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" A '?' denotes no useful value is available. b If differentiated.

c The densities are the estimated values in situ, i.e. they are (slightly) compressed densities. The large ranges for Europa, Ganymede, and Titan correspond to various possible compositions for the cores.

" A '?' denotes no useful value is available. b If differentiated.

c The densities are the estimated values in situ, i.e. they are (slightly) compressed densities. The large ranges for Europa, Ganymede, and Titan correspond to various possible compositions for the cores.

Figure 5.7 shows a model of Pluto's interior, along with models of Titan, Triton, and the four Galilean satellites. Table 5.3 gives further data from typical models.

The EKO Eris, which is slightly larger than Pluto, has a small satellite. Its orbit will enable Eris's mass to be determined and hence its mean density. Several other EKOs have companions, which have yielded densities around 200 kg m-3, indicating a loosely consolidated structure, rather like the nuclei of comets, as expected.

Question 5.5

How do solar nebular theories account for Pluto being an icy-rocky body, and being so small? 5.2.3 The Galilean Satellites of Jupiter

Much has been learned about the Galilean satellites from the flybys of Voyagers 1 and 2 and from the Galileo Orbiter (Table 4.1). Figure 5.7 shows interior models, Table 5.3 gives central temperatures, densities, and pressures, and Figure 1.6 shows their orbits.

Io is the innermost of the Galilean satellites of Jupiter. It is slightly larger than the Moon, and somewhat more dense. The mean density, 3530 kg m-3, indicates a predominantly silicate plus iron/FeS composition, and the value of C/MR2 of 0.378 is sufficiently less than the uniform-sphere value of 0.4 to require concentration of denser materials into a core. The model in Figure 5.7 has a predominantly iron core extending about half way to the surface, thus accounting for about one-eighth of the volume. The Galileo Orbiter obtained inconclusive evidence for a magnetic dipole moment, somewhat larger than that of Mercury, so the core could be (partly) molten. This is also indicated by Io's density. This is too low for any reasonable proportion of iron or FeS, unless a proportion is liquid.

For the core to be partly molten the interior of Io would have to be hot, and there is dramatic evidence that it is - Io is the most volcanically active of all the planetary bodies in the Solar System (Plate 12)! The mantle, throughout most of its volume, is thought to be an asthenosphere in which solid state convection is occurring, and is overlain by a thin lithosphere that includes a silicate crust rich in sulphur. Partial melting within the asthenosphere would provide the observed volcanic outflows, which are observed to consist of silicates, sulphur, and sulphur dioxide (SO2).

It came as a surprise to most astronomers that such a small world has a sufficiently hot interior to be so volcanically active. □ Why was this surprising?

Equation (4.13) (Section 4.5.4) indicates that small worlds lose energy rapidly, so should now be cool to considerable depth. Indeed, the Moon is comparable in size and mass with Io yet has little or no present-day volcanic activity, and nor does Mercury, which is larger and more massive than Io. Moreover, volcanism is an efficient way for a body to lose heat. We therefore need to find a considerable interior energy source for Io. There is radiogenic heating, but this is far from sufficient. The only plausible additional source is tidal energy.

In Section 4.5.1 you saw that tidal energy will be generated in a body by its rotation, which sweeps the material of the body through the tidal elongation. In the case of Io the rotation period is the same as its orbital period - synchronous rotation - and this is itself a result of tidal effects. Were the orbit circular, Io would keep the same face to Jupiter, as in Figure 5.8(a), and material would not be swept through the tidal elongation - the dot is fixed with respect to the surface. There would then be no tidal heating by this means. Moreover, in a circular orbit Io's distance from Jupiter would be constant, so there would also be no tidal energy generated through variations in the Jupiter-Io distance.

In fact, the orbit of Io is not quite circular. Therefore, there is tidal input through its distance from Jupiter varying. Moreover, there is now a contribution from Io's rotation. The rate of rotation is constant, but the rate of motion around the orbit varies, just as the rate of motion of a planet around its elliptical orbit varies in accord with Kepler's second law. Therefore, as seen from Jupiter, Io seems to swing to and fro as it orbits the planet, as shown in Figure 5.8(b), and so material now oscillates through the tidal elongation. Were it not for mean motion resonances with Europa and Ganymede - the orbital periods of Io, Europa, Ganymede are in the ratios 1:2:4 - Io's orbit would be much more circular, and tidal heating would be reduced (equation (4.13)).

Figure 5.8 Synchronous rotation (a) in a circular respect to the surface of the small body.

orbit and (b) in an elliptical orbit. The dot is fixed with

Figure 5.8 Synchronous rotation (a) in a circular respect to the surface of the small body.

orbit and (b) in an elliptical orbit. The dot is fixed with

Question 5.6

The Moon is in synchronous rotation in its orbit around the Earth. With the aid of Tables 1.1 and 1.2 and the answer to Question 4.9, show that the tidal field across the Moon is only 0.004 times that across Io. In relation to tidal heating, why must this factor more than offset the greater eccentricity of the lunar orbit than that of Io?

Europa

Europa, another Moon-sized world, is the next nearest Galilean satellite to Jupiter. Its surface is covered in water ice, though its mean density, 3010kgm-3, is only slightly less than that of the Moon, indicating a predominantly silicate composition.

□ What does the value of C/MR in Table 4.2 indicate?

The value of C/MR is less than that of Io, which can be met by a greater concentration of denser materials as depth increases. If there is a dry rocky core of uniform composition (mainly silicates plus FeS), overlain by a water mantle, ice, or ice plus liquid, then one model meets the observational constraints with a mantle 150 km thick. A dry core is indicated by thermal models. However, it is likely that the rocky core itself is divided into two zones, the inner zone being iron-rich, perhaps with FeS and/or iron oxides. The Galileo Orbiter obtained inconclusive evidence regarding a magnetic dipole moment. Various detailed compositions, with or without an iron-rich core, lead to a range of models, but there is general agreement that Europa's water mantle is 100-200 km thick.

The same tidal input operates as in Io, though the rate at which energy is released in the shell of water and in the interior is roughly 20 times less, because of Europa's greater distance from Jupiter, which more than offsets the larger eccentricity of Europa's orbit (see equation(4.13) and the answer to Question 5.6). We thus expect Europa to have a cooler interior, though ongoing tidal and radiogenic heating, supplemented by solar radiation and residual primordial heat, should be sufficient to liquefy the lower part of the water shell. There might even be a modest amount of volcanic activity on the ocean floor. The very smooth icy surface indicates an icy crust that could be as little as a few kilometres thick, and though this could be underlain by icy slush rather than by liquid oceans, most astronomers believe that there are widespread oceans. Temperatures throughout most of the mantle are too low for pure water to be liquid. However, salts will be present, notably NaCl, which lower the freezing temperature, and this can be lowered still further by the presence of NH3, which combines with H2O to form NH3.H2O.

Ganymede and Callisto

The two outer Galilean satellites Ganymede and Callisto have surfaces of water ice, with a thin veneer of silicates covering much of Callisto. Their mean densities, 1940 kgm-3 and 1830 kgm-3 respectively, require a substantial proportion of ice - unlike Io and Europa these are icy-rocky bodies. The conditions in which Ganymede and Callisto formed, and their observed surface composition, mean that the icy component is predominantly water, probably salty, plus a few percent of NH3 in Callisto, rather less in Ganymede. NH3.H2O is also expected to be present.

□ From Figure 5.7, what is the proportion of the volume of Ganymede that is water ice?

If Ganymede's water is essentially all in its icy mantle, then the proportion that is not water ice is the cube of the radius of the silicate-rich mantle divided by the cube of Ganymede's radius. From Figure 5.7 this ratio is 0.24. Therefore, the proportion of the volume that is water ice is

0.76. However, the proportion that is water by mass is about 50%, because water is much less dense than silicates and iron-rich substances.

The low value of 0.311 for C/MR2 indicates that the silicates and iron-rich materials in Ganymede are concentrated into the core shown in Figure 5.7, perhaps with further concentration of iron-rich materials into an inner core. Such extensive differentiation is to be expected in such a massive body, the most massive in the Solar System. Ganymede has a magnetic dipole moment about three times that of Mercury, which suggests that the core is at least partly molten and convecting vigorously. Vigorous convection requires greater energy input than at present. In the past this might have been driven by greater tides resulting from a more eccentric orbit. It is likely that the orbits of all the Galilean satellites have evolved, and it is possible that Ganymede's eccentricity was substantially higher within the last 1000 Ma or so. The surface of Ganymede reveals relatively recent and extensive geological activity, consistent with a warm interior, and there is also evidence for differentiation at some time in the past (Section 7.4.2). However, it is not clear whether convection driven at some earlier time could still be occurring. Another explanation of the magnetic field is that there is a shell of magnetite, Fe3O4, that became permanently magnetized by Jupiter's magnetic field when the shell solidified, perhaps 2000 Ma ago.

A third explanation of the magnetic field is indicated by surface features (Section 7.4.2) that suggest a liquid layer a few kilometres thick at a depth of about 170 km. This would be kept liquid as a result of radiogenic and tidal heating. It would be salty, and therefore electrically conducting.

For Callisto, the value of 0.358 for C/MR2 is significantly less than the value of 0.38 that would correspond to self-compression of an undifferentiated ice-rock mixture. However, it is not small enough to indicate full differentiation, and so there is only a modest degree of concentration of rocky materials towards the centre. Any core is predominantly rocky-icy, though a small core free of icy materials cannot be ruled out. The surface of Callisto suggests that it has always had a cooler interior than Ganymede, and this is consistent with limited differentiation. A likely reason is negligible tidal heating, a result of the low eccentricity of Callisto's orbit, the lack of orbital resonances, and its greater distance from Jupiter. Further factors are the smaller mass ratio of rocky to icy materials in Callisto, resulting in less radiogenic heating, and the possibility of solid state convection in the rocky-icy core that hastened the cooling of the interior. The absence of such a core in Ganymede would have helped promote its more complete differentiation. □ Would you expect Callisto to have a magnetic dipole moment?

If Callisto has a cool interior then the magnetic dipole moment should be zero. Callisto is sufficiently far from Jupiter that the Jovian magnetic field is weak, allowing very weak local fields to be detected. This has allowed the Galileo Orbiter to place a very low upper limit on any magnetic dipole moment, entirely consistent with Callisto's other properties. Callisto does, however, disturb Jupiter's magnetic field, indicating the presence of electrically conducting liquids. A liquid shell of water rich in NH3, NH3.H2O, and salts, thus lowering the freezing temperature, could be present in the icy mantle. This is also an explanation of the absence of chaotic impact features diametrically opposite the impact basin Valhalla (Section 7.4.2).

The Galilean satellites as a group

Among the Galilean satellites, the proportion of icy materials increases as we go out from Jupiter, from zero for Io, to over 50% by mass for Callisto. Unless these satellites formed further out, and migrated inwards, the explanation is that Io formed too close to proto-Jupiter ever to have had an icy component. Europa acquired a small amount of ice, and Ganymede and Callisto substantial amounts. Water ice would have dominated - the solar nebula in the Jovian region would have been too warm to allow as much of the more volatile ices to condense, or remain condensed.

Increasing distance from Jupiter also correlates with the inferred thermal histories, with greater cooling from Io to Europa, to Ganymede, to Callisto. This trend is largely because of the decrease in tidal energy input with increasing distance from Jupiter.

5.2.4 Small Satellites

There remain the host of small satellites, the asteroids, and the comets. The interiors of the asteroids and the comets were discussed briefly in Chapter 3, and we shall say no more about them here, but concentrate on the small satellites.

The smallest body we have so far considered is Pluto, which has a radius of 1153 km. Next down in size is Titania, the largest satellite of Uranus. This has a radius of 789 km so this is a real step down, and is a convenient point at which to break off discussion of satellite interiors in any detail. Most of the small satellites that orbit the giants will have a composition roughly the same as the large icy-rocky satellites - by mass about half icy materials and half rocky materials. The densities of some of the innermost satellites of Saturn have been estimated from their effect on the rings and on other satellites, and the values are very low - less than the density of water ice (917kgm-3 at 273 K and 105Pa, denser at lower temperatures, but not very sensitive to pressure). □ What does this indicate?

Such low densities indicate quite a high degree of porosity. Satellites very close to Jupiter have been warmed, either tidally or by the luminosity of the young giant, to the extent that they are very probably depleted in icy materials. One of these, Amalthea, mean radius 84 km, has had its mass measured by the Galileo Orbiter. This gives a density of about 860Kg m-3, which for an ice-free body indicates high porosity, to the extent that it is probably a rocky rubble pile, loosely reassembled after collisional disruption. Its highly non-spherical shape is consistent with this.

Just five small satellites are known not to orbit giants. These are the Martian satellites Phobos and Deimos, rocky bodies that are probably captured asteroids, Pluto's icy-rocky satellite Charon, and its two tiny satellites Nix and Hydra. Tidal heating is likely to have ensured that Charon is fully differentiated. The smallest satellites of all might not have differentiated even if they have been warmed. This is because in very small bodies gravity is relatively weak, and so the chemical forces between constituents can override the gravitational trend towards differentiation.

The surfaces of some of the small satellites are more remarkable than their interiors, so we shall return to them in Chapter 7.

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