Axial tilt

Over the course of an orbital period, the obliquity usually does not change considerably, and the orientation of the axis remains the same relative to the background of stars.

[10] About 830 CE, the Caliph Al-Mamun of Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years.

[12] During the Middle Ages, it was widely believed that both precession and Earth's obliquity oscillated around a mean value, with a period of 672 years, an idea known as trepidation of the equinoxes.

Earth's axis remains tilted in the same direction with reference to the background stars throughout a year (regardless of where it is in its orbit) – this is known as axial parallelism.

Variations in Earth's axial tilt can influence the seasons and is likely a factor in long-term climatic change (also see Milankovitch cycles).

[17] From 1984, the Jet Propulsion Laboratory's DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac.

[24] Using numerical methods to simulate Solar System behavior over a period of several million years, long-term changes in Earth's orbit, and hence its obliquity, have been investigated.

As the Moon continues to recede from Earth due to tidal acceleration, resonances may occur which will cause large oscillations of the obliquity.

But the axis of rotation can also move (axial precession), due to torque exerted by the Sun on a planet's equatorial bulge.

When a planet's precession rate approaches certain values, orbital resonances may cause large changes in obliquity.

[26][33] Some authors dispute that Mars's obliquity is chaotic, and show that tidal dissipation and viscous core-mantle coupling are adequate for it to have reached a fully damped state, similar to Mercury and Venus.

The stellar obliquity ψs, i.e. the axial tilt of a star with respect to the orbital plane of one of its planets, has been determined for only a few systems.

The rotational flattening of the planet and the entourage of moons and/or rings, which are traceable with high-precision photometry provide access to planetary obliquity, ψp.

It has been shown that the obliquities of exoplanets in the habitable zone around low-mass stars tend to be eroded in less than 109 years,[42][43] which means that they would not have tilt-induced seasons as Earth has.

The positive pole of a planet is defined by the right-hand rule : if the fingers of the right hand are curled in the direction of the rotation then the thumb points to the positive pole. The axial tilt is defined as the angle between the direction of the positive pole and the normal to the orbital plane. The angles for Earth, Uranus, and Venus are approximately 23°, 97°, and 177° respectively.
An illustration of axial parallelism . The axis of Earth remains oriented in the same direction with reference to the background stars regardless of where it is in its orbit . Northern hemisphere summer occurs at the right side of this diagram, where the north pole (red) is directed toward the Sun, winter at the left.
Relationship between Earth's axial tilt (ε) to the tropical and polar circles
Obliquity of the ecliptic for 20,000 years, from Laskar (1986). The red point represents the year 2000.
Axial tilt of eight planets and two dwarf planets, Ceres and Pluto