Editing Sun (section)

== Motion ==
{{main|Galactic year}}
{{Further|Stellar kinematics}}
[[File:Motion of Sun, Earth and Moon around the Milky Way.jpg|thumb|The general motion and orientation of the Sun, with Earth and the moon as its Solar System satellites]]

The Sun, taking along the whole Solar System, orbits [[Galactic Center|the galaxy's centre of mass]] at an average speed of 230&nbsp;km/s (828,000&nbsp;km/h),<ref name="StarChild">{{cite web |url=http://starchild.gsfc.nasa.gov/docs/StarChild/questions/question18.html |website=NASA |title=StarChild Question of the Month – Does the Sun move around the Milky Way? |date=February 2000 |url-status=live |archive-url=https://web.archive.org/web/20231030090914/https://starchild.gsfc.nasa.gov/docs/StarChild/questions/question18.html |archive-date=30 October 2023}}</ref> taking about 220–250&nbsp;million [[Earth year]]s to complete a revolution (a [[galactic year]]), having done so about 20 times since the Sun's formation.<ref name="Currin 2020 t043">{{cite web |last=Currin |first=Grant |title=How long is a galactic year? |website=Live Science |date=30 August 2020 |url=https://www.livescience.com/how-long-galactic-year.html |access-date=25 November 2023 |archive-date=25 November 2023 |archive-url=https://web.archive.org/web/20231125013457/https://www.livescience.com/how-long-galactic-year.html |url-status=live}}</ref><ref name="fn10">{{cite book |last=Leong |first=S. |title=Period of the Sun's Orbit around the Galaxy (Cosmic Year) |url=http://hypertextbook.com/facts/2002/StacyLeong.shtml |publisher=The Physics Factbook |date=2002 |access-date=10 May 2007 |archive-date=22 August 2011 |archive-url=https://www.webcitation.org/617GgQWCh?url=http://hypertextbook.com/facts/2002/StacyLeong.shtml |url-status=live}}</ref> The direction of the Sun's motion, the [[Solar apex]], is roughly in the direction of the star [[Vega]].<ref>{{cite book |title=Three Hundred and Sixty Five Starry Nights: An Introduction to Astronomy for Every Night of the Year |first=Chet |last=Raymo |year=1990 |publisher=Touchstone |isbn=9780671766061 |url=https://books.google.com/books?id=rTe5HaRsAS4C&pg=PA114}}</ref>

[[File:Milky Way Arms ssc2008-10.svg|thumb|The Sun's idealised orbit around the galactic centre in an artist's top-down depiction of the current layout of the Milky Way]]

A simple model of the motion of a star in the galaxy gives the [[galactic coordinates]] {{mvar|X}}, {{mvar|Y}}, and {{mvar|Z}} (rotating coordinates so that the centre of the galaxy is always in the {{mvar|X}} direction) as:

<math display="block">X(t)=X(0)+\frac{U(0)}\kappa\sin(\kappa t)+\frac{V(0)}{2B}(1-\cos(\kappa t))</math>

<math display="block">Y(t)=Y(0)+2A\left(X(0)+\frac{V(0)}{2B}\right)t-\frac{\Omega_0}{B\kappa}V(0)\sin(\kappa t)+\frac{2\Omega_0}{\kappa^2}U(0)(1-\cos(\kappa t))</math>

<math display="block">Z(t)=\frac{W(0)}\nu\sin(\nu t)+Z(0)\cos(\nu t)</math>

where {{mvar|U}}, {{mvar|V}}, and {{mvar|W}} are the respective velocities with respect to the [[local standard of rest]], {{mvar|A}} and {{mvar|B}} are the [[Oort constants]], <math>\Omega_0=A-B</math> is the angular velocity of galactic rotation for the local standard of rest, <math>\kappa=\sqrt{-4\Omega_0B}</math> is the "epicyclic frequency", and ν is the vertical oscillation frequency.<ref>{{cite journal |last1=B. Fuchs |display-authors=etal |title=The search for the origin of the Local Bubble redivivus |journal=[[MNRAS]] |volume=373 |issue=3 |pages=993–1003 |year=2006 |doi=10.1111/j.1365-2966.2006.11044.x |doi-access=free |arxiv=astro-ph/0609227 |bibcode=2006MNRAS.373..993F|s2cid=15460224 }}</ref> For the sun, the present values of {{mvar|U}}, {{mvar|V}}, and {{mvar|W}} are estimated as <math>(U(0),V(0),W(0))=(10.00, 5.25, 7.17)</math> km/s, and estimates for the other constants are {{mvar|A}}&nbsp;=&nbsp;15.5&nbsp;km/s/[[kiloparsec|kpc]], {{mvar|B}}&nbsp;=&nbsp;−12.2&nbsp;km/s/kpc, κ&nbsp;=&nbsp;37&nbsp;km/s/kpc, and ν=74&nbsp;km/s/kpc. We take {{math|''X''(0)}} and {{math|''Y''(0)}} to be zero and {{math|''Z''(0)}} is estimated to be 17 parsecs.<ref>{{cite journal |last=Bobylev |first=Vadim V. |year=2010 |title=Searching for Stars Closely Encountering with the Solar System |journal=Astronomy Letters |volume=36 |issue=3 |pages=220–226 |doi=10.1134/S1063773710030060 |arxiv=1003.2160 |bibcode=2010AstL...36..220B|s2cid=118374161 }}</ref> This model implies that the Sun circulates around a point that is itself going around the galaxy. The period of the Sun's circulation around the point is <math>2\pi/\kappa</math>. which comes to 166&nbsp;million years, shorter than the time it takes for the point to go around the galaxy. In the ({{mvar|X, Y}}) coordinates, the Sun describes an ellipse around the point, whose length in the {{mvar|Y}} direction is

<math display="block">2\times\sqrt{\left(\frac{2\Omega_0}{\kappa^2}U(0)\right)^2+\left(\frac{\Omega_0}{B\kappa}V(0)\right)^2}=1035\text{ parsec}.</math>

and whose width in the {{mvar|X}} direction is

<math display="block">2\times\sqrt{\left(\frac{U(0)}\kappa\right)^2+\left(\frac{V(0)}{2B}\right)^2}=691\text{ parsec}</math>

(Compare this to the distance of the sun from the centre of the galaxy, around 7 or 8 kiloparsecs.)
The ratio of length to width of this ellipse, the same for all stars in our neighborhood, is <math>2\Omega/\kappa\approx 1.50.</math>
The moving point is presently at

<math display="block">X=\frac{V(0)}{2B}=-215\text{ parsec}</math>

<math display="block">Y=\frac{2\Omega_0}{\kappa^2}U(0)=405\text{ parsec}.</math>

The oscillation in the {{mvar|Z}} direction takes the Sun

<math display="block">\sqrt{\left(\frac{W(0)}\nu\right)^2+Z(0)^2}=98\text{ parsec}</math>

above the galactic plane and the same distance below it, with a period of <math>2\pi/\nu</math> or 83&nbsp;million years, approximately 2.7 times per orbit.<ref>{{cite book |last1=Moore |first1=Patrick |last2=Rees |first2=Robin |title=Patrick Moore's Data Book of Astronomy |year=2014 |publisher=Cambridge University Press |location=Cambridge |isbn=978-1-139-49522-6}}</ref> Although <math>2\pi/\Omega_0</math> is 222&nbsp;million years, the value of <math>\Omega</math> at the point around which the Sun circulates is

<math display="block">\Omega\approx\Omega_0-\frac{2A}{R_0}\Delta X\approx 26.1\text{ km/s/kpc}</math>,

corresponding to 235&nbsp;million years (see [[Oort constants]]), and this is the time that the point takes to go once around the galaxy. Other stars with the same value of <math>X+V/(2B)</math> have to take the same amount of time to go around the galaxy as the sun and thus remain in the same general vicinity as the Sun.

The Sun's orbit around the Milky Way is perturbed due to the non-uniform mass distribution in Milky Way, such as that in and between the galactic spiral arms. It has been argued that the Sun's passage through the higher density spiral arms often coincides with [[mass extinction]]s on Earth, perhaps due to increased [[impact events]].<ref name="extinction">{{Cite journal |last1=Gillman |first1=M. |last2=Erenler |first2=H. |title=The galactic cycle of extinction |journal=[[International Journal of Astrobiology]] |volume=7 |issue=1 |pages=17–26 |date=2008 |doi=10.1017/S1473550408004047 |bibcode=2008IJAsB...7...17G |url=http://oro.open.ac.uk/11603/1/S1473550408004047a.pdf |citeseerx=10.1.1.384.9224 |s2cid=31391193 |access-date=26 October 2017 |archive-date=1 June 2019 |archive-url=https://web.archive.org/web/20190601165347/http://oro.open.ac.uk/11603/1/S1473550408004047a.pdf |url-status=live }}</ref> It takes the Solar System about 225–250&nbsp;million years to complete one orbit through the Milky Way (a ''[[galactic year]]''),<ref name="fn10" /> so it is thought to have completed 20–25 orbits during the lifetime of the Sun. The [[orbital speed]] of the Solar System about the centre of the Milky Way is approximately 251&nbsp;km/s (156&nbsp;mi/s).<ref name="space.newscientist.com">{{Cite journal |last=Croswell |first=Ken |author-link=Ken Croswell |date=2008 |title=Milky Way keeps tight grip on its neighbor |url=https://www.newscientist.com/article/dn12652-milky-way-keeps-a-light-grip-on-speedy-neighbours.html#.VQ7JD46WnCY |journal=[[New Scientist]] |volume=199 |issue=2669 |page=8 |doi=10.1016/S0262-4079(08)62026-6 |access-date=15 September 2017 |archive-date=11 May 2020 |archive-url=https://web.archive.org/web/20200511052658/https://www.newscientist.com/article/dn12652-milky-way-keeps-a-light-grip-on-speedy-neighbours/?ignored=irrelevant#.VQ7JD46WnCY |url-status=live }}</ref> At this speed, it takes around 1,190 years for the Solar System to travel a distance of 1 light-year, or 7 days to travel {{val|1|u=AU}}.<ref>{{Cite book |last=Garlick |first=M. A. |title=The Story of the Solar System |page=[https://archive.org/details/storyofsolarsyst00garl/page/46 46] |publisher=[[Cambridge University Press]] |date=2002 |isbn=978-0-521-80336-6 |url=https://archive.org/details/storyofsolarsyst00garl/page/46}}</ref>

The Milky Way is moving with respect to the [[cosmic microwave background radiation]] (CMB) in the direction of the constellation [[Hydra (constellation)|Hydra]] with a speed of 550&nbsp;km/s, but since the sun is moving with respect to the galactic centre in the direction of Cygnus (galactic longitude 90°; latitude 0°) at more than 200{{nbsp}}km/sec, the resultant velocity with respect to the CMB is about 370&nbsp;km/s in the direction of [[Crater (constellation)|Crater]] or [[Leo (constellation)|Leo]] (galactic latitude 264°, latitude 48°).<ref>Table 3 of {{Cite journal |last=Kogut |first=A. |date=1993 |title=Dipole Anisotropy in the COBE Differential Microwave Radiometers First-Year Sky Maps |journal=[[The Astrophysical Journal]] |volume=419 |issue=1993 |page=1 |arxiv=astro-ph/9312056 |doi=10.1086/173453 |bibcode=1993ApJ...419....1K |display-authors=etal}}</ref> This is 132° away from Cygnus.