Abstract
Aims. We aim to determine whether Jupiter’s obliquity is bound to remain exceptionally small in the Solar System, or if it could grow in the future and reach values comparable to those of the other giant planets. Methods. The spin-axis of Jupiter is subject to the gravitational torques from its regular satellites and from the Sun. These torques evolve over time due to the long-term variations of its orbit and to the migration of its satellites. With numerical simulations, we explore the future evolution of Jupiter’s spin axis for different values of its moment of inertia and for different migration rates of its satellites. Analytical formulas show the location and properties of all relevant resonances. Results. Because of the migration of the Galilean satellites, Jupiter’s obliquity is currently increasing, as it adiabatically follows the drift of a secular spin-orbit resonance with the nodal precession mode of Uranus. Using the current estimates of the migration rate of the satellites, the obliquity of Jupiter can reach values ranging from 6° to 37° after 5 Gyr from now, according to the precise value of its polar moment of inertia. A faster migration for the satellites would produce a larger increase in obliquity, as long as the drift remains adiabatic. Conclusions. Despite its peculiarly small current value, the obliquity of Jupiter is no different from other obliquities in the Solar System: It is equally sensitive to secular spin-orbit resonances and it will probably reach comparable values in the future.
Highlights
The obliquity of a planet is the angle between its spin axis and the normal to its orbit
We aim to determine whether Jupiter’s obliquity is bound to remain exceptionally small in the Solar System, or if it could grow in the future and reach values comparable to those of the other giant planets
We explore the future evolution of Jupiter’s spin axis for different values of its moment of inertia and for different migration rates of its satellites
Summary
The obliquity of a planet is the angle between its spin axis and the normal to its orbit. For the giant planets of the Solar System, the secular spinorbit resonances are relatively thin today and well separated from each other This is why it is so difficult to explain the large obliquity of Uranus by a spin-orbit coupling, that the precession of Uranus’ spin axis is far from any first-order resonances The dynamics of Jupiter’s spin axis seems to be affected by secular spin-orbit resonances as other planets in the Solar System This was confirmed by Brasser & Lee (2015) and Vokrouhlický & Nesvorný (2015), who show that models of the late planetary migration have to be finely tuned to avoid overexciting Jupiter’s obliquity by spin-orbit coupling, while tilting Saturn to its current orientation. It depends on the spin rate of the planet and of its mass distribution, through the formula: α=
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