page_title: Ecliptic
section_title: Obliquity of the ecliptic
hierarchical_section_title: Ecliptic / Obliquity of the ecliptic
caption_attribution_description: Graph of obliquity of the ecliptic vs time for +/- 10,000 years; from Laskar, J. (1986), "Secular Terms of Classical Planetary Theories Using the Results of General Relativity"
context_page_description: The ecliptic is the plane of Earth's orbit around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars. The ecliptic is an important reference plane and is the basis of the ecliptic coordinate system.
context_section_description: Obliquity of the ecliptic is the term used by astronomers for the inclination of Earth's equator with respect to the ecliptic, or of Earth's rotation axis to a perpendicular to the ecliptic. It is about 23.4° and is currently decreasing 0.013 degrees (47 arcseconds) per hundred years because of planetary perturbations.
  The angular value of the obliquity is found by observation of the motions of Earth and other 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.
  Until 1983 the obliquity for any date was calculated from work of Newcomb, who analyzed positions of the planets until about 1895:
  ε = 23° 27′ 08″.26 − 46″.845 T − 0″.0059 T² + 0″.00181 T³
  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:
  ε = 23° 26′ 21″.45 − 46″.815 T − 0″.0006 T² + 0″.00181 T³
  where hereafter T is Julian centuries from J2000.0.
  JPL's fundamental ephemerides have been continually updated. The Astronomical Almanac for 2010 specifies:
  ε = 23° 26′ 21″.406 − 46″.836769 T − 0″.0001831 T² + 0″.00200340 T³ − 0″.576×10⁻⁶ T⁴ − 4″.34×10⁻⁸ T⁵
  These expressions for the obliquity are intended for high precision over a relatively short time span, perhaps ± several centuries. 
  J. Laskar computed an expression to order T¹⁰ good to 0″.04/1000 years over 10,000 years.
  All of these expressions are for the mean obliquity, that is, without the nutation of the equator included. The true or instantaneous obliquity includes the nutation.
caption: Obliquity of the ecliptic for 20,000 years, from Laskar (1986).[14] Note that the obliquity varies only from 24.2° to 22.5° during this time. The red point represents the year 2000.
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