Another important quantity is the radiometric (or integral) albedo. This is the fraction of the total solar radiation energy that is

Wavelength, A

FIGURE 4.4. Dependence of the Bond albedo of Mars on the wavelength.

Wavelength, A

FIGURE 4.4. Dependence of the Bond albedo of Mars on the wavelength.

reflected by the planet in all directions. If the radiometric albedo is represented by A*, then 1 —A* is the fraction of the Sun's radiation absorbed by the planet. The determination of A* is hampered by a lack of observational data, but the value of 0.295, suggested by G. de Vaucouleurs in 1964, was accepted for a time. A more recent analysis, made by R. G. Walker and C. Sagan in 1968, however, indicates that A* is closer to 0.23, and this will be adopted here. The fraction of the solar energy falling on Mars and being absorbed by the planet is thus 1 — 0.23, that is, 0.77.

Energy from the Sun reaches Earth at the rate of 2.0 cal/cm2/min. As Mars is farther from the Sun, the solar radiation energy is somewhat less. The actual rate, which is inversely proportional to the square of the distance from the Sun (p. 54), ranges from 0.72, when Mars is farthest from the Sun, to 1.05 cal/cm2/min, when Mars is closest to the Sun. The mean value over the whole of the Martian orbit is 0.86 cal/cm2/min. Because only the fraction 0.77 is absorbed, the average rate at which solar energy is taken up by the Martian surface is 0.86X0.77 = 0.66 cal/cm2/

The Interior of Mars

There has been considerable speculation and many differences of opinion concerning the nature of the interior of Mars. All that can be said definitely at the present time is based on the absence of a significant magnetic field. This implies that Mars either has no core of liquid heavy metals, such as Earth has, or if it does have a liquid core it must be relatively small. Because the average density of Mars is substantially less than that of Earth, it might be thought that Mars has a smaller proportion of the heavier (high-density) metallic elements, such as iron and nickel, which would be present in a core. This is not necessarily true. If the heavy elements were in the form of oxides, rather than in the metallic state, the average density of Mars would be lower, even though the overall elementary composition (including the atmosphere) were the same as it is for Earth.

In 1743, the French mathematician A. C. Clairaut considered the properties of a rotating, compressible fluid body. He made use of a quantity, commonly represented by <f>, which is the ratio of the centrifugal force at the equator of the rotating body to the force of gravity at the same location. Numerically, <f> is found to be equal to 37r/GPp, where G is the universal constant of gravitation, given on page 62, P is the sidereal period of rotation, and p is the average density of the body. Clairaut showed that for a rotating homogeneous body, that is, one with a uniform distribution of mass throughout its interior, the ratio f/<f>, where / is the dynamical flattening, should be 1.25. On the other hand, if all the mass of the body is concentrated at its center, then f/<j> should be 0.5.

In applying the foregoing criterion to Mars, use of 0.00525 for the dynamical flattening makes f/<f> equal to about 1.15. As the average density is somewhat uncertain, so also is the value of the ratio //<£. For comparison, the value of //<£ for Earth is 0.97. Hence, it would appear that the interior of Mars is much more uniform than Earth's interior, because 1.15 is closer than is 0.97 to the ideal value of 1.25 for a completely uniform body.

If the optical flattening were used in determining f/<f>, the value would be 2.3; this would imply that the density of Mars is much less at the center than in the outer layers. Such a highly improbable situation suggests that the actual surface of Mars, as implied by the optical flattening, is not indicative of the mass distribution in the interior. Lamar has claimed, however, that if allowance is made for the equatorial bulge which he postulated (p. 62), the optical flattening leads to a value of between 1.05 and 1.09 for the //</> ratio.

A considerable amount of information about the interior of Earth has been inferred from the velocity of propagation of seismic waves and from oscillations accompanying earthquakes. The general view at the present time is that there are three main concentric regions in Earth's interior; they are, first, a very dense central core, then a less dense mantle, and finally a relatively thin crust (fig. 4.5). The core is probably divided into a solid inner zone and a liquid outer one. Both of these zones are believed to consist mainly of iron with about 10 percent nickel. Motions within the liquid part of the core are thought to be responsible for the terrestrial magnetic field. Both the mantle and the crust are probably made up of silicates of iron, magnesium, and aluminium. In the crust, which varies in thickness from about 5 to 50 kilometers (3 to 30 miles), aluminium predominates, but the exact composition of the mantle, which extends to a depth of about 2900 kilometers (1800 miles), is uncertain.

Most authorities agree that Earth and the other planets, at least those, like Mars, which are similar to Earth, were formed by the accretion of relatively cold (or moderately warm) particles. In the course of time, energy released by the radioactive decay of uranium, thorium, and potassium-40, in particular, resulted in a considerable increase of temperature. In Earth's interior the temperature rose high enough to permit iron and nickel to melt; the heavy liquid then sank and collected near the center of the planet to form the core, part of which later solidified under the existing high pressure. As a result of this process of differentiation, as it is called, the proportion of iron in the mantle and crust are less than the average in Earth's interior.

FIGURE 4.5. Section through Earth's interior showing different regions.

FIGURE 4.5. Section through Earth's interior showing different regions.

By analogy with Earth, it is assumed that Mars also consists of concentric regions, but it is not certain whether there are two or three. Thermal calculations have been made based on certain assumptions (postulates) concerning the initial temperature of the planet when it was first formed, the amounts and distribution of radioactive elements, and the methods of heat transfer from one point to another in the interior. Some scientists find that the temperatures attained were never high enough to permit iron to melt, so that Mars could not have a central metal core, as Earth does. Others, using slightly different postulates, claim that the formation of a liquid metal core is possible. The insignificant magnetic field of the planet suggests, however, that if such a core exists it must be small.

There are indications, as will be seen in chapter VI, that the surface of Mars may contain considerable quantities of iron oxides, with a normal density approaching 4 g/cm3. Although this is close to the average density of the whole planet, it must be remembered that much of the interior is probably at a high temperature as well as at a high pressure ; the average density of the planetary ma terial under normal conditions might thus be significantly higher. Nevertheless, it would seem that the outer layers of Mars may contain a larger proportion of iron than do the crust and mantle of Earth. This would suggest that differentiation, leading to a liquid metal core, may not have occurred on Mars, at least not to any great extent. There is a possibility, however, as will be seen on page 111, that the high iron content of the Martian surface may be the result of the deposition of meteorites.

The value of the Clairaut ratio f/<j> for Mars (about 1.1) is less than that expected for a completely homogeneous (uniform) body (1.25), but is greater than //</> for Earth (0.97). It would seem reasonable to assume, therefore, that most, if not all, of the interior of Mars consists of two concentric regions. These have been compared to the crust and mantle of Earth, although the Martian crust might be somewhat thicker than the terrestrial one.

Even if the temperatures in the interior of Mars have never been as high as the melting point of iron (from 1500° to about 2000° C at the pressures in the interior of Mars), the conditions of temperature and pressure would be adequate to permit the formation of various silicates. The separation into two regions might then be caused either by differences in chemical composition (and density) or to a change in phase; that is, in the crystalline form (and density) at a particular temperature and pressure. The more dense region would form the equivalent of the mantle, whereas the less dense one would constitute the outer layers (or crust) of Mars.

It must be admitted that relatively little is known about the structure of the interior of Mars. Furthermore, calculations are hampered by uncertainties in the average density, the radii, the dynamical flattening, and the composition. It will probably be necessary to wait until seismic instruments can be landed on the surface and spacecraft can be placed in orbit around the planet before more detailed knowledge will be available concerning the Martian interior.

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