Editing Ecliptic (section)

== Obliquity of the ecliptic {{anchor|Obliquity}}==
{{main|Obliquity of the ecliptic}}

''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.<ref>
{{cite book 
 | last = Chauvenet
 | first = William
 | title = A Manual of Spherical and Practical Astronomy
 | publisher = J.B. Lippincott Co., Philadelphia
 | date = 1906
 | volume = I
 |url=https://books.google.com/books?id=yobvAAAAMAAJ
}}, art. 365–367, p. 694–695, at Google books</ref>

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 ephemeris|fundamental ephemerides]] as the accuracy of [[Observational astronomy|observation]] improves and as the understanding of the [[Analytical dynamics|dynamics]] increases, and from these ephemerides various astronomical values, including the obliquity, are derived.

[[File:Obliquity of the ecliptic laskar.PNG|thumb|upright=1.4|left|Obliquity of the ecliptic for 20,000 years, from Laskar (1986).<ref name="laskar"/> Note that the obliquity varies only from 24.2° to 22.5° during this time. The red point represents the year 2000.]]

Until 1983 the obliquity for any date was calculated from [[Newcomb's Tables of the Sun|work of Newcomb]], who analyzed positions of the planets until about 1895:

{{math|''ε'' {{=}} 23°27′08.26″ − 46.845″ ''T'' − 0.0059″ ''T''<sup>2</sup> + 0.00181″ ''T''<sup>3</sup>}}

where {{math|''ε''}} is the obliquity and {{math|''T''}} is [[Tropical year|tropical centuries]] from [[Epoch (astronomy)|B1900.0]] to the date in question.<ref>''Explanatory Supplement'' (1961), sec. 2B</ref>

From 1984, the [[Jet Propulsion Laboratory Development Ephemeris|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:

{{math|''ε'' {{=}} 23°26′21.45″ − 46.815″ ''T'' − 0.0006″ ''T''<sup>2</sup> + 0.00181″ ''T''<sup>3</sup>}}

where hereafter {{math|''T''}} is [[Julian year (astronomy)|Julian centuries]] from [[Epoch (astronomy)|J2000.0]].<ref>
{{cite book 
 | last = U.S. Naval Observatory
 | first =Nautical Almanac Office
 |author2=H.M. Nautical Almanac Office
 | title = The Astronomical Almanac for the Year 1990
 | publisher = U.S. Govt. Printing Office
 | date = 1989
 | isbn = 0-11-886934-5
}}, p. B18</ref>

JPL's fundamental ephemerides have been continually updated. The ''Astronomical Almanac'' for 2010 specifies:<ref>''Astronomical Almanac 2010'', p. B52</ref>

{{math|''ε'' {{=}} 23°26′21.406″ − 46.836769″ ''T'' − 0.0001831″ ''T''<sup>2</sup> + 0.00200340″ ''T''<sup>3</sup> − 0.576×10<sup>−6</sup>″ ''T''<sup>4</sup> − 4.34×10<sup>−8</sup>″ ''T''<sup>5</sup>}}

These expressions for the obliquity are intended for high precision over a relatively short time span, perhaps several centuries.<ref>
{{cite book
 |url = https://archive.org/details/acompendiumsphe00newcgoog
 |title = A Compendium of Spherical Astronomy
 |last = Newcomb
 |first = Simon
 |date = 1906
 |publisher=MacMillan Co., New York
}}, p. 226-227, at Google books</ref> J. Laskar computed an expression to order {{math|''T''<sup>10</sup>}} good to {{math|0.04″}}/1000 years over 10,000 years.<ref name="laskar">
{{Cite journal|title = Secular Terms of Classical Planetary Theories Using the Results of General Relativity
 |last = Laskar
 |first = J.
 |journal = Astronomy and Astrophysics
 |date = 1986|volume = 157
 |issue = 1
 |page = 59
 |bibcode = 1986A&A...157...59L
}}, table 8, at SAO/NASA ADS</ref>

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.<ref>
{{cite book 
 | last = Meeus
 | first = Jean
 | title = Astronomical Algorithms
 | publisher = Willmann-Bell, Inc., Richmond, VA
 | date = 1991
 |isbn=0-943396-35-2
}}, chap. 21</ref>

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