Axial tilt

Earth's orbital plane is known as the ecliptic plane, and Earth's tilt is known to astronomers as the obliquity of the ecliptic, being the angle between the ecliptic and the celestial equator on the celestial sphere.

Earth currently has an axial tilt of about 23.44°. This value remains about the same relative to a stationary orbital plane throughout the cycles of axial precession. | doi-access=free

History

The ancient Greeks had good measurements of the obliquity since about 350 BCE, when Pytheas of Marseilles measured the shadow of a gnomon at the summer solstice.

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. Perhaps the first to realize this was incorrect (during historic time) was Ibn al-Shatir in the fourteenth century{{cite book

Seasons

Main article: Season

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. This means that one pole (and the associated hemisphere of Earth) will be directed away from the Sun at one side of the orbit, and half an orbit later (half a year later) this pole will be directed towards the Sun. This is the cause of Earth's seasons. Summer occurs in the Northern Hemisphere when the North Pole is directed toward and the South Pole away from the Sun. Variations in Earth's axial tilt can influence the seasons and is likely a factor in long-term climatic change (also see Milankovitch cycles).

Oscillation

Short term

The exact angular value of the obliquity is found by observation of the motions of Earth and planets over many years. Astronomers produce new fundamental ephemerides as the accuracy of observation improves and as the understanding of the dynamics increases, and from these ephemerides various astronomical values, including the obliquity, are derived.

Annual almanacs are published listing the derived values and methods of use. Until 1983, the Astronomical Almanac's angular value of the mean obliquity for any date was calculated based on the work of Newcomb, who analyzed positions of the planets until about 1895:

:

where ε is the obliquity and T is tropical centuries from B1900.0 to the date in question.

From 1984, the Jet Propulsion Laboratory's DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated:

:

where hereafter T is Julian centuries from J2000.0.

JPL's fundamental ephemerides have been continually updated. For instance, according to IAU resolution in 2006 in favor of the P03 astronomical model, the Astronomical Almanac for 2010 specifies:

:

These expressions for the obliquity are intended for high precision over a relatively short time span, perhaps ± several centuries.

:

where here t is multiples of 10,000 Julian years from J2000.0.See table 8 and eq. 35 in {{cite journal

These expressions are for the so-called mean obliquity, that is, the obliquity free from short-term variations. Periodic motions of the Moon and of Earth in its orbit cause much smaller (9.2 arcseconds) short-period (about 18.6 years) oscillations of the rotation axis of Earth, known as nutation, which add a periodic component to Earth's obliquity. |access-date=26 March 2015

Long term

Main article: Formation and evolution of the Solar System

Main article: Milankovitch cycles

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. For the past 5 million years, Earth's obliquity has varied between 22°2′33″ and 24°30′16″, with a mean period of 41,040 years. This cycle is a combination of precession and the largest term in the motion of the ecliptic. For the next 1 million years, the cycle will carry the obliquity between 22°13′44″ and 24°20′50″.

The Moon has a stabilizing effect on Earth's obliquity. Frequency map analysis conducted in 1993 suggested that, in the absence of the Moon, the obliquity could change rapidly due to orbital resonances and chaotic behavior of the Solar System, reaching as high as 90° in as little as a few million years (also see Orbit of the Moon). |url-status=dead |archive-url=https://web.archive.org/web/20121123093109/http://bugle.imcce.fr/fr/presentation/equipes/ASD/person/Laskar/misc_files/Laskar_Robutel_1993.pdf |archive-date=23 November 2012