Which Internal Energy Source is the Most Important in Continuing to Heat Terrestrial Planets Today

Evolution of the Earth

S. Karato , in Treatise on Geophysics (Second Edition), 2015

9.05.5.1.1 General introduction

Terrestrial planets are made of condensed materials. Therefore, condensation from a hot gas is the first stage by which the volatile content of terrestrial planet is controlled. Upon cooling, refractory materials are condensed in the early hot stage and volatile materials are condensed later in the cool stage. The condensed materials not only will sink to the equatorial plane of the nebula and eventually form planets but also may migrate toward or away from the star. When gaseous phases are blown off by the strong solar wind at the T Tauri stage of the mother star, condensation will cease and the condensed materials at this stage will become the source materials of terrestrial planets (strong radiation will blow off most of the solar nebula composition gas from terrestrial planets, but not from giant planets because of the strong gravity for the latter). (Large impact could also blow off the preexisting atmosphere, but the timing of a large impact is 10  s of Myr after the formation of the Sun, and therefore, it will be after the blowoff of the primary atmosphere by the solar radiation during the T Tauri stage.)

Assuming this scenario, the composition of the condensed materials that will become terrestrial planets can be calculated from the temperature of the nebula at the time of the T Tauri phase. Whenever the timing of the T Tauri stage is, the temperature in the nebula at any distance from the mother star decreases with distance. Consequently, there will be a gradient in chemical composition of the condensed matter. Lewis (1972) proposed that the composition of the terrestrial planets can be explained by the condensation temperatures of various materials. Similarly, Gradie and Tedesco (1982) reported that the composition of asteroids inferred from the reflection spectroscopy varies systematically as a function of the distance from the Sun. This is consistent with the condensation model. They also discussed that this observation suggests that there is not much orbital scattering of these bodies after their formation. However, recently, DeMeo and Carry (2014) showed a more complex compositional distribution in the asteroid belt, suggesting the importance of mixing. Also, Cassen (1996) developed a model to explain the variation of moderately volatile elements in some carbonaceous meteorites using such a model where radial transport of matter is also considered.

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Interior Structure and Evolution of Mars

Tim Van Hoolst , Attilio Rivoldini , in Encyclopedia of the Solar System (Third Edition), 2014

2 Formation and Differentiation of Mars

Terrestrial planets like Mars form when kilometer-sized planetesimals, which originate from the accumulation of dust grains in less than about 10,000  years, collide under the influence of the gravitational attraction between them and gas drag, a process called accretion. In less than a million years, tens to hundreds of planetary embryos are formed with masses between those of the Moon and Mars. By bringing planetesimal material with a Mars mass M from a far distance to a small region of space with Mars radius R, the gravitational potential energy decreases enormously by about 0.6GM ²/R, where G is the universal gravitational constant. This change in energy is mostly converted into heat. The associated temperature rise is about 0.6GM/(RC)   ≈   6000   K, where C  ≈   1200   J/K/kg is the specific heat of Mars, suggesting that Mars formed hot.

However, part of the massive amount of energy liberated by accretion will be radiated to space. For slow accretion over about 1   My of small planetesimals, even most of the gravitational energy could be lost by radiation and planets would not form hot but would be cold with temperatures of a few hundred Kelvin close to the temperature of the protoplanetary disk. The key to the hot origin of planets lies in how deep the energy can be deposited in a planet. If energy can be brought to the deep interior, a very efficient internal heat transport mechanism would be required for a cold formation to occur. The general consensus is that in particular the large impacts at the end of formation strongly heat the deep interior of a planet in a fraction of geological time and can melt at least part of the planet interior producing a magma ocean.

The final formation of Mars took less than about 10   My. This is faster than for the Earth, for which the last large impact that formed the Moon is thought to have occurred 30–50   My after the formation of the solar system. The much smaller mass of Mars and fast formation compared to the Earth suggest that Mars could be a remnant embryo. This embryo status of Mars could be explained in the accretion scenario if the outer edge of the planetesimal disk of the initial solar system was at about 1 AU (an Astronomical Unit is the distance between the Sun and the Earth). Such a small inner disk possibly formed by inward migration of Jupiter to the Sun in the early phases of the solar system to a distance of only about 1.5 AU.

Because of its fast formation, Mars probably suffered less violent impacts with respect to the Earth resulting in a more limited heating. Nevertheless, the decay of the short-lived radioactive isotope ²⁶Al with a half-life of 0.72   My could produce up to half the energy of accretion, more than sufficient for mantle melting and the formation of a magma ocean (half-life is the length of time needed for half of the parent atoms to decay into daughter atoms). Iron droplets in the magma ocean could then descend to form the core and at the same time mantle material crystallized at the cold surface layers to form the primordial crust. In the core formation process, additional gravitational energy is released and converted into heat, further increasing the internal temperature of Mars and facilitating core formation. Mars, therefore, quickly differentiated into a core, a mantle, and a crust, a process that already started during the formation. After solidification of the magma ocean, at least part of the mantle is thought to be gravitationally unstable because the lightest material most rich in magnesium solidifies first at the bottom of the magma ocean and the more iron-rich and denser silicates solidify later. As a result, the mantle overturns: the denser materials sink and the lighter materials rise producing a gravitationally stable stratification, a process that could have latest up to 100   My after core formation.

The chronology of the planetary formation has been possible to unravel thanks to the study of radioactive parent–daughter systems with half-lives of the order of 10   My. In particular, the hafnium–tungsten system is widely used to constrain the accretion timescale and to date core formation of planetary bodies. ¹⁸²Hf is a short-lived isotope that decays to ¹⁸²W with a half-life of 9   My. Hafnium is a lithophile, or "rock-loving", element meaning that it will stay in the mantle when the iron core forms. Tungsten on the other hand is a siderophile ("iron-loving") element and will follow the iron to the core on core formation. Therefore, part of the ¹⁸²W produced from ¹⁸²Hf will be in the core if the core formation time is comparable to the half-life of hafnium. By comparing the Hf/W ratio from the Martian mantle (estimated from Martian meteorites) with the initial ratio (derived from chondrite meteorites), the age of core formation of less than 10   My can be deduced.

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Physics of Terrestrial Planets and Moons

F. Sohl , G. Schubert , in Treatise on Geophysics (Second Edition), 2015

10.02.11 Summary and Outlook

The terrestrial planets Mercury, Venus, Earth, and Mars have low masses, small radii, and large densities in comparison with the giant planets in the outer solar system. This is also true for terrestrial-type bodies like the Moon and some of the outer planet satellites, and it provides important clues on their bulk compositions. Rotational, gravitational, and magnetic field observations indicate that the interiors of these bodies are strongly differentiated and subdivided like that of the Earth into iron-rich cores, silicate mantles, and rocky crusts derived from partial mantle melts. Isotope data reveal that the cores and the primary crusts formed early and rapidly. Geodetic observations of the rotational state and/or tidal response suggest that the interiors are warm enough to maintain liquid outer core shells or entirely liquid cores. For Mars, Venus, and Earth, mantle pressures are sufficient to permit mineral phase transformations from olivine and pyroxene assemblages to spinel or even perovskite and postperovskite phases. Since the phase transition depths also depend on the ambient temperature and the iron content of the mantle rocks, future seismological observations complemented by electromagnetic induction data and heat flow measurements have the potential to provide additional information on the thermal states and compositional differences of the terrestrial planets. Single-plate planets, the Moon, Mercury, Mars, and Venus, are believed to be cooling by lithospheric thickening, while the deep interior remains relatively warm. It is likely, therefore, that due to the progressive cooling of the planet's outer portion, thermoelastic stresses will be occasionally released at preexisting faults, thereby causing local seismic activity at a level detectable by seismometers. The discovery of rocky exoplanets relies on current detection limits of ground-based observational methods. Structural models of solid exoplanet interiors can be constructed by using equations of state for the radial density distribution, which are compliant with the thermodynamics of the high-pressure limit. The modeling results imply that mass–radius relationships are robust and can be used to classify low-mass exoplanets such as CoRoT-7b and Kepler-10b in terms of their bulk compositions.

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Comparative planetary evolution

Kent C. Condie , in Earth as an Evolving Planetary System (Fourth Edition), 2022

Comparative planetary evolution

The terrestrial planets all have low masses, small radii, and large densities compared to the giant planets in the outer solar system ( Table 10.2). This is also true for the Moon and many of the satellites of the outer planets. Rotational, gravitational, and magnetic field observations indicate that the interiors of these "rocky" bodies are differentiated and layered into iron-rich cores, silicate mantles, and crusts, the latter derived from partial melting of the mantles. Furthermore, geodetic observations suggest that the interiors are hot enough to maintain partially to completely liquid iron cores. For Mars, Venus, and Earth, mantle pressures are sufficient for mineral phase transitions from olivine, pyroxenes, and garnet at low pressures to bridgmanite and postperovskite phases at high pressures.

From our survey of the solar system, it seems clear that no two bodies in the solar system have identical histories. Although the terrestrial planets have many features in common, as do the outer giant planets, each planet has its own unique history. At least from our perspective, Earth seems to be most peculiar. Not only is it the only planet with oceans, an oxygen-bearing atmosphere, and living organisms, but it is the only planet in which plate-tectonic processes are known to be active.

As we have seen, the terrestrial planets and the Moon have similar densities (Table 10.2) and thus, on the whole, similar bulk compositions. Each of them is evolving toward a stage of thermal and tectonic stability and quiescence as they cool. The rate at which a planet approaches this final stage is dependent upon a variety of factors, which directly or indirectly control the loss of heat (Carlson, 1994; Taylor, 1992, 1999). First of all, the position of a planet in the solar system is important because, as we have seen, it reflects the condensation sequence of elements from the cooling molecular cloud. Also important are the abundances of radiogenic isotopes that contribute to heating planetary bodies. The Moon, for instance, contains considerably smaller amounts of U, Th, and K than Earth, and as such will not produce as much radiogenic heat. Analyses of fine-grained materials from various sites on Mars suggest that it is also depleted in radiogenic isotopes compared to Earth. Planetary mass is important in that the amount of accretional and gravitational energy is directly dependent upon mass. Planetary size is also important, in that greater area/mass ratios result in more rapid heat loss from planetary surfaces. For instance, the Moon, Mars, and Mercury should cool much faster than Venus and Earth because of their higher area/mass ratios (Table 10.2). Also important is the size of the iron core, in that some of initial planetary heat is produced during core formation. Except for Mercury, Earth has the highest core/mantle ratio, followed by slightly lower values for Venus and Mars. As discussed previously, the very high core/mantle ratio for Mercury is probably a result of loss of some of the mercurian mantle by an early giant impact, and thus is not indicative of a large contribution of heat from core formation. The volatile contents and especially the water content of planetary mantles and the rate of volatile release are important in controlling atmosphere development, the amount of melting, fractional crystallization trends, and the viscosity of planetary interiors which, in turn, affect the rate of cooling. Convection or/and mantle plume activity are the primary mechanisms by which heat is lost from the terrestrial planets. Only Earth, however, does convection support plate tectonics.

Although every planet has its own unique history, the primary differences in planetary thermal history are controlled chiefly by heat productivities, volatile element contents, and cooling rates. Distance from the Sun is also an important variable, especially in terms of planetary composition and atmosphere evolution. A qualitative portrayal of planetary thermal histories is illustrated in Fig. 10.39. The temperature scale is schematic. All terrestrial planets underwent rapid heating during late stages of accretion, reaching maximum temperatures between 4.55 and 4.50   Ga, at which time widespread magma oceans were produced. Just prior to or coincident with this time, molten iron descended to planetary centers forming metal cores, and planetary mantles rapidly degassed. Rapid, chaotic convection in the magma oceans resulted in rapid cooling and crystallization producing a transient primary crust, perhaps of anorthositic composition. Partial melting of recycled crust or/and mantle ultramafic rocks gave rise to widespread secondary basaltic crusts on all of the terrestrial planets, a process that is still occurring on Earth as ocean-ridge basalts and oceanic plateaus are produced. At least on Earth and Venus, where substantial heat was available, early crust and lithosphere were rapidly recycled into the mantle, aided by intense giant impacts, which continued to about 3.9   Ga with the Late Heavy Bombardment (Fig. 10.39).

Fig. 10.39. Schematic thermal evolution of the terrestrial planets and the Moon. Lower threshold temperatures for planetary processes: Tc, convection; Tp, mantle plume generation at the core-mantle boundary; Tm, magmatism.

Although continental crust is not preserved on Earth until 4   Ga, it may have been produced and rapidly recycled into the mantle before this time (Chapter 5). Rapid cooling of the smaller planets, including Mercury and probably Mars, led to thickened and strong lithospheres by 4.5   Ga. These planets, as well as the Moon, are typical one-plate planets, because their thick, strong planet-wide lithosphere is basically all one plate. Most of the magmatic activity on these planets resulted from mantle plume and heat pipe activity and occurred before 3.9   Ga. The Moon formed by accretion of material blasted from Earth by a giant impact about 4.53   Ga, and it rapidly heated and melted forming a magma ocean, which crystallized by 4.5   Ga producing the anorthositic lunar highlands crust. The youngest volcanism on the Moon appears to have been about 2.5   Ga, perhaps 1.5   Ga on Mercury, and maybe as recent as 200   Ma on Mars.

Because of their greater initial heat, Venus and Earth cooled more slowly than the other terrestrial planets. Venus may have passed through the minimum temperature for convection some 2   Ga, while Earth has not yet reached that point in its cooling history (Fig. 10.39). If the resurfacing of Venus at 800–300   Ma was caused by a catastrophic mantle plume event, it may have been the last such event, as suggested by the intersection of the Venus cooling curve with Tp, the lower temperature limit for plume production at the core-mantle interface. Volcanism is probably still active on Venus, however. The most intriguing question, i.e., that of why Venus and Earth followed such different cooling paths, yet both planets are similar in mass and density, remains problematic. One possibility is that while Earth cooled chiefly by convection and plate tectonics, Venus cooled by mantle plumes and conduction through the lithosphere in a stagnant lid regime. If this is the case, we are still left with the question of why different cooling mechanisms dominated in each planet. Some investigators suggest it has to do with the absence of water on Venus. They argue that in a dry planet the lithosphere is thick and strong as it may be on Venus, and there is no melting to produce a low-velocity zone, and thus plates cannot move about or subduct. Taking this one step further, we might ask why is Venus dry, yet Earth is wet? As suggested previously, Venus may have rapidly lost its water as hydrogen escaped from the atmosphere soon after or during planetary accretion, because the surface of the planet was too hot for oceans to survive. And why was the surface too hot? Perhaps because Venus is closer to the Sun than Earth. If this line of reasoning is correct, it may be that the position that a planet accretes in a molecular cloud is one of the most important variables controlling its evolution. The reason Mars did not sustain plate tectonics or accumulate an ocean may be due to its small mass and rapid cooling, resulting in a lithosphere too thick and strong to subduct. If there was enough water to form Martian oceans, it either escaped by hydrogen loss or is trapped in the interior of the planet. It is also important to consider changes in orbit and distance to parent star during their planetary evolution.

If the earlier mentioned scenario bears any resemblance to what really happened, it would appear that two important features led to a unique history for Earth: (1) its position in the solar system, and (2) its relatively large mass. Without both of these, Earth may have evolved into quite a different planet than the one we live on.

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CLIMATE AND CLIMATE CHANGE | Radiative–Convective Equilibrium Climate Models

N.O. Renno , X. Huang , in Encyclopedia of Atmospheric Sciences (Second Edition), 2015

Introduction

The terrestrial planets emit as much energy to space in the form of thermal radiation as they receive from the sun in the form of solar radiation. On Earth, the incident solar radiation is absorbed mostly at the surface, but it is also scattered and absorbed by atmospheric gases, aerosols, and clouds. The absorption of solar radiation, its redistribution by dynamic and radiative processes, and the emission of thermal radiation back to space determine the mean surface temperature and the mean vertical thermodynamic structure of the atmosphere. Radiative–convective models simulate these processes and give insights into their effects on the energy budget, the vertical structure, and the stability of planetary atmospheres.

Radiative–convective models are ideal for studying general principles and testing fundamental ideas. Their major drawback is the inability to calculate the feedbacks between the horizontal heat transports and the temperature structure from first principles. Radiative–convective models are widely used not only to simulate the thermodynamic structure of the atmosphere of the Earth and other planets but also to study their sensitivity to changes in the concentration of greenhouse gases, convective processes, clouds, and the flux of incoming solar radiation.

In the classical radiative–convective models developed in the 1960s, the atmosphere's water vapor mixing ratio is either fixed or diagnosed based on the climatological profile of relative humidity. In addition, these models use simple numerical procedures to parameterize the cumulus convection, the processes responsible for the distribution of water vapor into the atmosphere. Since water vapor is the most important greenhouse gas, it is desirable to explicitly calculate its content and vertical distribution. The radiative–convective models developed during the last 2 decades do this by explicitly calculating the hydrological cycle. Furthermore, they employ complex parameterization schemes similar to those that global climate models use to represent the cumulus convection and therefore to distribute the heat and water vapor and to produce the precipitation.

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Physics of Terrestrial Planets and Moons

T. Van Hoolst , in Treatise on Geophysics (Second Edition), 2015

10.04.2.1.2 Nutation, polar motion, and length-of-day variations

Because terrestrial planets move on elliptical orbits and have a nonzero obliquity and a nonspherically symmetrical form, the external gravitational torque from the Sun on them is time-dependent. Nutation of the angular momentum axis of a planet is the resulting small, time-dependent motion of that axis in space and can be expressed as a sum of periodic terms, whose main periods are subharmonics of the orbital period of the planet (for the Earth, see Chapter 3.10). Other planets and satellites can also exert a torque on the planet and cause additional nutational motion, but these nutations are generally negligible with respect to those related to the solar torque, except for the Earth's nutations due to the Moon.

Equation [1] shows that the change in angular momentum is entirely due to the external torque and further does not depend on the interior of the planet. This suggests that nutation observations would have no geophysical interest, other than providing a value for the relative moment of inertia difference (J ₂/C), in addition to but less precise than precession (see eqn [5] and also eqns [65] and [66]). However, observations do not measure orientation changes of the angular momentum axis but of the figure axis or the rotation axis of the mantle. In studies of periodic rotation variations, three different polar axes are distinguished: the rotation axis, the figure axis, and the angular momentum axis. The figure axis is defined as the axis of greatest moment of inertia, and the rotation axis is the axis of rotation of the solid outer part of the planet, that is, the mantle and crust, if the (outer) core is liquid. In general, the rotation and figure axes do not coincide with the angular momentum axis, and their orientations do depend on the interior of the planet. We will see that the relation between both axes and the angular momentum axis depends in a complex way on the interior and that nutation observations give direct access to the properties of the interior of a terrestrial planet.

To analyze the nutation of figure and rotation axes, it is more convenient to rewrite eqn [1] in a reference frame attached to the rotating planet. Let ${\overrightarrow{\mathit{e}}}_1,{\overrightarrow{\mathit{e}}}_2,{\overrightarrow{\mathit{e}}}_3$ represent three orthonormal vectors along corotating, body-fixed axes, rotating with instantaneous angular velocity $\overrightarrow{\mathit{\omega }}$ with respect to an inertial reference frame. We will choose the rotation axis to be close to the third axis. For both the inertial and the corotating reference frames, the center of mass of the planet is chosen as the origin O. For any vector $\overrightarrow{\mathit{V}}$ , the time derivative with respect to the corotating reference frame is related to the time derivative with respect to the inertial reference frame as

[6] $\frac{\mathrm{d}\overrightarrow{\mathit{V}}}{\mathrm{d}\mathit{t}}\left|\mathrm{inertial}=\frac{\mathrm{d}\overrightarrow{\mathit{V}}}{\mathrm{d}\mathit{t}}\right|\mathrm{co}‐\mathrm{rotating}+\mathit{\omega }\times \overrightarrow{\mathit{V}}$

(e.g., Goldstein, 1950), and conservation eqn [1] can be expressed as

[7] $\frac{\mathrm{d}\overrightarrow{\mathit{H}}}{\mathrm{d}\mathit{t}}+\overrightarrow{\mathit{\omega }}\times \overrightarrow{\mathit{H}}=\overrightarrow{\mathit{L}}$

where the time derivative is with respect to the body-fixed reference frame.

The angular momentum vector can be written as an integral over the total volume V of the planet as

[8] $\overrightarrow{\mathit{H}}={\displaystyle {\int }_{\mathit{V}}\overrightarrow{\mathit{r}}\times \overrightarrow{\mathit{v}}\mathit{\rho }\mathrm{d}\mathit{V}}$

where $\overrightarrow{\mathit{r}}$ is the coordinate vector, $\overrightarrow{\mathit{v}}$ the velocity, and ρ the density of the mass elements. For a rigid planet, we have

[9] $\overrightarrow{\mathit{H}}={\displaystyle {\int }_{\mathit{V}}\overrightarrow{\mathit{r}}\times \left(\overrightarrow{\mathit{\omega }}\times \overrightarrow{\mathit{r}}\right)\mathit{\rho }\mathrm{d}\mathit{V}}$

which can, by introducing the inertia tensor I with components

[10] ${\mathit{I}}_{\mathit{ij}}={\displaystyle {\int }_{\mathit{V}}\left[\left({\mathit{x}}_1^2+{\mathit{x}}_2^2+{\mathit{x}}_3^2\right){\mathit{\delta }}_{\mathit{ij}}-{\mathit{x}}_{\mathit{i}}{\mathit{x}}_{\mathit{j}}\right]\mathit{\rho }\mathrm{d}\mathit{V}}$

be written as

[11] $\overrightarrow{\mathit{H}}=\mathbf{I}\cdot \overrightarrow{\mathit{\omega }}.$

Here, x_i are the rectangular Cartesian coordinates of the mass elements. By a suitable choice of coordinate axes, the inertia tensor can be brought to diagonal form and the angular momentum components reduce to

[12] $\left.\begin{array}{l}{\mathit{H}}_1=\mathit{A}{\mathit{\omega }}_1,\\ {\mathit{H}}_2=\mathit{B}{\mathit{\omega }}_2,\\ {\mathit{H}}_3=\mathit{C}{\mathit{\omega }}_3.\end{array}\right\}$

For principal axis rotation, it follows that the figure axis and the rotation axis coincide with the angular momentum axis for a rigid planet.

By substituting eqn [12] into eqn [7], we obtain Euler equations for a rigid planet:

[13] $\mathit{A}\frac{\mathrm{d}{\mathit{\omega }}_1}{\mathrm{d}\mathit{t}}+\left(\mathit{C}-\mathit{B}\right){\mathit{\omega }}_2{\mathit{\omega }}_3={\mathit{L}}_1$

[14] $\mathit{B}\frac{\mathrm{d}{\mathit{\omega }}_2}{\mathrm{d}\mathit{t}}+\left(\mathit{A}-\mathit{C}\right){\mathit{\omega }}_1{\mathit{\omega }}_3={\mathit{L}}_2$

[15] $\mathit{C}\frac{\mathrm{d}{\mathit{\omega }}_3}{\mathrm{d}\mathit{t}}+\left(\mathit{B}-\mathit{A}\right){\mathit{\omega }}_1{\mathit{\omega }}_2={\mathit{L}}_3$

For rapidly spinning planets like the Earth and Mars, deviations from spherical symmetry are dominated by the flattening induced by rotation, which is symmetrical about the mean rotation axis x ₃, so that the approximation A  = B can be used. For the Earth, for example, the relative difference between A and B is more than 100 times smaller than the relative difference between A and C. In the absence of external torques $\overrightarrow{\mathit{L}}$ , the solution of Euler equations can then be written as

[16] $\left.\begin{array}{l}{\mathit{\omega }}_1=\mathit{a}cos\left({\mathit{\sigma }}_{\mathrm{E}}\mathit{t}+\mathit{f}\right),\\ {\mathit{\omega }}_2=\mathit{a}sin\left({\mathit{\sigma }}_{\mathrm{E}}\mathit{t}+\mathit{f}\right),\\ {\mathit{\omega }}_3=\mathit{\Omega },\end{array}\right\}$

where a is the amplitude and f the phase of the free polar motion. The motion is said to be free since both the amplitude and the phase depend only on the initial conditions if dissipation is neglected. Given an initial deviation of the rotation axis from the figure axis, the rotation axis rotates, or wobbles, about the figure axis with the Euler frequency:

[17] ${\mathit{\sigma }}_{\mathrm{E}}=\frac{\mathit{C}-\mathit{A}}{\mathit{A}}\mathit{\Omega }.$

This Euler wobble is a manifestation of the conservation of angular momentum when the figure axis and the rotation axis do not coincide. Solution (Borderies, 1980) is an example of wobble or polar motion, which in general describes the orientation variations of the rotation axis with respect to a body-fixed polar axis (for more precise definitions of polar motion and wobble, see Chapters 3.10 and 3.09). Polar motion can also be forced by motion in fluid planetary layers, such as an atmosphere and oceans, by redistributing mass and carrying additional angular moment (see Section 10.04.2 ). These motions can also cause periodic variations in the ω ₃-component of the rota vector or changes in the rotation speed. As these variations imply changes in the length of the day, they are, in the geophysical literature, mostly referred to as length-of-day variations (ΔLOD).

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The Crust

R.L. Rudnick , S. Gao , in Treatise on Geochemistry (Second Edition), 2014

4.1.6 Earth's Crust in a Planetary Perspective

The other terrestrial planets show a variety of crustal types, but none that are similar to that of the Earth. Mercury has an ancient, heavily cratered crust with a high albedo (see review of Taylor and Scott ( Chapter 1.18)). Its brightness plus the detection of sodium, and more recently the refractory element calcium, in the Mercurian atmosphere (Bida et al., 2000) has led to the speculation that Mercury's crust may be anorthositic, like the lunar highlands (see Taylor, 1992 and references therein). The MESSENGER mission (http://messenger.jhuapl.edu/), currently planned to rendezvous with Mercury in 2007, should considerably illuminate the nature of the crust on Mercury.

In contrast to Mercury's ancient crust, high-resolution radar mapping of Venus' cloaked surface has revealed an active planet, both tectonically and volcanically (see review of Fegley (Chapter 1.19) and references therein). Crater densities are relatively constant, suggesting a relatively young surface (~300–500   Ma, Phillips et al., 1992; Schaber et al., 1992; Strom et al., 1994). It has been suggested that this statistically random crater distribution may reflect episodes of mantle overturn followed by periods of quiescence (Schaber et al., 1992; Strom et al., 1994). Most Venusian volcanoes appear to erupt basaltic magmas, but a few are pancake-shaped, which may signify the eruption of a highly viscous lava such as rhyolite (e.g., Ivanov and Head, 1999). The unimodal topography of Venus is distinct from that of the Earth and there appear to be no equivalents to Earth's oceanic and continental dichotomy. It is possible that the high elevations on Venus were produced tectonically by compression of basaltic rocks made rigid by the virtual absence of water (Mackwell et al., 1998).

Of the terrestrial planets, only Mars has the bimodal topographic distribution seen on the Earth (Smith et al., 1999). In addition, evolved igneous rocks, similar to the andesites found in the continents on Earth, have also been observed on the Martian surface, although their significance and relative abundance is a matter of contention (see review by McSween (Chapter 1.22)). However, the bimodal topography of Mars appears to be an ancient feature (Frey et al., 2002), unlike the Earth's, which is a product of active plate tectonics. It remains to be seen whether the rocks that compose the high-standing southern highlands of Mars bear any resemblance to those of Earth's continental crust (McLennan, 2001a; Wanke et al., 2001).

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The Mantle and Core

K. Righter , ... K. Domanik , in Treatise on Geochemistry (Second Edition), 2014

3.12.1 Planetary Differentiation

Differentiation of terrestrial planets includes separation of a metallic core and possible later fractionation of mineral phases within either a solid or molten mantle ( Figure 1 ). Lithophile and siderophile elements can be used to understand these two different physical processes, and ascertain whether they operated in the early Earth. The distribution of elements in planets can be understood by measuring partition coefficients, D (D  =   ratio of concentrations of an element in different phases (minerals, metals, or melts)).

Figure 1. Schematic cross section through the Earth, showing an early magma ocean stage and a later cool and differentiated stage.

The siderophile elements (iron-loving) encompass over 30 elements and are defined as those elements that have D metal/silicate >1. Siderophile elements are useful for deciphering the details of core formation. This group of elements is commonly broken up into several subclasses (e.g., Righter, 2003), including the slightly siderophile elements (1   < D  <   10), moderately siderophile elements (MSE; 10   < D  <   10   000), and highly siderophile elements (HSE; D  >   10   000). Because these three groups encompass a wide range of partition coefficient values, they can be very useful in trying to determine the conditions under which metal may have equilibrated with the mantle (or a magma ocean). Because metal and silicate may equilibrate by several different mechanisms, such as at the base of a deep magma ocean, or as metal droplets descend through a molten mantle, partition coefficients can potentially shed light on which mechanism may be most important, thus linking the physics and chemistry of core formation. In the first part of this chapter, the metal/silicate partitioning of siderophile elements and how they may be used to understand planetary core formation is summarized.

Once a planet is differentiated into core and mantle, its mantle will cool during convection. Following core formation, the mantle can be initially molten, solid, or a mixture of both, depending on the initial thermal conditions. If hot enough, minerals will crystallize from a molten mantle, and become entrained in the convecting melt, or eventually settle out at the bottom of the magma ocean. The entrainment and settling process has been studied in detail (e.g., Solomotov, 2000; Tonks and Melosh, 1990), and is a potential mechanism for differentiation between the deep and shallow parts of Earth's mantle early in Earth's history. The lithophile elements, those elements that have D metal/silicate   ≪1, fall into many different subclasses and all hold information about the deep mineral structure of the mantle. Rare earth elements (REE) have proven to be useful: Eu anomalies have helped elucidate the role of plagioclase in lunar crust formation (e.g., Schnetzler and Philpotts, 1971; Weill et al., 1974), and LREE/HREE depletion and enrichment are indicators of partial melting in the presence of garnet in the mantle. High field strength elements (HFSE), Nb, Zr, Ta, and Hf, are all refractory and therefore not as susceptible to fractionation processes in the accretion disk prior to planetary formation, such as volatility or condensation. HFSE also have an affinity for ilmenite and rutile, and can explain differences between lunar and Martian samples as well as features of Earth's continental crust (Taylor and McLennan, 1985). Alkaline earth and alkaline elements include Rb, Sr, Ba, K, Cs, and Ca, some of which are involved in radioactive decay couples such as Rb–Sr and K–Ar. The latter is important in understanding the contribution of radioactive decay to planetary heat production, and potential deep sources of radiogenic Ar. Rb and K are further useful as tracers of hydrous phases such as mica and amphibole, and are also both volatile. Possible fractionation of any of these elements from chondritic or bulk Earth abundances (see Chapter 3.1) can be assessed with knowledge of partition coefficients. In the second part of this chapter, our understanding of mineral/melt fractionation of minor and trace elements at high pressures and temperatures is summarized and the implications for mantle differentiation is discussed.

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Physics of Terrestrial Planets and Moons

D. Breuer , W.B. Moore , in Treatise on Geophysics (Second Edition), 2015

10.08.1 Introduction

Unraveling a terrestrial planet's evolution in order to understand the observed processes and features is a difficult task that requires the integration of evidence from a wide variety of fields into consistent models. Geology, geophysics, mineralogy, and cosmochemistry, as well as chemistry, physics, and even biology, all influence the thermal and chemical evolution of terrestrial bodies. Our knowledge of the other terrestrial bodies stems not only mostly from remote sensing satellites but also, in some cases, from in situ chemical measurements and even from surface samples, in the case of the Moon, and meteorites – in the case of the Moon and Mars. These samples have been of immense value for the Moon and Mars science as they provide information not only about the composition but also about processes such as the formation of the core and the crust of those bodies. A fundamental process in planetary evolution is the thermal evolution of its interior, which depends on the internal heat sources, on thermophysical properties, and, to a large extent, on the dynamics of the planet's mantle through which heat is transported by thermal convection. It has been understood since the beginning of the twentieth century that thermal convection is capable of driving mantle circulation. If the mantle is heated from within (or from below) and is cooled from above, it can become gravitationally unstable and thermal convection can occur as colder rock descends into the mantle and hotter rock ascends toward the surface. This circulation of material transports heat toward the planet's surface and tends to cool the interior, while heat produced within, for example, by the decay of radioactive elements, tends to warm it. The motions driven by convective heat transport result in surface stresses and deformation, producing many geologic features observed on the terrestrial bodies today. An understanding of planetary thermal evolution is critical for interpreting these surface features in terms of interior processes including the dynamics of the mantle and the core.

The plate tectonics of the Earth are a unique expression of mantle convection among the terrestrial planets. Our planet's otherwise stiff lithosphere is segmented by weak zones into distinct plates. Where plates diverge, new lithosphere is created, and where they converge, the lithosphere descends into the mantle. This recycling process transfers heat out of the interior very effectively. One consequence of this process is that the Earth has a very young oceanic crust, generally less than 200 million years old (e.g., Condie, 1997). In addition to the oceanic crust, a less dense continental crust exists that usually does not recycle into the interior and has an average age of about 2000   Ma (e.g., Kemp and Hawkesworth, 2003). Comparing the Earth with the other terrestrial planets, the most striking difference at first glance is the state of the surface (including the crust), which is indicative of the way heat is transported. The surfaces of other planets are not segmented but consist of single plates, the so-called stagnant lids, beneath which the mantle convects. Heat flow through the lid is mainly by conduction, with some minor contribution by volcanic heat transport through this stagnant lid. The difference in the heat transport mechanism for the planets is also reflected in their thermal evolution.

In this chapter, we describe the thermal evolution and the mantle dynamics and related processes like crustal formation and the magnetic field evolution of the terrestrial bodies other than the Earth, that is, Mercury, Venus, Mars, and the Moon. The Galilean satellite Io is included in this chapter since this body consists, like the terrestrial planets and the Moon, of an iron-rich core and a silicate outer shell. The close orbit about Jupiter and the resonant orbital interaction among Io, Europa, and Ganymede make Io, however, special among the other terrestrial bodies. In its interior, tidal deformation plays an important role and provides an extremely large internal heat source. The consequence is a very different thermal evolution for Io than for the other bodies; therefore, we discuss Io in a separate section of this chapter.

The chapter is organized as follows: First, we describe the relevant physical and chemical properties of planets and planetary materials bearing on mantle dynamics and thermal evolution models. In the next section, the concept of mantle convection is introduced and the relationships between the convective parameters and the planform of the flow are discussed. A description of parameterized convection models follows with a comparison of three main heat transport mechanisms: plate tectonics, stagnant lid convection, and lithosphere delamination. In the next section, the crustal formation and magnetic field generation of terrestrial planets are described since both strongly depend on the thermal evolution of a planet and can be used as constraints for the models. The chapter concludes with separate reviews of the thermochemical evolution and mantle dynamics of Mercury, Venus, the Moon, Mars, and Io and includes a summary section.

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Physics of Terrestrial Planets and Moons

S.C. Werner , B.A. Ivanov , in Treatise on Geophysics (Second Edition), 2015

Abstract

Impact craters on terrestrial planets are key to studying planetary geology and geophysics as well as the planetary evolution remaining as geologic features at a planet's surface. To best use the cratering record history and interpret the planetary evolution, one needs to combine a wide set of processes and parameters. This chapter reviews impact cratering processes, estimates of average impact velocities, and impact probabilities for terrestrial planets. The basics of the impact crater scaling are outlined at an up-to-date level, describing the correlation of a measured impact crater diameter and the mass and size of a body that created the impact structure. Scaling laws for large impact craters are compared with the results of the direct numerical modeling of impact cratering.

The accumulation rate for impact craters on terrestrial planets is univocally considered to be constant (within a factor of 2) during the youngest 3   Ga of the solar system history, while crater-forming projectile flux evolution for the very earliest phase is debated and relates to the preferred solar system evolution concept. The intermediate flux is constrained by observations from the Earth's Moon. Different cratering chronology models are described. Measuring the number of accumulated craters at predefined sizes in a geologically outlined area of interest, one can estimate the relative and model absolute ages of the visible surface, assuming older surfaces accumulate larger number of craters. Possible challenges for this technique and the interpretation of measured size–frequency distributions of impact craters are discussed, including secondary cratering, atmospheric breakup, geologic activity, and target properties, which all modify the cratering record.

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Source: https://www.sciencedirect.com/topics/earth-and-planetary-sciences/terrestrial-planet

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