Editing Aberration (astronomy) (section)

==Types==
The ''[[Astronomical Almanac]]'' describes several different types of aberration, arising from differing components of the Earth's and observed object's motion:
* '''Stellar aberration:'''  "The apparent angular displacement of the observed position of a celestial body resulting from the motion of the observer. Stellar aberration is divided into diurnal, annual, and secular components."
** '''[[#Annual aberration|Annual aberration]]:'''  "The component of stellar aberration resulting from the motion of the Earth about the Sun."
** '''[[#Diurnal aberration|Diurnal aberration]]:'''  "The component of stellar aberration resulting from the observer's diurnal motion about the center of the Earth due to the Earth's rotation."
** '''[[#Secular aberration|Secular aberration]]:'''  "The component of stellar aberration resulting from the essentially uniform and almost rectilinear motion of the entire solar system in space. Secular aberration is usually disregarded."
* '''Planetary aberration:'''  "The apparent angular displacement of the observed position of a solar system body from its instantaneous geocentric direction as would be seen by an observer at the geocenter. This displacement is caused by the aberration of light and [[Light-time correction|light-time displacement]]."<ref>{{ cite book | author = U.S. Nautical Almanac Office | author-link = U.S. Nautical Almanac Office | publication-date = 2014 | title = Astronomical Almanac for the Year 2015 and Its Companion, The Astronomical Almanac Online | chapter = Glossary | date = 21 March 2014 | publisher = U.S. Government Printing Office | publication-place = Washington, DC | page = M1 | isbn = 9780707741499 | url = https://books.google.com/books?id=Pr0H9aSEfKYC&dq=%22Annual+aberration%22+%22Diurnal+aberration%22+%22Secular+aberration%22&pg=SL13-PA1 }}</ref>

===Annual aberration===
[[File:Aberration3.svg|thumb|250px|Stars at the [[ecliptic pole]]s appear to move in circles, stars exactly in the ecliptic plane move in lines, and stars at intermediate angles move in ellipses. Shown here are the apparent motions of stars with the [[ecliptic latitude]]s corresponding to these cases, and with [[ecliptic longitude]] of 270°.]]
[[File:aberrationseasons.svg|thumb|250px|The direction of aberration of a star at the northern ecliptic pole differs at different times of the year]]
{{see also|Stellar parallax}}

Annual aberration is caused by the motion of an observer on [[Earth]] as the planet revolves around the [[Sun]]. Due to [[orbital eccentricity]], the [[orbital speed|orbital velocity]] <math>v</math> of Earth (in the Sun's rest frame) [[Kepler orbit|varies]] periodically during the year as the planet traverses its [[elliptic orbit]] and consequently the aberration also varies periodically, typically causing stars to [[stellar parallax|appear to move]] in small [[ellipse]]s.

Approximating [[Earth's orbit]] as circular, the maximum displacement of a star due to annual aberration is known as the ''constant of aberration'', conventionally represented by <math>\kappa</math>. It may be calculated using the relation <math>\kappa = \theta-\phi \approx v/c </math> substituting the Earth's average speed in the Sun's frame for <math>v</math> and the [[speed of light]] <math>c</math>. Its accepted value is 20.49552&nbsp;[[arcsecond]]s (sec) or 0.000099365&nbsp;[[radian]]s (rad) (at [[J2000]]).<ref name="kovalevsky">{{cite book |first1=Jean |last1=Kovalevsky |first2=P. Kenneth |last2=Seidelmann |name-list-style=amp |date=2004 |title=Fundamentals of Astrometry
|publisher=[[Cambridge University Press]] |location=Cambridge |isbn=0-521-64216-7}}</ref>

Assuming a [[circular orbit]], annual aberration causes stars exactly on the [[ecliptic]] (the plane of Earth's orbit) to appear to move back and forth along a straight line, varying by <math>\kappa</math> on either side of their position in the Sun's frame. A star that is precisely at one of the [[ecliptic pole]]s (at 90° from the ecliptic plane) will appear to move in a circle of radius <math>\kappa</math> about its true position, and stars at intermediate [[ecliptic coordinate system|ecliptic latitudes]] will appear to move along a small [[ellipse]].

For illustration, consider a star at the northern ecliptic pole viewed by an observer at a point on the [[Arctic Circle]]. Such an observer will see the star [[culmination|transit]] at the [[zenith]], once every day (strictly speaking [[sidereal day]]). At the time of the [[March equinox]], Earth's orbit carries the observer in a southwards direction, and the star's apparent [[declination]] is therefore displaced to the south by an angle of <math>\kappa</math>. On the [[September equinox]], the star's position is displaced to the north by an equal and opposite amount. On either [[solstice]], the displacement in declination is 0. Conversely, the amount of displacement in [[right ascension]] is 0 on either [[equinox]] and at maximum on either solstice.

<!-- In the [[equatorial coordinate system]], the aberration's effect in [[right ascension]] (east-west) is larger than the effect in [[declination]] (north-south) except at the ecliptic poles. Despite this, its effect in declination was the first observed because very accurate clocks are needed to measure such a small variation in right ascension, but a [[transit telescope]] calibrated with a [[plumb bob|plumb line]] can detect very small changes in declination.
-->
In actuality, Earth's orbit is slightly elliptic rather than circular, and its speed varies somewhat over the course of its orbit, which means the description above is only approximate. Aberration is more accurately calculated using  Earth's instantaneous velocity relative to the [[barycenter]] of the Solar System.<ref name=kovalevsky/>

Note that the displacement due to aberration is orthogonal to any displacement due to [[parallax]]. If parallax is detectable, the maximum displacement to the south would occur in December, and the maximum displacement to the north in June. It is this apparently anomalous motion that so mystified early astronomers.

====Solar annual aberration====
A special case of annual aberration is the nearly constant deflection of the Sun from its position in the Sun's rest frame by <math>\kappa</math> towards the ''west'' (as viewed from Earth), opposite to the apparent motion of the Sun along the ecliptic (which is from west to east, as seen from Earth). The deflection thus makes the Sun appear to be behind (or retarded) from its rest-frame position on the ecliptic by a position or angle <math>\kappa</math>.

This deflection may equivalently be described as a light-time effect due to motion of the Earth during the 8.3&nbsp;minutes that it takes light to travel from the Sun to Earth. The relation with <math>\kappa</math> is : [0.000099365&nbsp;rad / 2&nbsp;π&nbsp;rad] x [365.25&nbsp;d x 24&nbsp;h/d x 60&nbsp;min/h] = 8.3167&nbsp;min ≈ 8&nbsp;min&nbsp;19&nbsp;sec = 499&nbsp;sec. This is possible since the transit time of sunlight is short relative to the orbital period of the Earth, so the Earth's frame may be approximated as inertial. In the Earth's frame, the Sun moves, at a mean velocity v = 29.789&nbsp;km/s, by a distance <math>\Delta x = vt</math> ≈ 14,864.7&nbsp;km in the time it takes light to reach Earth, <math>t=R/c</math> ≈ 499&nbsp;sec for the orbit of mean radius <math>R</math> = 1&nbsp;AU = 149,597,870.7&nbsp;km. This gives an angular correction <math>\tan(\theta) \approx \theta = \Delta x/R</math> ≈ 0.000099364&nbsp;rad = 20.49539&nbsp;sec, which can be solved to give <math>\theta = v/c = \kappa</math> ≈ 0.000099365&nbsp;rad = 20.49559&nbsp;sec, very nearly the same as the aberrational correction (here <math>\kappa</math> is in radian and not in arcsecond).

===Diurnal aberration===
Diurnal aberration is caused by the velocity of the observer on the surface of the [[Earth's rotation|rotating Earth]]. It is therefore dependent not only on the time of the observation, but also the [[latitude]] and [[longitude]] of the observer. Its effect is much smaller than that of annual aberration, and is only 0.32&nbsp;arcseconds in the case of an observer at the [[Equator]], where the rotational velocity is greatest.<ref name="newcomb">
{{cite book
|last=Newcomb
|first=Simon 
|author-link= Simon Newcomb
|title=A Compendium of Spherical Astronomy
|date=1960 
|publisher=Macmillan, 1906 – republished by [[Dover Publications|Dover]]}}</ref>

===Secular aberration===
The secular component of aberration, caused by the motion of the Solar System in space, has been further subdivided into several components: aberration resulting from the motion of the solar system barycenter around [[Galactic Center|the center of our Galaxy]], aberration resulting from the motion of the Galaxy relative to the [[Local Group]], and aberration resulting from the motion of the Local Group relative to the [[cosmic microwave background]].<ref name = "Charlot"/>{{rp|p=6}} Secular aberration affects the apparent positions of stars and [[extragalactic astronomy|extragalactic]] objects. The large, constant part of secular aberration cannot be directly observed and "It has been standard practice to absorb this large, nearly constant effect into the reported"<ref name= "MacMillan"/>{{rp|p=1}} positions of stars.<ref>{{cite journal | last = Hagihara | first = Yusuke | date = 1933 | title = On the Theory of Secular Aberration | journal = [[Proceedings of the Physico-Mathematical Society of Japan]] |series=3rd Series | volume = 15 | issue = 3–6 | page = 175 | doi = 10.11429/ppmsj1919.15.3-6_155 | quote =  the correction of star places  with  secular aberration is not at all  necessary and  is even inconvenient, so long as the solar motion remains uniform and rectilinear.}}</ref>

In about 200 million years, the Sun circles the galactic center, whose measured location is near right ascension (α = 266.4°) and declination (δ = −29.0°).<ref name= "MacMillan"/>{{rp|p=2}} The constant, unobservable, effect of the solar system's motion around the galactic center has been computed variously as 150<ref>{{ cite journal | last = Kovalevsky | first = J. | date = 2003 | title = Aberration in proper motions | journal = Astronomy and Astrophysics | volume =   404| issue =   2| pages =  743–747| doi = 10.1051/0004-6361:20030560 | bibcode = 2003A&A...404..743K | doi-access = free }}</ref>{{rp|p=743}} or 165<ref name= "MacMillan"/>{{rp|p=1}} arcseconds.  The other, observable, part is an acceleration toward the galactic center of approximately 2.5&nbsp;×&nbsp;10<sup>−10</sup>&nbsp;m/s<sup>2</sup>, which yields a change of aberration of about 5&nbsp;μas/yr.<ref>{{ cite journal | last1 = Kopeikin | first1 = S. | last2 = Makarov | first2 = V. | date = 2006 | title = Astrometric effects of secular aberration | journal = The Astronomical Journal  | volume =   131| issue =   3| pages =  1471–1478| doi = 10.1086/500170 | bibcode = 2006AJ....131.1471K | doi-access = free | arxiv = astro-ph/0508505 }}</ref> Highly precise measurements extending over several years can observe this change in secular aberration, often called the secular aberration drift or the acceleration of the Solar System, as a small apparent [[proper motion]].<ref name = "Titov 2011"/>{{rp|p=1}}<ref name= "MacMillan">{{ cite journal | last1 = MacMillan | first1 = D. S. | last2 = Fey | first2 = A. | last3 = Gipson | first3 = J. M. | display-authors = etal | date = 2019 | title = Galactocentric acceleration in VLBI analysis| journal = Astronomy and Astrophysics | volume =   630| issue =   | pages =  A93| doi = 10.1051/0004-6361/201935379 | bibcode = 2019A&A...630A..93M | s2cid = 198471325 }}</ref>{{rp|p=1}}

Recently, highly precise [[astrometry]] of extragalactic objects using both [[Very Long Baseline Interferometry]] and the [[Gaia (spacecraft)|''Gaia'' space observatory]] have successfully measured this small effect.<ref name = "Titov 2011">{{ cite journal | last1 = Titov | first1 = O. | last2 = Lambert | first2 = S. B. | last3 = Gontier | first3 = A.-M.  | date = 2011 | title = VLBI measurement of the secular aberration drift | journal = Astronomy and Astrophysics | volume =   529| issue =   | pages =   A91| doi = 10.1051/0004-6361/201015718 | arxiv = 1009.3698 | bibcode = 2011A&A...529A..91T | s2cid = 119305429 }}</ref> The first VLBI measurement of the apparent motion, over a period of 20 years, of 555 extragalactic objects towards the center of [[Milky Way|our galaxy]] at equatorial coordinates of α = 263° and δ = −20° indicated a secular aberration drift 6.4 ±1.5 μas/yr.<ref name = "Titov 2011"/>{{rp|p=1}} Later determinations using a series of VLBI measurements extending over almost 40 years determined the secular aberration drift to be 5.83&nbsp;±&nbsp;0.23&nbsp;μas/yr in the direction α = 270.2&nbsp;±&nbsp;2.3° and δ = −20.2°&nbsp;±&nbsp;3.6°.<ref name = "Charlot">{{ cite journal | last1 = Charlot | first1 = P. | last2 = Jacobs | first2 = C. S. | last3 = Gordon | first3 = D. | last4 = Lambert | first4 = S. | display-authors = etal | date = 2020 | title = The third realization of the International Celestial Reference Frame by very long baseline interferometry | journal = Astronomy and Astrophysics | volume =   644| issue =   | pages =   A159| doi = 10.1051/0004-6361/202038368 | arxiv = 2010.13625 | bibcode = 2020A&A...644A.159C | s2cid = 225068756 }}</ref>{{rp|p=7}} Optical observations using only 33 months of ''Gaia'' satellite data of 1.6 million extragalactic sources indicated an acceleration of the solar system of 2.32&nbsp;±&nbsp;0.16&nbsp;×&nbsp;10<sup>−10</sup>&nbsp;m/s<sup>2</sup> and a corresponding secular aberration drift of 5.05&nbsp;±&nbsp;0.35&nbsp;μas/yr in the direction of α = 269.1°&nbsp;±&nbsp;5.4°, δ = −31.6°&nbsp;±&nbsp;4.1°. It is expected that [[Gaia (spacecraft)#Future releases|later ''Gaia'' data releases]], incorporating about 66 and 120 months of data, will reduce the random errors of these results by factors of 0.35 and 0.15.<ref>{{cite web | date = 3 December 2020 | title = Gaia's measurement of the solar system acceleration with respect to the distant universe | url = https://www.cosmos.esa.int/web/gaia/edr3-acceleration-solar-system | accessdate = 14 September 2022 | website = esa.int | publisher = [[European Space Agency]] }}</ref><ref>{{ cite journal | author = Gaia Collaboration  | last2 = Klioner | first2 =  S. A. | display-authors = etal | date = 2021 | title = Gaia Early Data Release 3: Acceleration of the Solar System from Gaia astrometry | journal = Astronomy & Astrophysics  | volume = 649 | issue =  | page = A9 | doi = 10.1051/0004-6361/202039734 | arxiv = 2012.02036 | bibcode = 2021A&A...649A...9G }}</ref>{{rp|p=1,14}} The latest edition of the [[International Celestial Reference System and its realizations#ICRF3|International Celestial Reference Frame]] (ICRF3) adopted a recommended galactocentric aberration constant of 5.8&nbsp;μas/yr<ref name= "MacMillan"/>{{rp|p=5,7}} and recommended a correction for secular aberration to obtain the highest positional accuracy for times other than the [[Epoch (astronomy)|reference epoch]] 2015.0.<ref name = "Charlot"/>{{rp|p=17–19}}

===Planetary aberration===
{{see also|Light-time correction}}
Planetary aberration is the combination of the aberration of light (due to Earth's velocity) and light-time correction (due to the object's motion and distance), as calculated in the rest frame of the Solar System. Both are determined at the instant when the moving object's light reaches the moving observer on Earth. It is so called because it is usually applied to planets and other objects in the Solar System whose motion and distance are accurately known.