Axial tilt

<h2 id="standards">Standards</h2>
There are two standard methods of specifying a planet's tilt. One way is based on the planet's north pole, defined in relation to the direction of Earth's north pole, and the other way is based on the planet's positive pole, defined by the <a href="/facts/Axis%25E2%2580%2593angle_representation/WDfmToVP">right-hand rule</a>:

<ul><li>The <a href="/facts/International_Astronomical_Union/GMFPImXo">International Astronomical Union</a> (IAU) defines the north pole of a planet as that which lies on Earth's north side of the <a href="/facts/Invariable_plane/SSoYrjeR">invariable plane</a> of the <a href="/facts/Solar_System/QIcLSazQ">Solar System</a>;<a class="footnote-ref" id="fnref:2" href="#fn:2">2</a> under this system, <a href="/facts/Venus/pADnueP6">Venus</a> is tilted 3° and rotates <a href="/facts/Retrograde_motion/1HCbwQqy">retrograde</a>, opposite that of most of the other planets.<a class="footnote-ref" id="fnref:3" href="#fn:3">3</a><a class="footnote-ref" id="fnref:4" href="#fn:4">4</a></li>
<li>The IAU also uses the right-hand rule to define a positive pole<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a> for the purpose of determining orientation. Using this convention, Venus is tilted 177° ("upside down") and rotates prograde.</li></ul>
<h2 id="earth">Earth</h2>
Further information: <a href="/facts/Ecliptic/cJxXDDDW">Ecliptic § Obliquity of the ecliptic</a>
See also: <a href="/facts/Earth%2527s_rotation/mDbXcKUx">Earth's rotation</a> and <a href="/facts/Earth-centered_inertial/yxaIGqoT">Earth-centered inertial</a>
<a href="/facts/Earth/HLLmDfj0">Earth</a>'s <a href="/facts/Orbit/nD2TPySG">orbital plane</a> is known as the <a href="/facts/Ecliptic/cJxXDDDW">ecliptic</a> plane, and <a href="/facts/Earth/HLLmDfj0">Earth's tilt</a> is known to astronomers as the obliquity of the ecliptic, being the angle between the ecliptic and the <a href="/facts/Celestial_equator/P9Lyq2DE">celestial equator</a> on the <a href="/facts/Celestial_sphere/TYAtXgor">celestial sphere</a>.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a> It is denoted by the <a href="/facts/Greek_letter/1cHwB8Dg">Greek letter</a> Epsilon <a href="/facts/Epsilon/3G846hlN">ε</a>.
Earth currently has an axial tilt of about 23.44°.<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a> This value remains about the same relative to a stationary orbital plane throughout the cycles of <a href="/facts/Axial_precession/NQ79x3m3">axial precession</a>.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a> But the ecliptic (i.e., Earth's orbit) moves due to planetary <a href="/facts/Perturbation_(astronomy)/og5hPpjQ">perturbations</a>, and the obliquity of the ecliptic is not a fixed quantity. At present, it is decreasing at a rate of about <a href="/facts/Second_of_arc/tybs6YGC">46.8″</a><a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> per <a href="/facts/Century/HGNNAxYj">century</a> (see details in Short term below).

<h3>History</h3>
The ancient Greeks had good measurements of the obliquity since about 350 BCE, when <a href="/facts/Pytheas/Ducfwbbs">Pytheas</a> of Marseilles measured the shadow of a <a href="/facts/Gnomon/J23dXDvD">gnomon</a> at the summer solstice.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a> About 830 CE, the Caliph <a href="/facts/Al-Mamun/aaHmoQ9g">Al-Mamun</a> of Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years.<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a> In 1437, <a href="/facts/Ulugh_Beg/daFnvQn4">Ulugh Beg</a> determined the Earth's axial tilt as 23°30′17″ (23.5047°).<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a>
During the <a href="/facts/Middle_Ages/RqzEKB9v">Middle Ages</a>, 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 <a href="/facts/Trepidation_(astronomy)/TVpwVE3y">trepidation</a> of the equinoxes. Perhaps the first to realize this was incorrect (during historic time) was <a href="/facts/Ibn_al-Shatir/AaQkf0Dq">Ibn al-Shatir</a> in the fourteenth century<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a> and the first to realize that the obliquity is decreasing at a relatively constant rate was <a href="/facts/Fracastoro/tF8SfRzv">Fracastoro</a> in 1538.<a class="footnote-ref" id="fnref:14" href="#fn:14">14</a> The first accurate, modern, western observations of the obliquity were probably those of <a href="/facts/Tycho_Brahe/HroPxnCq">Tycho Brahe</a> from <a href="/facts/Denmark/KVtykzsw">Denmark</a>, about 1584,<a class="footnote-ref" id="fnref:15" href="#fn:15">15</a> although observations by several others, including <a href="/facts/Al-Ma%2527mun/aaHmoQ9g">al-Ma'mun</a>, <a href="/facts/Sharaf_al-D%25C4%25ABn_al-T%25C5%25ABs%25C4%25AB/uYR64wm4">al-Tusi</a>,<a class="footnote-ref" id="fnref:16" href="#fn:16">16</a> <a href="/facts/Georg_Purbach/VCAn8Ecd">Purbach</a>, <a href="/facts/Regiomontanus/CrMSdtQU">Regiomontanus</a>, and <a href="/facts/Bernhard_Walther/mn1jLxGW">Walther</a>, could have provided similar information.

<h3>Seasons</h3>
Main article: <a href="/facts/Season/20vCqJWN">Season</a>

<a href="/facts/Earth/HLLmDfj0">Earth</a>'s axis remains tilted in the same direction with reference to the background stars throughout a year (regardless of where it is in its <a href="/facts/Orbit/nD2TPySG">orbit</a>) – this is known as <a href="/facts/Axial_parallelism/fEXp32US">axial parallelism</a>. This means that one pole (and the associated <a href="/facts/Hemispheres_of_the_Earth/2a3eATpx">hemisphere of Earth</a>) 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 <a href="/facts/Season/20vCqJWN">seasons</a>. <a href="/facts/Summer/v3DY22Uq">Summer</a> occurs in the <a href="/facts/Northern_hemisphere/EFwyqL25">Northern hemisphere</a> 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 <a href="/facts/Climate_change_(general_concept)/D3X6Ulbu">climatic change</a> (also see <a href="/facts/Milankovitch_cycles/SxLbHrWX">Milankovitch cycles</a>).

<h3>Oscillation</h3>
<h4>Short term</h4>

The exact angular value of the obliquity is found by observation of the motions of Earth and <a href="/facts/Planets/rbPjE6Bx">planets</a> over many years. Astronomers produce new <a href="/facts/Fundamental_ephemeris/Q2EmvKt1">fundamental ephemerides</a> as the accuracy of <a href="/facts/Observational_astronomy/PKgYt9PX">observation</a> improves and as the understanding of the <a href="/facts/Analytical_dynamics/3yqJfP8l">dynamics</a> increases, and from these ephemerides various astronomical values, including the obliquity, are derived.
Annual <a href="/facts/Almanac/LFaK6BWr">almanacs</a> are published listing the derived values and methods of use. Until 1983, the <a href="/facts/Astronomical_Almanac/kvC8j448">Astronomical Almanac</a>'s angular value of the mean obliquity for any date was calculated based on the <a href="/facts/Newcomb%2527s_Tables_of_the_Sun/yCwAvQdy">work of Newcomb</a>, who analyzed positions of the planets until about 1895:

ε = 23°27′8.26″ − 46.845″ T − 0.0059″ T2 + 0.00181″ T3
where ε is the obliquity and T is <a href="/facts/Tropical_year/ASBLWNMY">tropical centuries</a> from <a href="/facts/Epoch_(astronomy)/RDdj6SmA">B1900.0</a> to the date in question.<a class="footnote-ref" id="fnref:17" href="#fn:17">17</a>
From 1984, the <a href="/facts/Jet_Propulsion_Laboratory_Development_Ephemeris/SeCNLYkt">Jet Propulsion Laboratory's DE series</a> of computer-generated ephemerides took over as the <a href="/facts/Fundamental_ephemeris/Q2EmvKt1">fundamental ephemeris</a> of the <a href="/facts/Astronomical_Almanac/kvC8j448">Astronomical Almanac</a>. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated:

ε = 23°26′21.448″ − 46.8150″ T − 0.00059″ T2 + 0.001813″ T3
where hereafter T is <a href="/facts/Julian_year_(astronomy)/EVdRNUe3">Julian centuries</a> from <a href="/facts/Epoch_(astronomy)/RDdj6SmA">J2000.0</a>.<a class="footnote-ref" id="fnref:18" href="#fn:18">18</a>
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:<a class="footnote-ref" id="fnref:19" href="#fn:19">19</a>

ε = 23°26′21.406″ − 46.836769″ T − 0.0001831″ T2 + 0.00200340″ T3 − 5.76″ × 10−7 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.<a class="footnote-ref" id="fnref:20" href="#fn:20">20</a> <a href="/facts/Jacques_Laskar/ttgg0YFs">Jacques Laskar</a> computed an expression to order T10 good to 0.02″ over 1000 years and several <a href="/facts/Minute_of_arc/tybs6YGC">arcseconds</a> over 10,000 years.

ε = 23°26′21.448″ − 4680.93″ t − 1.55″ t2 + 1999.25″ t3 − 51.38″ t4 − 249.67″ t5 − 39.05″ t6 + 7.12″ t7 + 27.87″ t8 + 5.79″ t9 + 2.45″ t10
where here t is multiples of 10,000 <a href="/facts/Julian_day/mLwtKoYQ">Julian years</a> from <a href="/facts/Epoch_(astronomy)/RDdj6SmA">J2000.0</a>.<a class="footnote-ref" id="fnref:21" href="#fn:21">21</a>
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 <a href="/facts/Minute_of_arc/tybs6YGC">arcseconds</a>) short-period (about 18.6 years) oscillations of the rotation axis of Earth, known as <a href="/facts/Astronomical_nutation/Rv0HN28Y">nutation</a>, which add a periodic component to Earth's obliquity.<a class="footnote-ref" id="fnref:22" href="#fn:22">22</a><a class="footnote-ref" id="fnref:23" href="#fn:23">23</a> The true or instantaneous obliquity includes this nutation.<a class="footnote-ref" id="fnref:24" href="#fn:24">24</a>

<h4>Long term</h4>
Main article: <a href="/facts/Formation_and_evolution_of_the_Solar_System/cgElXHpM">Formation and evolution of the Solar System</a>
Main article: <a href="/facts/Milankovitch_cycles/SxLbHrWX">Milankovitch cycles</a>
Using <a href="/facts/Numerical_methods/QT9cYa9z">numerical methods</a> to simulate <a href="/facts/Solar_System/QIcLSazQ">Solar System</a> behavior over a period of several million years, long-term changes in Earth's <a href="/facts/Orbit/nD2TPySG">orbit</a>, 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 <a href="/facts/Addend/apFWJBFB">term</a> in the motion of the <a href="/facts/Ecliptic/cJxXDDDW">ecliptic</a>. For the next 1 million years, the cycle will carry the obliquity between 22°13′44″ and 24°20′50″.<a class="footnote-ref" id="fnref:25" href="#fn:25">25</a>
The <a href="/facts/Moon/zKHqEMPb">Moon</a> 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 <a href="/facts/Orbital_resonance/eQLMfBWu">orbital resonances</a> and <a href="/facts/Stability_of_the_Solar_System/p0lxUH5h">chaotic behavior of the Solar System</a>, reaching as high as 90° in as little as a few million years (also see <a href="/facts/Orbit_of_the_Moon/wroMzfS2">Orbit of the Moon</a>).<a class="footnote-ref" id="fnref:26" href="#fn:26">26</a><a class="footnote-ref" id="fnref:27" href="#fn:27">27</a> However, more recent numerical simulations<a class="footnote-ref" id="fnref:28" href="#fn:28">28</a> made in 2011 indicated that even in the absence of the Moon, Earth's obliquity might not be quite so unstable; varying only by about 20–25°. To resolve this contradiction, diffusion rate of obliquity has been calculated, and it was found that it takes more than billions of years for Earth's obliquity to reach near 90°.<a class="footnote-ref" id="fnref:29" href="#fn:29">29</a> The Moon's stabilizing effect will continue for less than two billion years. As the Moon continues to recede from Earth due to <a href="/facts/Tidal_acceleration/PwDTMyjb">tidal acceleration</a>, resonances may occur which will cause large oscillations of the obliquity.<a class="footnote-ref" id="fnref:30" href="#fn:30">30</a>

Long-term obliquity of the ecliptic. Left: for the past 5 million years; the obliquity varies only from about 22.0° to 24.5°. Right: for the next 1 million years; note the approx. 41,000-year period of variation. In both graphs, the red point represents the year 1850.<a class="footnote-ref" id="fnref:31" href="#fn:31">31</a>
<h2 id="solar-system-bodies">Solar System bodies</h2>
See also: <a href="/facts/Poles_of_astronomical_bodies/HEz90QFn">Poles of astronomical bodies § Poles of rotation</a>
All four of the innermost, rocky planets of the <a href="/facts/Solar_System/QIcLSazQ">Solar System</a> may have had large variations of their obliquity in the past. Since obliquity is the angle between the axis of rotation and the direction perpendicular to the orbital plane, it changes as the orbital plane changes due to the influence of other planets. But the axis of rotation can also move (<a href="/facts/Axial_precession/NQ79x3m3">axial precession</a>), due to torque exerted by the Sun on a planet's equatorial bulge. Like Earth, all of the rocky planets show axial precession. If the precession rate were very fast the obliquity would actually remain fairly constant even as the orbital plane changes.<a class="footnote-ref" id="fnref:32" href="#fn:32">32</a> The rate varies due to <a href="/facts/Tidal_acceleration/PwDTMyjb">tidal dissipation</a> and <a href="/facts/Planetary_core/LyQ7DbAl">core</a>-<a href="/facts/Mantle_(geology)/RpDdtjCr">mantle</a> interaction, among other things. When a planet's precession rate approaches certain values, <a href="/facts/Orbital_resonance/eQLMfBWu">orbital resonances</a> may cause large changes in obliquity. The amplitude of the contribution having one of the resonant rates is divided by the difference between the resonant rate and the precession rate, so it becomes large when the two are similar.<a class="footnote-ref" id="fnref:33" href="#fn:33">33</a>
<a href="/facts/Mercury_(planet)/lVa1GIyX">Mercury</a> and <a href="/facts/Venus/pADnueP6">Venus</a> have most likely been stabilized by the tidal dissipation of the Sun. Earth was stabilized by the Moon, as mentioned above, but before its <a href="/facts/Moon/zKHqEMPb">formation</a>, Earth, too, could have passed through times of instability. <a href="/facts/Mars/AQGtVvz0">Mars</a>'s obliquity is quite variable over millions of years and may be in a chaotic state; it varies as much as 0° to 60° over some millions of years, depending on <a href="/facts/Perturbation_(astronomy)/og5hPpjQ">perturbations</a> of the planets.<a class="footnote-ref" id="fnref:34" href="#fn:34">34</a><a class="footnote-ref" id="fnref:35" href="#fn:35">35</a> 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.<a class="footnote-ref" id="fnref:36" href="#fn:36">36</a><a class="footnote-ref" id="fnref:37" href="#fn:37">37</a>
The occasional shifts in the axial tilt of Mars have been suggested as an explanation for the appearance and disappearance of rivers and lakes over the course of the existence of Mars. A shift could cause a burst of methane into the atmosphere, causing warming, but then the methane would be destroyed and the climate would become arid again.<a class="footnote-ref" id="fnref:38" href="#fn:38">38</a><a class="footnote-ref" id="fnref:39" href="#fn:39">39</a>
The obliquities of the outer planets are considered relatively stable.

Axis and rotation of selected Solar System bodies<table><tbody><tr><th rowspan="3">Body</th><th colspan="4"><a href="/facts/NASA/TIMCV0yV">NASA</a>, <a href="/facts/J2000/RDdj6SmA">J2000</a>.0<a class="footnote-ref" id="fnref:40" href="#fn:40">40</a> epoch</th><th colspan="4"><a href="/facts/IAU/cbnG5Ccz">IAU</a>, 0h 0 January 2010 <a href="/facts/Terrestrial_time/DqoNFINq">TT</a><a class="footnote-ref" id="fnref:41" href="#fn:41">41</a> epoch</th></tr><tr><th rowspan="2">Axial tilt (degrees)</th><th colspan="2">North Pole</th><th rowspan="2">Rotational period (hours)</th><th rowspan="2">Axial tilt (degrees)</th><th colspan="2">North Pole</th><th rowspan="2">Rotation (deg./day)</th></tr><tr><th><a href="/facts/Right_ascension/z4CEsTFu">R.A.</a> (degrees)</th><th><a href="/facts/Declination/5X4S4k9u">Dec.</a> (degrees)</th><th><a href="/facts/Right_ascension/z4CEsTFu">R.A.</a> (degrees)</th><th><a href="/facts/Declination/5X4S4k9u">Dec.</a> (degrees)</th></tr><tr><td><a href="/facts/Sun/CadPCVHh">Sun</a></td><td>7.25</td><td>286.13</td><td>63.87</td><td>609.12<a class="footnote-ref" id="fnref:42" href="#fn:42">42</a></td><td>7.25<a class="footnote-ref" id="fnref:43" href="#fn:43">43</a></td><td>286.15</td><td>63.89</td><td>14.18</td></tr><tr><td><a href="/facts/Mercury_(planet)/lVa1GIyX">Mercury</a></td><td>0.03</td><td>281.01</td><td>61.41</td><td>1407.6</td><td>0.01</td><td>281.01</td><td>61.45</td><td>6.14</td></tr><tr><td><a href="/facts/Venus/pADnueP6">Venus</a></td><td>2.64</td><td>272.76</td><td>67.16</td><td>−5832.6</td><td>2.64</td><td>272.76</td><td>67.16</td><td>−1.48</td></tr><tr><td><a href="/facts/Earth/HLLmDfj0">Earth</a></td><td>23.44</td><td>0.00</td><td>90.00</td><td>23.93</td><td>23.44</td><td>Undefined</td><td>90.00</td><td>360.99</td></tr><tr><td><a href="/facts/Moon/zKHqEMPb">Moon</a></td><td>6.68</td><td>–</td><td>–</td><td>655.73</td><td>1.54<a class="footnote-ref" id="fnref:44" href="#fn:44">44</a></td><td>270.00</td><td>66.54</td><td>13.18</td></tr><tr><td><a href="/facts/Mars/AQGtVvz0">Mars</a></td><td>25.19</td><td>317.68</td><td>52.89</td><td>24.62</td><td>25.19</td><td>317.67</td><td>52.88</td><td>350.89</td></tr><tr><td><a href="/facts/Jupiter/95m7XjMT">Jupiter</a></td><td>3.13</td><td>268.06</td><td>64.50</td><td>9.93<a class="footnote-ref" id="fnref:45" href="#fn:45">45</a></td><td>3.12</td><td>268.06</td><td>64.50</td><td>870.54<a class="footnote-ref" id="fnref:46" href="#fn:46">46</a></td></tr><tr><td><a href="/facts/Saturn/D54LcGJ9">Saturn</a></td><td>26.73</td><td>40.59</td><td>83.54</td><td>10.66<a class="footnote-ref" id="fnref:47" href="#fn:47">47</a></td><td>26.73</td><td>40.59</td><td>83.54</td><td>810.79<a class="footnote-ref" id="fnref:48" href="#fn:48">48</a></td></tr><tr><td><a href="/facts/Uranus/x7YwT1ar">Uranus</a></td><td>97.77</td><td>257.31</td><td>−15.18</td><td>−17.24<a class="footnote-ref" id="fnref:49" href="#fn:49">49</a></td><td>97.77</td><td>257.31</td><td>−15.18</td><td>−501.16<a class="footnote-ref" id="fnref:50" href="#fn:50">50</a></td></tr><tr><td><a href="/facts/Neptune/1eucwHIC">Neptune</a></td><td>28.32</td><td>299.33</td><td>42.95</td><td>16.11<a class="footnote-ref" id="fnref:51" href="#fn:51">51</a></td><td>28.33</td><td>299.40</td><td>42.95</td><td>536.31<a class="footnote-ref" id="fnref:52" href="#fn:52">52</a></td></tr><tr><td><a href="/facts/Pluto/egq7MBeR">Pluto</a><a class="footnote-ref" id="fnref:53" href="#fn:53">53</a></td><td>57.47</td><td>312.99<a class="footnote-ref" id="fnref:54" href="#fn:54">54</a></td><td>6.16<a class="footnote-ref" id="fnref:55" href="#fn:55">55</a></td><td>−153.29</td><td>60.41</td><td>312.99</td><td>6.16</td><td>−56.36</td></tr><tr><td colspan="9"></td></tr></tbody></table>
<h2 id="extrasolar-planets">Extrasolar planets</h2>
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. By 2012, 49 stars have had sky-projected spin-orbit misalignment λ has been observed,<a class="footnote-ref" id="fnref:56" href="#fn:56">56</a> which serves as a lower limit to ψs. Most of these measurements rely on the <a href="/facts/Rossiter%25E2%2580%2593McLaughlin_effect/QEMgxao5">Rossiter–McLaughlin effect</a>.
As of 2024 the axial tilt of 4 exoplanets have been measured with one of them VHS 1256 b having a Uranus like tilt of 90 degrees ± 25 degrees.<a class="footnote-ref" id="fnref:57" href="#fn:57">57</a>
Astrophysicists have applied tidal theories to predict the obliquity of <a href="/facts/Extrasolar_planets/zjfmqfUf">extrasolar planets</a>. It has been shown that the obliquities of exoplanets in the <a href="/facts/Habitable_zone/bjgaUkfB">habitable zone</a> around low-mass stars tend to be eroded in less than a billion years,<a class="footnote-ref" id="fnref:58" href="#fn:58">58</a><a class="footnote-ref" id="fnref:59" href="#fn:59">59</a> which means that they would not have tilt-induced seasons as Earth has.

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Axial_parallelism/fEXp32US">Axial parallelism</a></li>
<li><a href="/facts/Milankovitch_cycles/SxLbHrWX">Milankovitch cycles</a></li>
<li><a href="/facts/Polar_motion/79TCTF3k">Polar motion</a></li>
<li><a href="/facts/Pole_shift/kstwmLoL">Pole shift</a></li>
<li><a href="/facts/Rotation_around_a_fixed_axis/PGcg3IY5">Rotation around a fixed axis</a></li>
<li><a href="/facts/True_polar_wander/D6rcdgGz">True polar wander</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="https://nssdc.gsfc.nasa.gov/planetary/">National Space Science Data Center</a></li>
<li>Seidelmann, P. Kenneth; Archinal, Brent A.; A'Hearn, Michael F.; et al. (2007). <a href="https://doi.org/10.1007%2Fs10569-007-9072-y">"Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements: 2006"</a>. Celestial Mechanics and Dynamical Astronomy. 98 (3): 155–180. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2007CeMDA..98..155S">2007CeMDA..98..155S</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2Fs10569-007-9072-y">10.1007/s10569-007-9072-y</a>.</li>
<li><a href="http://neoprogrammics.com/obliquity_of_the_ecliptic/">Obliquity of the Ecliptic Calculator</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">U.S. Naval Observatory Nautical Almanac Office (1992). P. Kenneth Seidelmann (ed.). Explanatory Supplement to the Astronomical Almanac. University Science Books. p. 733. ISBN 978-0-935702-68-2. <a href="978-0-935702-68-2" target="_blank">978-0-935702-68-2</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Explanatory Supplement 1992, p. 384 <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Correia, Alexandre C. M.; Laskar, Jacques; de Surgy, Olivier Néron (May 2003). "Long-term evolution of the spin of Venus I. theory" (PDF). Icarus. 163 (1): 1–23. Bibcode:2003Icar..163....1C. doi:10.1016/S0019-1035(03)00042-3. Archived (PDF) from the original on 9 October 2022. <a href="http://www.imcce.fr/Equipes/ASD/preprints/prep.2002/venus1.2002.pdf" target="_blank">http://www.imcce.fr/Equipes/ASD/preprints/prep.2002/venus1.2002.pdf</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Correia, A. C. M.; Laskar, J. (2003). "Long-term evolution of the spin of Venus: II. numerical simulations" (PDF). Icarus. 163 (1): 24–45. Bibcode:2003Icar..163...24C. doi:10.1016/S0019-1035(03)00043-5. Archived (PDF) from the original on 9 October 2022. <a href="http://www.imcce.fr/Equipes/ASD/preprints/prep.2002/venus2.2002.pdf" target="_blank">http://www.imcce.fr/Equipes/ASD/preprints/prep.2002/venus2.2002.pdf</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Seidelmann, P. Kenneth; Archinal, B. A.; a'Hearn, M. F.; Conrad, A.; Consolmagno, G. J.; Hestroffer, D.; Hilton, J. L.; Krasinsky, G. A.; Neumann, G.; Oberst, J.; Stooke, P.; Tedesco, E. F.; Tholen, D. J.; Thomas, P. C.; Williams, I. P. (2007). "Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements: 2006". Celestial Mechanics and Dynamical Astronomy. 98 (3): 155–180. Bibcode:2007CeMDA..98..155S. doi:10.1007/s10569-007-9072-y. <a href="https://doi.org/10.1007%2Fs10569-007-9072-y" target="_blank">https://doi.org/10.1007%2Fs10569-007-9072-y</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">U.S. Naval Observatory Nautical Almanac Office; U.K. Hydrographic Office; H.M. Nautical Almanac Office (2008). The Astronomical Almanac for the Year 2010. US Government Printing Office. p. M11. ISBN 978-0-7077-4082-9. <a href="978-0-7077-4082-9" target="_blank">978-0-7077-4082-9</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">"Glossary" in Astronomical Almanac Online. (2023). Washington DC: United States Naval Observatory. s.v. obliquity. <a href="https://aa.usno.navy.mil/faq/asa_glossary" target="_blank">https://aa.usno.navy.mil/faq/asa_glossary</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">Chauvenet, William (1906). A Manual of Spherical and Practical Astronomy. Vol. 1. J. B. Lippincott. pp. 604–605. <a href="https://books.google.com/books?id=yobvAAAAMAAJ" target="_blank">https://books.google.com/books?id=yobvAAAAMAAJ</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">Ray, Richard D.; Erofeeva, Svetlana Y. (4 February 2014). "Long-period tidal variations in the length of day". Journal of Geophysical Research: Solid Earth. 119 (2): 1498–1509. Bibcode:2014JGRB..119.1498R. doi:10.1002/2013JB010830. <a href="https://doi.org/10.1002%2F2013JB010830" target="_blank">https://doi.org/10.1002%2F2013JB010830</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Gore, J. E. (1907). Astronomical Essays Historical and Descriptive. Chatto & Windus. p. 61. <a href="https://archive.org/details/astronomicaless00goregoog" target="_blank">https://archive.org/details/astronomicaless00goregoog</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">Marmery, J. V. (1895). Progress of Science. Chapman and Hall, ld. p. 33. <a href="https://archive.org/details/in.ernet.dli.2015.45033" target="_blank">https://archive.org/details/in.ernet.dli.2015.45033</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">Sédillot, L.P.E.A. (1853). Prolégomènes des tables astronomiques d'OlougBeg: Traduction et commentaire. Paris: Firmin Didot Frères. pp. 87 & 253. <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">Saliba, George (1994). A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam. p. 235. <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">Dreyer, J. L. E. (1890). Tycho Brahe. A. & C. Black. p. 355. <a href="https://archive.org/details/tychobraheapict00dreygoog" target="_blank">https://archive.org/details/tychobraheapict00dreygoog</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">Dreyer (1890), p. 123 <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
<li id="fn:16">Sayili, Aydin (1981). The Observatory in Islam. p. 78. <a href="#fnref:16" class="footnote-back-ref">↩</a></li>
<li id="fn:17">U.S. Naval Observatory Nautical Almanac Office; H.M. Nautical Almanac Office (1961). Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac. H.M. Stationery Office. Section 2B. <a href="/wiki/H.M._Stationery_Office" target="_blank">/wiki/H.M._Stationery_Office</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></li>
<li id="fn:18">U.S. Naval Observatory; H.M. Nautical Almanac Office (1989). The Astronomical Almanac for the Year 1990. US Government Printing Office. p. B18. ISBN 978-0-11-886934-8. <a href="978-0-11-886934-8" target="_blank">978-0-11-886934-8</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></li>
<li id="fn:19">Astronomical Almanac 2010, p. B52 <a href="#fnref:19" class="footnote-back-ref">↩</a></li>
<li id="fn:20">Newcomb, Simon (1906). A Compendium of Spherical Astronomy. MacMillan. pp. 226–227. <a href="https://archive.org/details/acompendiumsphe00newcgoog" target="_blank">https://archive.org/details/acompendiumsphe00newcgoog</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></li>
<li id="fn:21">See table 8 and eq. 35 in Laskar, J. (1986). "Secular terms of classical planetary theories using the results of general theory". Astronomy and Astrophysics. 157 (1): 59–70. Bibcode:1986A&A...157...59L. and erratum to article
Laskar, J. (1986). "Erratum: Secular terms of classical planetary theories using the results of general theory". Astronomy and Astrophysics. 164: 437. Bibcode:1986A&A...164..437L. Units in article are arcseconds, which may be more convenient. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></li>
<li id="fn:22">Explanatory Supplement (1961), sec. 2C <a href="#fnref:22" class="footnote-back-ref">↩</a></li>
<li id="fn:23">"Basics of Space Flight, Chapter 2". Jet Propulsion Laboratory/NASA. 29 October 2013. Retrieved 26 March 2015. <a href="https://www2.jpl.nasa.gov/basics/bsf2-1.php#nutation" target="_blank">https://www2.jpl.nasa.gov/basics/bsf2-1.php#nutation</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></li>
<li id="fn:24">Meeus, Jean (1991). "Chapter 21". Astronomical Algorithms. Willmann-Bell. ISBN 978-0-943396-35-4. <a href="978-0-943396-35-4" target="_blank">978-0-943396-35-4</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></li>
<li id="fn:25">Berger, A.L. (1976). "Obliquity and Precession for the Last 5000000 Years". Astronomy and Astrophysics. 51 (1): 127–135. Bibcode:1976A&A....51..127B. <a href="/wiki/Astronomy_and_Astrophysics" target="_blank">/wiki/Astronomy_and_Astrophysics</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></li>
<li id="fn:26">Laskar, J.; Robutel, P. (1993). "The Chaotic Obliquity of the Planets" (PDF). Nature. 361 (6413): 608–612. Bibcode:1993Natur.361..608L. doi:10.1038/361608a0. S2CID 4372237. Archived from the original (PDF) on 23 November 2012. <a href="https://web.archive.org/web/20121123093109/http://bugle.imcce.fr/fr/presentation/equipes/ASD/person/Laskar/misc_files/Laskar_Robutel_1993.pdf" target="_blank">https://web.archive.org/web/20121123093109/http://bugle.imcce.fr/fr/presentation/equipes/ASD/person/Laskar/misc_files/Laskar_Robutel_1993.pdf</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></li>
<li id="fn:27">Laskar, J.; Joutel, F.; Robutel, P. (1993). "Stabilization of the Earth's Obliquity by the Moon" (PDF). Nature. 361 (6413): 615–617. Bibcode:1993Natur.361..615L. doi:10.1038/361615a0. S2CID 4233758. Archived (PDF) from the original on 9 October 2022. <a href="http://www.imcce.fr/Equipes/ASD/person/Laskar/misc_files/Laskar_Joutel_Robutel_1993.pdf" target="_blank">http://www.imcce.fr/Equipes/ASD/person/Laskar/misc_files/Laskar_Joutel_Robutel_1993.pdf</a> <a href="#fnref:27" class="footnote-back-ref">↩</a></li>
<li id="fn:28">Lissauer, J.J.; Barnes, J.W.; Chambers, J.E. (2011). "Obliquity variations of a moonless Earth" (PDF). Icarus. 217 (1): 77–87. Bibcode:2012Icar..217...77L. doi:10.1016/j.icarus.2011.10.013. Archived (PDF) from the original on 8 June 2013. <a href="http://barnesos.net/publications/papers/2012.01.Icarus.Barnes.Moonless.Earth.pdf" target="_blank">http://barnesos.net/publications/papers/2012.01.Icarus.Barnes.Moonless.Earth.pdf</a> <a href="#fnref:28" class="footnote-back-ref">↩</a></li>
<li id="fn:29">Li, Gongjie; Batygin, Konstantin (20 July 2014). "On the Spin-axis Dynamics of a Moonless Earth". Astrophysical Journal. 790 (1): 69–76. arXiv:1404.7505. Bibcode:2014ApJ...790...69L. doi:10.1088/0004-637X/790/1/69. S2CID 119295403. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:29" class="footnote-back-ref">↩</a></li>
<li id="fn:30">Ward, W.R. (1982). "Comments on the Long-Term Stability of the Earth's Obliquity". Icarus. 50 (2–3): 444–448. Bibcode:1982Icar...50..444W. doi:10.1016/0019-1035(82)90134-8. <a href="/wiki/Icarus_(journal)" target="_blank">/wiki/Icarus_(journal)</a> <a href="#fnref:30" class="footnote-back-ref">↩</a></li>
<li id="fn:31">Berger, 1976. <a href="#fnref:31" class="footnote-back-ref">↩</a></li>
<li id="fn:32">William Ward (20 July 1973). "Large-Scale Variations in the Obliquity of Mars". Science. 181 (4096): 260–262. Bibcode:1973Sci...181..260W. doi:10.1126/science.181.4096.260. PMID 17730940. S2CID 41231503. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:32" class="footnote-back-ref">↩</a></li>
<li id="fn:33">William Ward (20 July 1973). "Large-Scale Variations in the Obliquity of Mars". Science. 181 (4096): 260–262. Bibcode:1973Sci...181..260W. doi:10.1126/science.181.4096.260. PMID 17730940. S2CID 41231503. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:33" class="footnote-back-ref">↩</a></li>
<li id="fn:34">Laskar, J.; Robutel, P. (1993). "The Chaotic Obliquity of the Planets" (PDF). Nature. 361 (6413): 608–612. Bibcode:1993Natur.361..608L. doi:10.1038/361608a0. S2CID 4372237. Archived from the original (PDF) on 23 November 2012. <a href="https://web.archive.org/web/20121123093109/http://bugle.imcce.fr/fr/presentation/equipes/ASD/person/Laskar/misc_files/Laskar_Robutel_1993.pdf" target="_blank">https://web.archive.org/web/20121123093109/http://bugle.imcce.fr/fr/presentation/equipes/ASD/person/Laskar/misc_files/Laskar_Robutel_1993.pdf</a> <a href="#fnref:34" class="footnote-back-ref">↩</a></li>
<li id="fn:35">Touma, J.; Wisdom, J. (1993). "The Chaotic Obliquity of Mars" (PDF). Science. 259 (5099): 1294–1297. Bibcode:1993Sci...259.1294T. doi:10.1126/science.259.5099.1294. PMID 17732249. S2CID 42933021. Archived (PDF) from the original on 25 June 2010. <a href="http://groups.csail.mit.edu/mac/users/wisdom/mars-obliquity.pdf" target="_blank">http://groups.csail.mit.edu/mac/users/wisdom/mars-obliquity.pdf</a> <a href="#fnref:35" class="footnote-back-ref">↩</a></li>
<li id="fn:36">Correia, Alexandre C. M.; Laskar, Jacques; de Surgy, Olivier Néron (May 2003). "Long-term evolution of the spin of Venus I. theory" (PDF). Icarus. 163 (1): 1–23. Bibcode:2003Icar..163....1C. doi:10.1016/S0019-1035(03)00042-3. Archived (PDF) from the original on 9 October 2022. <a href="http://www.imcce.fr/Equipes/ASD/preprints/prep.2002/venus1.2002.pdf" target="_blank">http://www.imcce.fr/Equipes/ASD/preprints/prep.2002/venus1.2002.pdf</a> <a href="#fnref:36" class="footnote-back-ref">↩</a></li>
<li id="fn:37">Correia, Alexandre C.M; Laskar, Jacques (2009). "Mercury's capture into the 3/2 spin-orbit resonance including the effect of core-mantle friction". Icarus. 201 (1): 1–11. arXiv:0901.1843. Bibcode:2009Icar..201....1C. doi:10.1016/j.icarus.2008.12.034. S2CID 14778204. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:37" class="footnote-back-ref">↩</a></li>
<li id="fn:38">Rebecca Boyle (7 October 2017). "Methane burps on young Mars helped it keep its liquid water". New Scientist. <a href="https://www.newscientist.com/article/mg23631464-100" target="_blank">https://www.newscientist.com/article/mg23631464-100</a> <a href="#fnref:38" class="footnote-back-ref">↩</a></li>
<li id="fn:39">Edwin Kite; et al. (2 October 2017). "Methane bursts as a trigger for intermittent lake-forming climates on post-Noachian Mars" (PDF). Nature Geoscience. 10 (10): 737–740. arXiv:1611.01717. Bibcode:2017NatGe..10..737K. doi:10.1038/ngeo3033. S2CID 102484593. Archived (PDF) from the original on 23 July 2018. <a href="https://authors.library.caltech.edu/80639/4/ngeo3033-s1.pdf" target="_blank">https://authors.library.caltech.edu/80639/4/ngeo3033-s1.pdf</a> <a href="#fnref:39" class="footnote-back-ref">↩</a></li>
<li id="fn:40">Planetary Fact Sheets, at http://nssdc.gsfc.nasa.gov <a href="https://nssdc.gsfc.nasa.gov/planetary/planetfact.html" target="_blank">https://nssdc.gsfc.nasa.gov/planetary/planetfact.html</a> <a href="#fnref:40" class="footnote-back-ref">↩</a></li>
<li id="fn:41">Astronomical Almanac 2010, pp. B52, C3, D2, E3, E55 <a href="#fnref:41" class="footnote-back-ref">↩</a></li>
<li id="fn:42">At 16° latitude; the Sun's rotation varies with latitude. <a href="#fnref:42" class="footnote-back-ref">↩</a></li>
<li id="fn:43">With respect to the ecliptic of 1850. <a href="/wiki/Ecliptic" target="_blank">/wiki/Ecliptic</a> <a href="#fnref:43" class="footnote-back-ref">↩</a></li>
<li id="fn:44">With respect to the ecliptic; the Moon's orbit is inclined 5.16° to the ecliptic. <a href="#fnref:44" class="footnote-back-ref">↩</a></li>
<li id="fn:45">From the origin of the radio emissions; the visible clouds generally rotate at different rate. <a href="#fnref:45" class="footnote-back-ref">↩</a></li>
<li id="fn:46">From the origin of the radio emissions; the visible clouds generally rotate at different rate. <a href="#fnref:46" class="footnote-back-ref">↩</a></li>
<li id="fn:47">From the origin of the radio emissions; the visible clouds generally rotate at different rate. <a href="#fnref:47" class="footnote-back-ref">↩</a></li>
<li id="fn:48">From the origin of the radio emissions; the visible clouds generally rotate at different rate. <a href="#fnref:48" class="footnote-back-ref">↩</a></li>
<li id="fn:49">From the origin of the radio emissions; the visible clouds generally rotate at different rate. <a href="#fnref:49" class="footnote-back-ref">↩</a></li>
<li id="fn:50">From the origin of the radio emissions; the visible clouds generally rotate at different rate. <a href="#fnref:50" class="footnote-back-ref">↩</a></li>
<li id="fn:51">From the origin of the radio emissions; the visible clouds generally rotate at different rate. <a href="#fnref:51" class="footnote-back-ref">↩</a></li>
<li id="fn:52">From the origin of the radio emissions; the visible clouds generally rotate at different rate. <a href="#fnref:52" class="footnote-back-ref">↩</a></li>
<li id="fn:53">NASA lists the coordinates of Pluto's positive pole; noted values have been reinterpreted to correspond to the north/negative pole. <a href="#fnref:53" class="footnote-back-ref">↩</a></li>
<li id="fn:54">NASA lists the coordinates of Pluto's positive pole; noted values have been reinterpreted to correspond to the north/negative pole. <a href="#fnref:54" class="footnote-back-ref">↩</a></li>
<li id="fn:55">NASA lists the coordinates of Pluto's positive pole; noted values have been reinterpreted to correspond to the north/negative pole. <a href="#fnref:55" class="footnote-back-ref">↩</a></li>
<li id="fn:56">Heller, R. "Holt-Rossiter-McLaughlin Encyclopaedia". René Heller. Retrieved 24 February 2012. <a href="http://www.aip.de/People/RHeller" target="_blank">http://www.aip.de/People/RHeller</a> <a href="#fnref:56" class="footnote-back-ref">↩</a></li>
<li id="fn:57">Leaning Sideways: VHS 1256-1257 b is a Super-Jupiter with a Uranus-like Obliquity, Michael Poon, Marta L. Bryan, Hanno Rein, Caroline V. Morley, Gregory Mace, Yifan Zhou, Brendan P. Bowler, 3 Oct 2024 <a href="https://arxiv.org/abs/2410.02672" target="_blank">https://arxiv.org/abs/2410.02672</a> <a href="#fnref:57" class="footnote-back-ref">↩</a></li>
<li id="fn:58">Heller, R.; Leconte, J.; Barnes, R. (2011). "Tidal obliquity evolution of potentially habitable planets". Astronomy and Astrophysics. 528: A27. arXiv:1101.2156. Bibcode:2011A&A...528A..27H. doi:10.1051/0004-6361/201015809. S2CID 118784209. <a href="/wiki/Astronomy_and_Astrophysics" target="_blank">/wiki/Astronomy_and_Astrophysics</a> <a href="#fnref:58" class="footnote-back-ref">↩</a></li>
<li id="fn:59">Heller, R.; Leconte, J.; Barnes, R. (2011). "Habitability of Extrasolar Planets and Tidal Spin Evolution". Origins of Life and Evolution of Biospheres. 41 (6): 539–43. arXiv:1108.4347. Bibcode:2011OLEB...41..539H. doi:10.1007/s11084-011-9252-3. PMID 22139513. S2CID 10154158. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:59" class="footnote-back-ref">↩</a></li>
</ol>

Axial tilt open-in-new

Axial tilt