t(104 years)

Fig. 4.9 A simulation of the formation of Jupiter through the accretion of solid material (continuous line), and gases (dotted line) (After J.B. Pollack et al., 62, 1996) Gas Giants and Ice Giants

It remains for us to explain why Uranus and Neptune (Fig. 4.10) have masses significantly lower than that of Jupiter and Saturn (see Table 4.2). Whereas the masses of Jupiter and Saturn are, respectively, 318 and 95 Earth masses, those of Uranus and Neptune are only 15 and 17 Earth masses, respectively, which means that more than 50 per cent of their mass consists of their initial core material. They certainly experienced the phase that saw the collapse of the surrounding gas, as is shown by their numerous regular satellites (i.e., those that lie in the planet's equatorial plane and have quasi-circular orbits), but the amount of gas accreted was not at all abundant. What is the explanation for this effect? Uranus and Neptune, being more distant from the Sun, possibly took longer (between a few million to ten million years) to form an initial core that had the critical mass to capture the surrounding gas. Phase 3 described above (a burst of gas accretion) must have occurred after the Sun's T-Tauri phase, during which almost all of the gas and planetoids were swept out of the pro-tosolar disk. So there was very little material available for the final phase in the formation of Uranus and Neptune. Other possible factors that should be taken into account are gaseous loss to the Sun and photo-evaporation.

Uranus Photographed Voyager
Fig. 4.10 Uranus (a) and Neptune (b), photographed during the Voyager 2 fly-bys in 1986 and 1989, respectively (image credit: courtesy NASA, JPL) Rings and Satellites in the Outer Solar System

The nucleation model for the formation of the giant planets naturally explains the existence of systems of rings and regular satellites - i.e., that lie in the equatorial plane - around these planets. These bodies must have formed within the sub-nebula that collapsed around the nucleus in the final phase of accretion. The rings lie in the immediate proximity to the planets, within the Roche limit, where the tidal forces are too strong to allow the particles to accrete into satellite. (The Roche limit generally lies at a distance of about 2.5 planetary radii.) The rings may also be fed by bodies captured by the planet that are broken up within the Roche limit. Beyond the Roche limit, any captured bodies become the giant planets' irregular satellites, which are characterized by high inclinations and strong eccentricities. Interaction of the Giant Planets with the Small Bodies in the Outer Solar System

Recent numerical-simulation models show that the giant planets may interact with the residual disk of planetesimals and with the other giant planets, and that this may result in migration relative to the location at which they formed. The presence of Pluto and Kuiper-Belt objects in a 3:2 resonance (see Appendix A.5) with Neptune, for example, suggests a process of mutual perturbations, where Jupiter has migrated slightly inwards, whereas the other giant planets have moved outwards. Neptune would have trapped Pluto and numerous other TNOs (the Plutinos), forcing them to migrate as well, which would explain their high eccentricities. Numerical simulations seem to indicate that at a certain time, Saturn and Jupiter were in a 2:1 resonance, which must have produced significant perturbations of the orbits of the asteroids, the other giant planets, and the TNOs. This event appears to be the source of the massive bombardment that occurred 3,800 million years ago, that is, 800 million years after the formation of the giant planets. Formation of the Terrestrial Planets

Whereas the duration of the formation of the giant planets is reckoned in millions of years, that for the formation of the terrestrial planets may have been, according to numerical simulations, ten to one hundred times as long. The major reason is the smaller quantity of material available within the ice line. The planets condensed within a narrow zone, the initial agglomeration phase having ended with some one hundred embryonic bodies the size of Mercury. From this situation, the numerical models end up, in an unpredictable manner, with a small number (less than ten) of planets with sizes comparable with those of the terrestrial planets. Once formed, the planets continued to be subject to a bombardment by planetesimals, notably originating from the outer regions of the Solar System, which (with the exception of Mercury) seems to be the principal source for the formation of their atmospheres.

Mercury, very close to the Sun, does not have a stable atmosphere. On the day side the temperature may reach 700 K, and the average molecular velocity is too high, when compared with the escape velocity at the surface (less than 5 ms-1), to allow a neutral atmosphere to be trapped - even one consisting of heavy gases. Mercury's density implies an abnormally high metal:silicate ratio, which is difficult to explain within the framework for the condensation of the protosolar disk. It is possible to explain this paradox by invoking a collision between a proto-Mercury that was already differentiated, with a body one fifth of its mass. The material lost (primarily silicates) would have been ejected towards the Sun.

The method by which the terrestrial planets formed, in which there is no accretion of surrounding gas, explains the absence of rings and the low number of satellites orbiting these planets. In the case of Mars, the small satellites Phobos and Deimos are probably asteroids captured by the planet a long time after is formation. As for the Earth-Moon system (Fig. 4.11), its origin remained unexplained for a very long time. A model has come to be accepted recently, thanks to developments in the numerical simulation of chaotic and hydrodynamic situations. In this scenario, the Earth-Moon pair is the result of a glancing impact on the proto-Earth by a body of about one tenth the mass, which led to the ejection into Earth orbit of a portion of the mantles of both bodies, accompanied by the merger of the heavy elements in the two cores. The fragments ejected into Earth orbit re-accreted to form the Moon. This scenario has the advantage of accounting for the Moon's low density, as well as for the Moon's initial orbit, which was strongly elliptical and highly inclined, as is deduced from the current rate of lunar recession (4 cm per year). The history of Mercury, like that of the Earth-Moon pair, illustrates the importance of collisions in the early phases of planetary formation. This type of collision may also be responsible for the deviation of Uranus' axis of rotation to lie almost in the plane of the ecliptic.

Fig. 4.11 The Earth-Moon system, photographed by the Galileo probe. Dynamical models show that the presence of the Moon may be explained by a collision between the proto-Earth and a body with one tenth of the mass (©c NASA)

4.4 The Physical and Chemical Properties of Solar-System Objects

In this section, we examine the physical and chemical properties of the different classes of object in the Solar System, stressing those that provide information on formation and evolutionary processes. This listing will also enable us to highlight the extreme diversity of planets and satellites, even within any given family.

4.4.1 The Electromagnetic Spectrum of the Objects in the Solar System

Study of the physical and chemical properties of celestial bodies depends greatly on observation of their electromagnetic spectrum. Objects in the Solar System receive energy from the Sun, part of which is reflected or scattered back to space, and the remainder of which is absorbed and converted into thermal energy. The effective temperature (that is, that of a black body emitting the same thermal energy) depends on the surface albedo (i.e., the fraction of the solar energy that is reflected) and their heliocentric distance, as expressed in the following equations:

for an object in rapid rotation (as with the giant planets), or

for an object rotating slowly (such as Venus).

In these equations, F is the solar flux at a heliocentric distance of 1 AU, D is the heliocentric distance, R is the radius of the object, A is its albedo, and o is Stefan's constant.

In CGS units, the effective temperature may be expressed as:

for a rapidly rotating object, and

for a slowly rotating object.

For the planets in the Solar System, the albedo is of the order of 0.3. The effective temperatures vary from 700 K (maximum) for Mercury to about 50 K for Neptune. The maxima for the corresponding thermal flux range from 4 |m

(Mercury) to 70 |m (Pluto). The radiation from Solar-System objects therefore primarily lies in the visible for the reflected component and in the infrared for the thermal component. The infrared region is also a favourable region for the observation of neutral molecules in planetary atmospheres, because it is the spectral region where the strongest rotational and vibrational transitions are found.

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