8. Phase path changes in radio signal from Mariner IV just prior to occultation.

2:29:10 2:29:50 2:30:30 2:31:10 Greenwich mean time

FIGURE 5.8. Phase path changes in radio signal from Mariner IV just prior to occultation.

kilometers ( 31 miles ). From this point on, the phase path change curve in figure 5.8 rises rapidly, as the signal penetrates deeper and deeper into the increasingly dense atmosphere of Mars. Finally, shortly after 02:31:11, the signal from Mariner IV ceased suddenly because of the onset of occultation of the spacecraft by Mars.

After emergence from occultation, the signal phase difference changed with time in a reverse manner to that in figure 5.8. In other words, it started at the right and proceeded to the left. The atmospheric portion of the curve was very similar to that before occultation, but the minimum attributed to the ionosphere was absent. This result was not altogether surprising because the Martian ionosphere might well disappear at night.

The shape of the atmospheric part of the curve in figure 5.8 can be correlated with the radio-wave refractive index close to the Martian surface and to the scale height of the atmosphere. The scale height is a measure of how the refractive index decreases with the altitude, and it can be used to calculate thé average gas temperature. From the refractive index, the number of gas molecules per unit volume (or molecular number density) can be estimated, provided the composition of the atmosphere is known. For calculation purposes, certain reasonable compositions are specified and the number density of the molecules is computed for each case. To determine the atmospheric pressure, the temperature is required and this can be derived from the scale height.

It can be shown that the scale height is numerically equal to RT/Mg, where R is the universal ideal gas constant (8.31 X 107 ergs per mole per degree), T is the temperature in degrees Kelvin (°K=°C + 273), M is the average molecular weight of the atmospheric gases, and g is the acceleration of gravity at the Martian surface (about 375 cm/sec/sec). If the atmosphere is assumed to consist entirely of carbon dioxide, M is 44. From the Mariner IV measurements, the scale height was estimated to be 8 to 10 kilometers; that is, 8X105 to 106 centimeters. Upon setting RT/Mg equal to these values, and using the data given above, the corresponding temperatures of the Martian atmosphere are found to be about 160° K and 200° K, respectively. The result is written as 180° ±20° K for an assumed atmosphere of carbon dioxide.

The pressure at the surface is equal to kTC, where k is the Boltzmann gas constant per single molecule (1.38 X 10~16 erg per degree), T is the calculated temperature, and C is the molecular number density in the atmosphere at the surface. As seen above, the value of C is estimated from the refractive index for an assumed atmospheric composition. If k is in ergs per degree Kelvin, T in °K, and C in molecules per cubic centimeter, the pressures will be in dynes per square centimeter. Upon multiplication by 1000, the values will be in millibars.

The results obtained in the foregoing manner from the Mariner IV data are summarized in the table on the next page for two atmospheric compositions: 100 percent carbon dioxide and 80 percent carbon dioxide plus 20 percent nitrogen. The pressures would be somewhat higher if there were a larger proportion of nitrogen. The molecular weight of argon (40) is not very different from that of carbon dioxide (44). For this reason, the presence of significant quantities of this gas in the Martian atmosphere would have only a minor effect on the calculated pressures.

It will be apparent from the data in the table that there was a marked difference in the results before and after occultation. A possible explanation is that the surface of Mars grazed by the signal immediately upon emersion from occultation may have been at a

Scale height (kilometers)

Surface number density (1017 molecules/cm'):

Surface temperature (°K):

Surface pressure (millibars):

Before

After

occultation

occultation

9±1

12± 1

1.9±0. 1

2. 25 ±0. 15

2. 1±0. 1

2. 45 ±0. 15

180 ±20°

240 ±20°

170±20°

220 ±20°

4. 9±0. 8

8. 4±1. 3

5. 2±0. 9

8. 8 ± 1. 3

lower altitude, and hence had a higher barometric pressure, than the surface just before occultation. The higher atmospheric temperature in the former case would then be in general agreement with expectation for the lower altitude of the surface.

In addition to giving the variation of the radio-wave refractive index with altitude, the scale height is also equal to the vertical distance, at constant temperature, in which the number density of gas molecules changes by a factor of e (that is, 2.72), the base of natural logarithms. By assuming a scale height of about 10 kilometers, the two atmospheric pressure values of 5 and 8.5 millibars before and after occultation, respectively, would correspond to a difference in elevation of some 5 kilometers (16 400 feet).

The occultation method for determining atmospheric pressure is inevitably biased in favor of the more elevated regions in the area where the radio wave grazes the surface of the planet just before and after occultation. So the pressure of the 8.5 millibars does not necessarily represent the maximum barometric pressure at the lowest levels on Mars. In fact, on the basis of certain radar reflection observations described in chapter VI, C. Sagan and J. B. Pollack of the Smithsonian Institution Astrophysical Observatory estimated in 1966 that at the very lowest levels, correspond ing roughly to the bottoms of deep oceans on Earth, the atmospheric pressures might be as high as 20 millibars. As already seen, values of 10 to 20 millibars have been derived from reflectivity, polarimetric, and spectroscopic studies.

Another point in connection with the Mariner IV data is worthy of mention. Just before occultation, the radio beam grazed a bright region of Mars at about latitude 50° S and longitude 183° W, between Electris and Mare Ghronium. After occultation, it appears that a dark area was grazed near 60° N and 34° W, at the north of Mare Acidalium. If the explanation of the observed pressure differences suggested above is correct, the particular dark area on Mars is at a lower altitude than the bright area. G. Sagan and J. B. Pollack have indicated, however, that within the limits of possible error, the area grazed by the radio waves after occultation may have been a bright one adjacent to dark areas. This matter is of some importance, as will be seen in the next chapter.

It may be noted, in any event, that barometric pressures do not indicate altitudes above the ideal physical surface of a planet (or distance from its center), but rather above a hypothetical equipotential surface of gravity. This is defined as a surface on which no work is required to move a mass from one point to another. The equipotential surface of Earth is very complex, with many undulations which are determined by the mass distribution below the surface of the planet. It is not at all unlikely that the equipotential surface of Mars is also complicated, and so it would be unsafe to draw conclusions concerning differences in altitude from atmospheric pressures measured at considerable distances apart. It is evident that much more needs to be known about Mars before the available data can be interpreted completely.

Variation of Atmospheric Pressure With Altitude

Before the Mariner IV occultation experiment, the only way in which the scale height of the Martian atmosphere could be determined was by calculating the value of RT/ Mg, using an estimated average molecular weight and temperature. On the basis of the assumption, accepted before 1963, that the atmosphere consisted mainly of nitrogen molecules (molecular weight 28) at a temperature of 180° K, the scale height was calculated to be about 14.5 kilometers. This may be compared with a scale height of approximately 7 kilometers in Earth's atmosphere.

The smaller the scale height, the more rapidly does the molecular-number density in the atmosphere decrease with increasing altitude. Hence, the atmospheric number density on Earth should decrease more rapidly than on Mars. For several years it was widely accepted that, above an altitude of some 50 kilometers (31 miles), the number density in the Martian atmosphere was actually greater than at the same altitudes above Earth, although at the surface it is much larger on Earth than on Mars.

The question of the atmospheric density at high altitudes over Mars is of more than a purely scientific interest. In order to design an orbiting spacecraft and to determine its orbit for a specific lifetime, a knowledge of the atmospheric density is a fundamental requirement. The larger the mass density, the number density multiplied by the molecular weight, the greater the resistance to motion of an orbiting spacecraft, and hence the shorter will be its lifetime.

It now appears that the scale height of the Martian atmosphere at high altitudes is only about 9 kilometers, and this is not greatly different from the scale height of the terrestrial atmosphere. It is probable, therefore, that the atmospheric mass density on Mars, at all altitudes of interest, is less than on Earth. The estimated mass densities, expressed in grams per cubic centimeter, for altitudes up to 140 kilometers (87 miles) are shown in figure 5.9.

Because the mass densities are less than those based on the older data, it should be possible to place a spacecraft in a lower orbit around Mars than had previously been considered possible. With a lower orbit, better

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