Editing Aberration (astronomy) (section)

===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.