The three orbital parameters that govern the seasonal and geographical distribution of insolation are the precession angle, obliquity, and eccentricity. All three change gradually on a scale of many thousands of years, owing basic laws of mechanics which apply to any planet in any solar system.
The evolution of the precession angle derives from a fairly elementary property of the mechanics of rigid-body rotation. The rotation axis of a rotating body subject to a net torque executes a rotation at constant rate about a second axis whose orientation is determined by the torque. The precession rate is determined by the magnitude of the torque and the angular momentum of the rotating body. The phenomenon of precession can be easily observed on a tabletop, by setting down a toy gyroscope with its axis inclined from the vertical. The top will precess, because there is a torque caused by the Earth's gravity and the force of the tabletop pushing up on the point of the top. For planets, the torque instead is provided by the slight deviations of the mass distribution from spherical symmetry. The equatorial bulge caused by rotation is a major player, but other asymmetries, including those due to the distribution of ice, and of major geographic features, are also of consequence.
Obliquity variations also stem from the basic properties of rigid-body rotation, but these variations arise from fluctuations in the torque on the planet, rather than the mean torque. The obliquity cycle is inextricably linked with the precessional cycle, which modulates the orientation of the aspherical planet with respect to the non-uniform gravitational field caused by the Sun, the planet's moon(s) (if sufficiently massive), and all the other planets.
Eccentricity evolves because the periodic elliptical orbit is a solution only of the two-body problem, consisting of a planet and its star in isolation. Although the gravity of the Sun greatly dominates that of the other planets in our Solar System (and most likely in other planetary systems as well) the relatively small tugs of the planets on each other causes eccentricity to change gradually. Early in the history of this subject, it was shown by Laplace and Lagrange that the semi-major axis remains very nearly constant in the course of such eccentricity changes. The results of the preceding section therefore imply that eccentricity cycles have only a weak effect on annual mean insolation, since the mean insolation changes little if the semi-major axis is held fixed, except for extremely non-circular orbits.
Tiny deviations of the stellar gravity field from the ideal 1/r2 law add up to significant effects on obliquity and eccentricity over sufficiently long periods of time. The fact that the Sun is not perfectly spherical enters the problem, and even general relativistic deviations from Newtonian gravity have major effects.
Eccentricity modulates the distance seasons, and precession determines whether they constructively or destructively interfere with the tilt seasons. Meanwhile, obliquity variations modu late the strength of the tilt seasons. The net result is a rich variety of rhythms and patterns in insolation, which may lead to dramatic cycles in the state of a planet's climate.
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