An approximate idea of the maximum and average temperatures of the surface of Mars can be obtained by supposing that the planet behaves as an ideal (blackbody) emitter of radiation. The rate E at which energy is radiated from a blackbody is related to the absolute temperature T in °K, which is 273° plus the temperature in °C, by the theoretical (Stefan-Boltzmann) expression
If it is assumed that the planet has attained temperature equilibrium with its surroundings, as is highly probable, then energy is emitted as radiation at the same rate as it is being absorbed from the Sun. The quantity E can then be taken to be equal to the rate of absorption of solar radiation.
At its average distance from the Sun, the surface of Mars absorbs solar radiation at the rate of 0.66 cal/cm2/min (p. 66). Hence, in the equation given above, E may be set equal to 0.66. The value of T is then found to be 299° K; that is, 299°-273° = 26° C (or 79° F). If Mars does not behave as an ideal radiator, as may well be the case, the calculated temperature would be a few degrees higher. This temperature refers to the surface of the planet at its average distance from the Sun. At perihelion, when Mars is closest to the Sun, the calculated temperature would be some 15° K still higher and it would be lower by roughly the same amount at aphelion, when Mars is farthest from the Sun.
The temperatures calculated in this manner represent those at the subsolar point of Mars, i.e., the point where the surface is intersected by a line joining the centers of Mars and the Sun. At this point, at the center of the Martian disk at full phase, not only is the surface closer to the Sun than at any other point but the solar radiation comes in directly from above. At other points, the incoming radiation strikes the surface at an angle, so that a given amount of energy is spread over a wider area. Thus, the blackbody temperature of 299° K, for the average Mars-Sun distance, is the maximum that could be expected, apart from possible allowance for nonideal emission of radiation. Such measurements as have been made, to be described shortly, give maximum temperatures in general agreement with the calculated value.
An average surface temperature can be estimated by noting that solar radiation is absorbed only on the part of the planet that is facing the Sun, over an area of 7ri?2, but it is lost from the whole surface area 4:ttR2, where R is the radius of Mars. Because the temperature is proportional to the fourth root of the radiation absorbed (or emitted), it follows that or
where 7 aT is the average temperature over the whole planet and T'max is the value calculated above. If Tmax is taken as 299° K, then Tav is 211° K; that is, -62° G (-80° F). This temperature also applies when Mars is at its average distance from the Sun. At perihelion it would be about 10° K higher and at aphelion about the same amount lower.
With a maximum daytime temperature of approximately 26° C and an estimated average of roughly — 62° C over the whole planet, it is obvious that surface temperatures well below —100° C may be expected on some parts of Mars, especially at night. During the local winter, the polar region does not receive any sunlight for periods up to half a Martian year, so the temperatures must drop to very low values.
Instead of assuming that the rate of emission of energy by Mars is equal to the average rate of absorption from solar radiation, the equation given earlier can be used to calculate the temperature .based on an actual determination of the rate at which the planet emits energy. This procedure has the advantage that it gives the temperature at the particular time, and even at a particular part of the Martian surface, for which the energy measurement is made. In calculating the temperature, it is assumed, as a first approximation, that the planet is a blackbody radiator. Then some allowance can be included for nonideal behavior.
The radiation from Mars as received on Earth consists of two parts: first, reflected or scattered sunlight from the planet's disk, and second, thermal radiation from the surface. It is the latter radiation which is dependent upon the surface temperature and is that required for calculating its value. The separation of the thermal radiation from the total radiation received has been based on the fact that the thermal radiation is essentially all of long wavelength (more than 3/*), and, therefore, is in the infrared region of the spectrum. The scattered sunlight, on the other hand, is nearly all of shorter wavelength.
The experimental technique originally used for determining the thermal radiation was to measure the total energy received in a given time from Mars by means of a heat-sensitive device, such as a vacuum thermopile. Another measurement of the energy of the same radiation after it had passed through a layer (cell) of water or a sheet of glass was then performed. The water or glass absorbed the infrared (thermal) radiation, but allowed the scattered sunlight to pass through. The difference between the two measurements then gave the value for the thermal radiation only. By substituting this quantity for E in the equation on page 131, the corresponding blackbody temperature was calculated.
The earliest radiation measurements for the purpose of determining the temperature of the surface of Mars were made during the 1922, 1924, and 1926 apparitions by W. W. Coblentz and C. O. Lampland at the Lowell Observatory and by E. Pettit and S. B. Nicholson at the Mount Wilson Observatory. As a general rule, the water-cell transmission method was employed to separate the thermal from the total radiation. Although the results indicated certain definite trends in the temperatures, some of which will be described later, there is doubt concerning the absolute accuracy of the values reported.
An improved technique for determining Martian surface temperatures was developed by W. M. Sinton and J. Strong during the 1954 apparition, utilizing the 200-inch telescope at Mount Palomar. They did not employ the water-cell method, because it is susceptible to considerable error, especially be cause it involves the difference between two small quantities. Instead, they used filters to restrict the radiation energy received to the infrared wavelength range of 7 to 13 ju,. Furthermore, the energy was measured by means of gas expansion in a Golay detector, which has about twice the sensitivity of a thermopile.
The results near the Martian equator obtained by Sinton and Strong, during the terrestrial nights of July 20 and 21, 1954, are indicated by the points in figure 6.21. The curve shown is based on theoretical considerations; it gives estimated temperatures during the Martian day as well as the night when no measurements are possible from Earth. As on Earth, the maximum temperature during the day is reached an hour or so after noon. This maximum is close to 300° K (27° C), and hence agrees well with the calculated maximum temperature at the subsolar point.
The estimated temperatures at night, even at the equator, are seen to be quite low, perhaps as low as 190° K ( - 83° C). The very large daily change in temperature, about 110° C, at the equator, is the result of the low atmospheric density and the poor thermal conductivity of the surface material. Consequently, a considerable amount of heat energy
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