Editing Speed of light (section)

=== Astronomical measurements ===
[[File:Io eclipse speed of light measurement.svg|thumb|upright=1.8|Measurement of the speed of light from the time it takes Io to orbit Jupiter, using eclipses of Io by Jupiter's shadow to precisely measure its orbit.]]
[[Outer space]] is a convenient setting for measuring the speed of light because of its large scale and nearly perfect [[vacuum]]. Typically, one measures the time needed for light to traverse some reference distance in the [[Solar System]], such as the [[radius]] of the Earth's orbit. Historically, such measurements could be made fairly accurately, compared to how accurately the length of the reference distance is known in Earth-based units.

[[Ole Rømer]] used an astronomical measurement to make [[Rømer's determination of the speed of light|the first quantitative estimate of the speed of light]] in the year 1676.<ref name=cohen>
{{Cite journal
 |last=Cohen |first=I. B. |author-link=I. Bernard Cohen
 |year=1940
 |title=Roemer and the first determination of the velocity of light (1676)
 |journal=[[Isis (journal)|Isis]]
 |volume=31 |issue=2 |pages=327–379
 |doi=10.1086/347594
 |ref=cohen-1940
 |hdl=2027/uc1.b4375710
 |s2cid=145428377
 |url=https://babel.hathitrust.org/cgi/imgsrv/download/pdf?id=uc1.b4375710;orient=0;size=100;seq=5;attachment=0
 |hdl-access=free
}}</ref><ref name=roemer>
{{Cite journal
 |year=1676
 |title=Demonstration tovchant le mouvement de la lumiere trouvé par M. Rŏmer de l'Académie Royale des Sciences
 |trans-title=Demonstration to the movement of light found by Mr. Römer of the Royal Academy of Sciences
 |language=fr
 |url=http://www-obs.univ-lyon1.fr/labo/fc/ama09/pages_jdsc/pages/jdsc_1676_lumiere.pdf
 |journal=[[Journal des sçavans]]
 |pages=233–236
 |ref=roemer-1676
}}<br />Translated in 
{{Cite journal
 |doi=10.1098/rstl.1677.0024
 |year=1677
 |title=A demonstration concerning the motion of light, communicated from Paris, in the Journal des Sçavans, and here made English
 |journal=[[Philosophical Transactions of the Royal Society]]
 |volume=12 |issue=136 |pages=893–895
 |ref=roemer-1676-EnglishTrans
 |bibcode=1677RSPT...12..893.|doi-access=free
}}<br />Reproduced in 
{{Cite book
 |editor1-last=Hutton |editor1-first=C.
 |editor2-last=Shaw |editor2-first=G.
 |editor3-last=Pearson |editor3-first=R.
 |year=1809
 |title=The Philosophical Transactions of the Royal Society of London, from Their Commencement in 1665, in the Year 1800: Abridged
 |chapter=On the Motion of Light by M. Romer
 |chapter-url=https://archive.org/stream/philosophicaltra02royarich#page/397/mode/1up
 |location=London |publisher=C. & R. Baldwin
 |volume=II. From 1673 to 1682 |pages=397–398
}}<br />
The account published in {{lang|fr|Journal des sçavans}} was based on a report that Rømer read to the [[French Academy of Sciences]] in November 1676 [[#cohen-1940|(Cohen, 1940, p.&nbsp;346)]].</ref> When measured from Earth, the periods of moons orbiting a distant planet are shorter when the Earth is approaching the planet than when the Earth is receding from it. The difference is small, but the cumulative time becomes significant when measured over months. The distance travelled by light from the planet (or its moon) to Earth is shorter when the Earth is at the point in its orbit that is closest to its planet than when the Earth is at the farthest point in its orbit, the difference in distance being the [[diameter]] of the Earth's orbit around the Sun. The observed change in the moon's orbital period is caused by the difference in the time it takes light to traverse the shorter or longer distance. Rømer observed this effect for [[Jupiter]]'s innermost major moon Io and deduced that light takes 22 minutes to cross the diameter of the Earth's orbit.<ref name="cohen" />

[[File:SoL Aberration.svg|thumb|upright|Aberration of light: light from a distant source appears to be from a different location for a moving telescope due to the finite speed of light.|alt=A star emits a light ray that hits the objective of a telescope. While the light travels down the telescope to its eyepiece, the telescope moves to the right. For the light to stay inside the telescope, the telescope must be tilted to the right, causing the distant source to appear at a different location to the right.]]
Another method is to use the [[aberration of light]], discovered and explained by [[James Bradley]] in the 18th century.<ref name="Bradley1729">
{{Cite journal
 |last=Bradley |first=J.
 |year=1729
 |title=Account of a new discovered Motion of the Fix'd Stars
 |url=http://gallica.bnf.fr/ark:/12148/bpt6k55840n.image.f375.langEN
 |journal=[[Philosophical Transactions]]
 |volume=35 |pages=637–660
}}</ref> This effect results from the [[vector addition]] of the velocity of light arriving from a distant source (such as a star) and the velocity of its observer (see diagram on the right). A moving observer thus sees the light coming from a slightly different direction and consequently sees the source at a position shifted from its original position. Since the direction of the Earth's velocity changes continuously as the Earth orbits the Sun, this effect causes the apparent position of stars to move around. From the angular difference in the position of stars (maximally 20.5 [[arcsecond]]s)<ref>
{{Cite book
 |last=Duffett-Smith
 |first=P.
 |year=1988
 |title=Practical Astronomy with your Calculator
 |url=https://archive.org/details/practicalastrono0000duff
 |url-access=registration
 |page=[https://archive.org/details/practicalastrono0000duff/page/62 62]
 |publisher=Cambridge University Press
 |isbn=978-0-521-35699-2
}} [https://archive.org/details/practicalastrono0000duff/page/62 Extract of page 62].</ref> it is possible to express the speed of light in terms of the Earth's velocity around the Sun, which with the known length of a year can be converted to the time needed to travel from the Sun to the Earth. In 1729, Bradley used this method to derive that light travelled {{val|10,210}} times faster than the Earth in its orbit (the modern figure is {{val|10,066}} times faster) or, equivalently, that it would take light 8&nbsp;minutes 12&nbsp;seconds to travel from the Sun to the Earth.<ref name="Bradley1729"/>

==== Astronomical unit ====
{{main|Astronomical unit}}
Historically the speed of light was used together with timing measurements to determine a value for the  astronomical unit (AU).<ref>{{Cite journal |last=Standish |first=E. M. |date=June 2004 |title=The Astronomical Unit now |url=https://www.cambridge.org/core/product/identifier/S1743921305001365/type/journal_article |journal=Proceedings of the International Astronomical Union |language=en |volume=2004 |issue=IAUC196 |pages=163–179 |doi=10.1017/S1743921305001365 |issn=1743-9213}}</ref> It was redefined in 2012 as exactly {{val|149597870700|u=m}}.<ref>{{Cite journal|journal=The International System of Units|title=Supplement 2014: Updates to the 8th edition (2006) of the SI Brochure|url=http://www.bipm.org/utils/common/pdf/si_supplement_2014.pdf|year=2014|publisher= International Bureau of Weights and Measures|page=14}}</ref><ref name=AU_redef>{{Cite web|title=Resolution B2 on the re-definition of the astronomical unit of length|url=https://www.iau.org/static/resolutions/IAU2012_English.pdf|year=2012|publisher=International Astronomical Union}}</ref> This redefinition is analogous to that of the metre and likewise has the effect of fixing the speed of light to an exact value in astronomical units per second (via the exact speed of light in metres per second).<ref>{{Cite journal|last=Brumfiel|first=Geoff|date=14 September 2012|title=The astronomical unit gets fixed|url=https://www.nature.com/articles/nature.2012.11416|journal=[[Nature (journal)|Nature]]|language=en|doi=10.1038/nature.2012.11416|s2cid=123424704|issn=1476-4687}}</ref>