Planet mean density

In estimating the bulk compositions of the other terrestrial planets, there are not nearly so many constraints. Determination of a planet s mass (obtained from its gravitational effect on the orbits of moons or nearby spacecraft) and volume (calculated from its diameter as measured by telescopes) enables the calculation of its mean density. A meaningful comparison of planet mean densities requires that we correct for the effects of self-compression due... 

The density estimates in Table 7.1 show a distinction between the structures of the planets, with Mercury, Venus, Earth and Mars all having mean densities consistent with a rocky internal structure. The Earth-like nature of their composition, orbital periods and distance from the Sun enable these to be classified as the terrestrial planets. Jupiter, Saturn and Uranus have very low densities and are simple gas giants, perhaps with a very small rocky core. Neptune and Pluto clearly contain more dense materials, perhaps a mixture of gas, rock and ice. 

Uncompressed mean densities of the terrestrial planets and the Moon (Taylor and McLennan, 2009) vary with the relative volume proportions of cores and mantles. 

The giant planets are composed mostly of hydrogen and helium. Uncompressed mean densities provide constraints on the proportion of rock to ice or gas, although the enormous internal pressures in some of these planets produce phase changes in hydrogen that complicate this determination (discussed below). 

In keeping with the theme of this book, we are most concerned with estimating planet bulk compositions, which then can be recast into mean density and moment of inertia. A number of different cosmochemical models have been attempted to estimate the bulk compositions of planets for which we have very few, or more likely no samples. 

The origin of the components that were accreted to make up the planets is the subject of intense discussion. Chondrite-mixing models attempt to build the planets using known chondritic materials. These models are constrained by the mean densities, moments of inertia, and, to the extent that they are known, the bulk chemical and isotopic compositions of the planets. Mars and 4 Vesta can be modeled reasonably well by known types of chondritic material (Righter et al., 2006). However, the Earth seems to have formed, at least in part, from materials that are not represented in our collections of chondritic meteorites (see below). 

Estimated compositions ofthe giant planets are given in Table 14.3, normalized to the solar composition. The relative proportions of rock and volatiles are estimated from mean densities, the rock compositions are assumed to be chondritic, and the ratios of hydrogen to helium are derived from spectroscopic or spacecraft measurements of atmosphere compositions. 

The mean density of Mercury is 5.43 0.01 g cm (Anderson et al., 1987). This corresponds to a reduced (or uncompressed) density of 5.31 (Kaula, 1986). The reduced density is the density a planet would have if it was not compressed, but was at high enough pressure to squeeze out all the pore spaces, —10 kbar (Kaula, 1986). Calculation of the reduced densities of the terrestrial planets assumes that the core is composed of iron and nickel, and that all the metal is in the core. The reduced density of Mercury is by far the largest of the terrestrial planets. Earth is the closest, with a reduced density of only 4.03 g cm. ... 

The accepted mean density of Mars, based on its measured volume and determination of its mass from spacecraft orbits, is 3.9335 0.0004 g cm (Lodders and Fegley, 1998). The density of the elastic lithosphere (approximately equivalent to the crust), estimated from models of the relationship between gravity and topography from Mars Global Surveyor data, is 2.95-2.99 g cm (McKenzie et al., 2002), which is similar to the density of basalt. The planet s dimensionless moment of inertia (0.3662 0.0017), calculated from Mars Pathfinder measurement of the rate at which its spin pole precesses (Folkner et al., 1997), constrains the core radius to —1,300-1,500 km, depending on core composition. 

From Triton s 5.866 day period of revolution around Neptune and its 220,000 mi (354,300 km) mean distance from it, astronomers estimated Neptune s mass to be 17.14 Earth masses, according to Kepler s third law. From Neptune s mean radius of 15,290 mi (24,625 km), a mean density (mass divided by volume) of 1.64 grams/cm was found. These values are similar to the ones found for Uranus. Uranus is slightly larger than Neptune, but Neptune is considerably more massive and denser than Uranus. Thus, Neptune is one of the Jovian planets, which are characterized by large sizes and masses but low mean densities (compared with Earth). The last characteristic implies that Jovian planets have extremely thick atmospheres and are largely or mostly composed of gases. 

The discovery of transiting planets with masses below 10 MEanh and radii consistent with rocky planetary models answered the important question as to whether planets more massive than Earth could be rocky. 10 Mgarth and 2 Earth radii are used as estimates from planet formation theories as the upper limit for rocky planet mass and size. For comparison, Uranus has about 14.5 MEanh and about 4 Earth radii. Above about 10 Earth masses a planet is thought to accumulate a substantial amount of gas that makes it akin to a gas giant with a substantial atmosphere, not a rocky planet with a thin outgassed atmosphere. Where exactly such a cut-off mass is that distinguishes rocky Super-Earths and gaseous Mini-Neptunes - if it exists at all - is an open question that mean density measurements of detected exoplanets currently explore. 

The blanket of air that cloaks our planet behaves as an ideal gas, but the atmosphere is bound to the Earth by gravitational attraction, not by confining walls. The pres-sure exerted by the atmosphere can be thought of as the pressure of a column of air. Just as the pressure exerted by mercuiy in a barometer is the pressure of the column of mercury. The higher we rise into the atmosphere, the less air there is above us. Less air above us means that the pressure exerted by the column of air is lower. Lower pressure, in turn, means lower molecular density, as indicated... 

Using the numbers quoted above and the derived mass of the Earth gives pc = 5.52 gem-3, which, by comparison with the density of other materials measured in the laboratory, means that the Earth must be made of rock, and heavy rock at that. The mass of the other planets can be determined from their orbital periods and their radii can be measured, for example, from rates of transit in front of the Sun, and so the density of the other planets within the solar system can then be determined (Table 7.1). 

Water has several attractive features as a solvent and, as we have said elsewhere, the best solvent is no solvent, but if one has to use a solvent then let it be water. Water is the most abundant molecule on the planet and is, hence, readily available and inexpensive. It is nonflammable and incombustible and odorless and colorless (making contamination easy to spot). It has a high thermal conductivity, heat capacity and heat of evaporation, which means that exothermic reactions can be controlled effectively. It readily separates from organic solvents owing to its polarity, density and because of the hydrophobic effect [12], which makes it eminently suitable for biphasic catalysis. Indeed, water forms biphasic systems with many organic solvents, with fluorous solvents, some ionic liquids and with scC02 [13]. 

From another point of view, air is the term we use to define a more complex structure known as the atmosphere, that is, the relatively thin layer of a low-density fluid a few hundred kilometers high surrounding our planet. On a scale of cubic meters, air can be considered as a homogeneous mixture of constant composition, but on a larger scale the atmosphere cannot be considered uniform. Where does the atmosphere end This is a difficult question, but practically all of its mass (i.e., an estimated annual mean of 5.13 x 1021 g) is within 100 kilometers. 

The moment of concrescence may occupy the same position with respect to time that a magnetic pole of the earth occupies relative to the geomagnetic field of the planet. Like the poles, which are physically characterized by climatological extreme, the temporal pole would mark a temporal extreme, the most extreme moment of density of the ingression of novelty, but like the poles, it would not be apparently different from its space-time environment. Such an understanding of time would mean no definitive concrescence could take place. 

Probably this requires timescales of <10 yr (Podosek and Cassen, 1994). In contrast, the most widely accepted dynamic models advocated for the formation of the terrestrial planets (Wetherill, 1986), involve protracted timescales —10 -10 yr. Application of these same models to the outer planets would mean even longer timescales. In fact, some of the outermost planets would not have yet formed. Therefore, the bimodal distribution of planetary density and its striking spatial distribution appear to require different accretion mechanisms in these two portions of the solar system. However, one simply cannot divide the accretion dynamics into two zones. A range of rate-limiting processes probably controlled accretion of both the terrestrial and Jovian planets and the debates about which of these processes may have been common to both is far from resolved. There almost certainly was some level of commonality. 

Saturn is the second-largest planet in the solar system, after Jupiter. Its equatorial radius is 37,448 miles (60,268 km), about nine times that of Earth, and its mass is 568.46 x 1024 kg, about 95 times that of Earth. As of early 2007, scientists had found 56 satellites of Saturn, the largest of which is Titan, with a radius of 8,448 feet (2,575 km, about 50 percent larger than that of Earth s Moon), and a mass of 1,345.5 x IO20 kg (about twice that of the Moon). Saturn s density is 0.687 g/cm3, less than that of water. This fact means that (if one could find a body of water large enough) Saturn would float on water. It is the only planet with a density less than that of water. 

The enormous progress of electronic computers has allowed the accurate description (by means of new disciplines like computational physics and theoretical chemishy) of physicochemical systems via numerical solution of the basic equations. An extended quantum mechanical description of the electron density in molecular systems (via self-consistent field or density functional theory) and molecular dynamics are now possible on more or less ab initio methods and are able to describe most of experimentally accessible physicochemical systems with accuracies of thermodynamic level, or even to provide presumably realistic descriptions of systems (like the ones at the interior of Jovian planets) which are not accessible to experiments. 

THE NEUTRINO is an electrically neutral elementary particle that has the unique capability of penetrating matter on the scale of stellar dimensions and densities. Neutrinos are produced abundantly in nuclear processes (including beta-decay) in the interior of stars and planets and by a variety of processes in the cosmos. The study of neutrino radiation from stars is a direct means of observing the energy production mechanism occurring in their interiors. In addition, intermediate mass stars at the end of their nuclear life, i.e., after exhausting their nuclear fuel, suffer a catastrophic collapse (supernovae) and emit an intense burst of... 

The Earth s Moon is the fifth largest satellite in the solar system. Its distance from the Earth is only 30 times the diameter of the Earth, the orbit is elliptical. The nearest distance to Earth (perigee) is 363 104 km, the largest distance (apogee) is 405 696 km. The semi major-axis is 384 399 km. The orbital period is 27 d 7 h 43.1 min which exactly corresponds to its rotational period. The orbit of the Moon is inclined to the plane of the ecliptic by about 5.1°. The mean radius of the Moon is 1737.1 km which is 0.273 that of the Earth s radius. The surface area is about 37 X 10 km. The density is relatively high and corresponds more to that of terrestrial planets and is 3.34 gcm . Our Moon is a relatively dark body with a surface albedo of 0.12. 

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