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Astron. Astrophys. 335, 281-286 (1998)

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3. Quantization of the satellite orbits

We have applied this method to the different satellite systems of the solar system. We have used only data concerning the most massive objects, having accurate and reliable parameters. The orbital data used in this paper are extracted from a compilation by Calvin J. Hamilton (Hamilton, 1997). The reader can also consult the following references: (J. K. Beatty, 1990), (Henbest, 1992), (Simon, 1992), (Thomas et al., 1983) and (L. A. Soderblom, 1982).

3.1. Jupiter system

The Fig. 4 shows the quantization of the main satellites of Jupiter, obtained by applying our method, the central mass M in this case being the mass of Jupiter. For all the following pictures, on the vertical axis, a is given in km, and M is given in terrestrial masses.

[FIGURE] Fig. 4. Main satellites of Jupiter. M is in Earth masses, an a in km.

We have taken into account only the satellites of Jupiter having a mass more than 10 kg: Amalthea, Io, Europa, Ganymede and Callisto. We have also reported the position of the equatorial radius of the planet.

3.2. Saturn system

The Fig. 5 shows the quantization of the orbits of the main satellites of Saturn, the central mass being the mass of Saturn. It appears that we have to classify Saturn's satellites in two systems: an inner and an outer system. Saturn is a complex system with rings and bodies orbiting some times at the same distance from the planet. On Fig. 5, for the inner system, the label Tethys refers to Tethys, Telesto and Calypso. The label Dione includes Dione and Helene.

[FIGURE] Fig. 5. Main satellites and rings of Saturn.

As an indication, we show also the position of a set including the D ring and the radius of Saturn itself, labeled 1 on the figure, a set including the B and the C ring labeled 2. The set labeled 3 includes the A ring, Pan, Atlas, Prometheus, Pandora, Epimetheus and Janus. For the outer system, we have not plotted the position of Hyperion which has a perturbed orbit due to the short time-scale resonance with Titan. One can also notice that the most heavy object of the inner system is Rhea, which corresponds roughly to the rank n of the outer system. This suggests that the inner system is maybe a sub-system obtained by the fragmentation process from the outer system.

3.3. Uranus system

The Fig. 6 shows the quantization of the main satellites of Uranus, the central mass being the mass of Uranus.

[FIGURE] Fig. 6. Main satellites and rings of Uranus.

The satellites of Uranus considered here are Miranda, Ariel, Umbriel, Titania and Oberon. The data labeled "other objects" are a set including the rings [FORMULA] and [FORMULA], and the moons Cordelia, Ophelia, Bianca, Cressida, Desdemona, Juliet, Portia, Rosalind, Belinda and Puck. All these objects have orbits that confer them a rank around n=3 in the diagram. But they could also be represented as an internal system, as shown in Fig. 7. But this last representation is questionable, in spite of the good correlation coefficient, because the values of rank are too high. That is why we show this picture only tentatively. The fact that these inner satellites of Uranus seem to be spread around n of the outer system, shows that there is a need for a second-order theory treating this system not as a simple 2 body problem, but also taking into account some other effects (tides, mutual effects...)

[FIGURE] Fig. 7. Possible inner system of Uranus.

Two new satellites have recently been discovered around Uranus (Gladman, 1997). But for the moment no orbital parameters are available, and we only have some positions . Therefore we are not able to add data concerning these satellites to our diagram.

3.4. Neptune system

Neptune is the most distant planet of the solar system for which we know the existence of satellites. Pluto-Charon looks more like a binary object. That is probably the reason why we know only its most distant satellites. We find here also high values of the ranks n, but as for Saturn and Uranus, it appears that there are two systems. We have computed the statistical significance only for the inner system that involves a set including Despina, Naiad and Thalassa, and Galatea and Larissa. Fig. 8 show a possible representation of the system, the outer system involving only two objects: Proteus and Triton.

Fig. 8. A possible representation of the satellite system of Neptune.

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© European Southern Observatory (ESO) 1998

Online publication: June 12, 1998