Editing Aberration (astronomy) (section)

==Discovery and first observations==
The discovery of the aberration of light was totally unexpected, and it was only by considerable perseverance and perspicacity that [[James Bradley]] was able to explain it in 1727. It originated from attempts to discover whether stars possessed appreciable [[stellar parallax|parallaxes]].

===Search for stellar parallax===
The [[Nicolaus Copernicus|Copernican]] [[heliocentricity|heliocentric]] theory of the [[Solar System]] had received confirmation by the observations of [[Galileo Galilei|Galileo]] and [[Tycho Brahe]] and the mathematical investigations of [[Johannes Kepler]] and [[Isaac Newton]].{{sfnp|Eppenstein|1911|p=54}} As early as 1573, [[Thomas Digges]] had suggested that parallactic shifting of the stars should occur according to the heliocentric model, and consequently if stellar parallax could be observed it would help confirm this theory.  Many observers claimed to have determined such parallaxes, but Tycho Brahe and [[Giovanni Battista Riccioli]] concluded that they existed only in the minds of the observers, and were due to instrumental and personal errors. However, in 1680 [[Jean Picard]], in his ''Voyage d'[[Uraniborg|Uranibourg]],'' stated, as a result of ten [[year]]s' observations, that [[Polaris]], the Pole Star, exhibited variations in its position amounting to 40{{pprime}} annually. Some astronomers endeavoured to explain this by parallax, but these attempts failed because the motion differed from that which parallax would produce. [[John Flamsteed]], from measurements made in 1689 and succeeding years with his mural quadrant, similarly concluded that the declination of Polaris was 40{{pprime}} less in July than in September. [[Robert Hooke]], in 1674, published his observations of [[Gamma Draconis|γ Draconis]], a star of [[apparent magnitude|magnitude]] 2<sup>m</sup> which passes practically overhead at the latitude of London (hence its observations are largely free from the complex corrections due to [[atmospheric refraction]]), and concluded that this star was 23{{pprime}} more northerly in July than in October.{{sfnp|Eppenstein|1911|p=54}}

===James Bradley's observations===
[[File:Bradley's observations of γ Draconis and 35 Camelopardalis as reduced by Busch.jpg|thumb|Bradley's observations of [[Gamma Draconis|γ Draconis]] and [[35 Camelopardalis]] as reduced by Busch to the year 1730.]]

Consequently, when Bradley and [[Samuel Molyneux]] entered this sphere of research in 1725, there was still considerable uncertainty as to whether stellar parallaxes had been observed or not, and it was with the intention of definitely answering this question that they erected a large telescope at Molyneux's house at [[Kew]].<ref name="Hirshfeld"/> They decided to reinvestigate the motion of γ Draconis with a telescope constructed by [[George Graham (clockmaker)|George Graham]] (1675–1751), a celebrated instrument-maker. This was fixed to a vertical chimney stack in such manner as to permit a small oscillation of the eyepiece, the amount of which (i.e. the deviation from the vertical) was regulated and measured by the introduction of a screw and a plumb line.{{sfnp|Eppenstein|1911|p=54}}

The instrument was set up in November 1725, and observations on γ Draconis were made starting in December. The star was observed to move 40{{pprime}} southwards between September and March, and then reversed its course from March to September. {{sfnp|Eppenstein|1911|p=54}} At the same time, [[HD 40873|35 Camelopardalis]], a star with a right ascension nearly exactly opposite to that of γ Draconis, was 19" more northerly at the beginning of March than in September.<ref>Bradley, James; Rigaud, Stephen Peter (1832). Miscellaneous works and correspondence of the Rev. James Bradley, D.D., F.R.S. Oxford: University Press. p. 11.</ref> The asymmetry of these results, which were expected to be mirror images of each other, were completely unexpected and inexplicable by existing theories.

===Early hypotheses===
[[File:Hypothetical movement of γ Draconis caused by parallax.jpg|thumb|Hypothetical observation of γ Draconis if its movement was caused by parallax.]]

[[File:Hypothetical movement of γ Draconis and 35 Camelopardalis caused by nutation.jpg|thumb|Hypothetical observation of γ Draconis and 35 Camelopardalis if their movements were caused by nutation.]]

Bradley and Molyneux discussed several hypotheses in the hope of finding the solution. Since the apparent motion was evidently caused neither by parallax nor observational errors, Bradley first hypothesized that it could be due to oscillations in the orientation of the Earth's axis relative to the celestial sphere&nbsp;– a phenomenon known as [[astronomical nutation|nutation]]. 35 Camelopardalis was seen to possess an apparent motion which could be consistent with nutation, but since its declination varied only one half as much as that of γ Draconis, it was obvious that nutation did not supply the answer{{sfnp|Eppenstein|1911|p=55}} (however, Bradley later went on to discover that the Earth does indeed nutate).<ref name=berry/> He also investigated the possibility that the motion was due to an irregular distribution of the [[Earth's atmosphere]], thus involving abnormal variations in the refractive index, but again obtained negative results.{{sfnp|Eppenstein|1911|p=55}}

On August 19, 1727, Bradley embarked upon a further series of observations using a telescope of his own erected at the Rectory, [[Wanstead]]. This instrument had the advantage of a larger field of view and he was able to obtain precise positions of a large number of stars over the course of about twenty years. During his first two years at Wanstead, he established the existence of the phenomenon of aberration beyond all doubt, and this also enabled him to formulate a set of rules that would allow the calculation of the effect on any given star at a specified date.

===Development of the theory of aberration===
Bradley eventually developed his explanation of aberration in about September 1728 and this theory was presented to the [[Royal Society]] in mid January the following year. One well-known story was that he saw the change of direction of a wind vane on a boat on the Thames, caused not by an alteration of the wind itself, but by a change of course of the boat relative to the wind direction.<ref name="berry">
{{cite book
|last=Berry
|first=Arthur 
|title=A Short History of Astronomy
|url=https://archive.org/details/shorthistoryofas0000berr
|url-access=registration
|date=1961
|orig-year=1898
|publisher=[[Dover Publications|Dover]]|isbn=9780486202105 
}}</ref>
However, there is no record of this incident in Bradley's own account of the discovery, and it may therefore be [[apocrypha]]l.

The following table shows the magnitude of deviation from true declination for γ Draconis and the direction, on the planes of the solstitial [[colure]] and ecliptic prime meridian, of the tangent of the velocity of the Earth in its orbit for each of the four months where the extremes are found, as well as expected deviation from true ecliptic longitude if Bradley had measured its deviation from right ascension:

{| class="wikitable"
|-
! Month !! Direction of tangential velocity of Earth on the plane of the solstitial colure !! Deviation from true declination of γ Draconis !! Direction of tangential velocity of Earth on the plane of the ecliptic prime meridian !! Expected deviation from true ecliptic longitude of γ Draconis
|-
| December || zero || none || ← (moving toward perihelion at fast velocity) || decrease of more than 20.2"
|-
| March || ← (moving toward aphelion) || 19.5" southward || zero || none
|-
| June || zero || none || → (moving toward aphelion at slow velocity) || increase of less than 20.2"
|-
| September || → (moving toward perihelion) || 19.5" northward || zero || none
|}

Bradley proposed that the aberration of light not only affected declination, but right ascension as well, so that a star in the pole of the ecliptic would describe a little ellipse with a diameter of about 40", but for simplicity, he assumed it to be a circle. Since he only observed the deviation in declination, and not in right ascension, his calculations for the maximum deviation of a star in the pole of the ecliptic are for its declination only, which will coincide with the diameter of the little circle described by such star. For eight different stars, his calculations are as follows:

{| class="wikitable"
|-
! Star !! Annual Variation (") !! Maximum deviation in declination of a star in the pole of the ecliptic (")
|-
| γ Draconis || 39 || 40.4
|-
| β Draconis || 39 || 40.2
|-
| η Ursa Maj. || 36 || 40.4
|-
| α Cass. || 34 || 40.8
|-
| τ Persei || 25 || 41.0
|-
| α Persei || 23 || 40.2
|-
| 35 Camel. || 19 || 40.2
|-
| Capella || 16 || 40.0
|-
| MEAN || || 40.4
|}

Based on these calculations, Bradley was able to estimate the constant of aberration at 20.2", which is equal to 0.00009793 radians, and with this was able to estimate the speed of light at {{convert|183300|mi|km}} per second.<ref name=EB>{{cite encyclopedia |editor-first=Dale H. |editor-last=Hoiberg |encyclopedia=Encyclopædia Britannica |title=aberration, constant of |edition=15th |date=2010 |publisher=Encyclopædia Britannica Inc. |volume=I: A-ak Bayes |location=Chicago, IL |isbn=978-1-59339-837-8 |pages=[https://archive.org/details/micropdiareadyre01chic/page/30/mode/2up 30] |url-access=registration |url=https://archive.org/details/micropdiareadyre01chic/page/30/mode/2up }}</ref> By projecting the little circle for a star in the pole of the ecliptic, he could simplify the calculation of the relationship between the speed of light and the speed of the Earth's annual motion in its orbit as follows:

:<math>\cos\left(\frac{1}{2}\pi-0.00009793\right) = \sin(0.00009793) = \frac{v}{c} </math>

Thus, the speed of light to the speed of the Earth's annual motion in its orbit is 10,210 to one, from whence it would follow, that light moves, or is propagated as far as from the Sun to the Earth in 8 minutes 12 seconds.<ref name=J_Bradley/>

The original motivation of the search for stellar parallax was to test the Copernican theory that the Earth revolves around the Sun. The change of aberration in the course of the year demonstrates the relative motion of the Earth and the stars.

===Retrodiction on Descartes' lightspeed argument===
In the prior century, [[René Descartes]] [[Speed of light#Early history|argued]] that if light were not instantaneous, then shadows of moving objects would lag; and if propagation delays over short terrestrial distances (as in experiments proposed by others at the time) were large enough to be humanly perceptible, then during a lunar eclipse the Sun, Earth, and Moon would be out of alignment by more than an hour's motion, contrary to observation. [[Christiaan Huygens|Huygens]] commented that, on [[Rømer's determination of the speed of light|Rømer's lightspeed data]] (implying an earth-moon round-trip time of only a few seconds), the lag angle would be undetectably small. What they both overlooked<ref>{{Cite journal |last=Sakellariadis |first=Spyros |date=1982 |title=Descartes' Experimental Proof of the Infinite Velocity of Light and Huygens' Rejoinder |url=https://www.jstor.org/stable/41133639 |journal=[[Archive for History of Exact Sciences]] |volume=26 |issue=1 |pages=1–12 |doi=10.1007/BF00348308 |jstor=41133639 |s2cid=118187860 |issn=0003-9519}}</ref> is that for observers being carried along by Earth's orbital motion, velocity aberration (as understood only later) would exactly counteract and perfectly conceal the lag even if large, leaving such eclipse-alignment analysis completely unrevealing about light speed. (Otherwise, shadow lag detection could be employed to sense absolute translational motion, contrary to a basic [[principle of relativity]].)