Editing Ole Rømer (section)

== Rømer and the speed of light ==
{{Main|Rømer's determination of the speed of light}}
The determination of [[longitude]] is a significant practical problem in [[cartography]] and [[navigation]]. [[Philip III of Spain]] offered a prize for a method to determine the longitude of a ship out of sight of land, and [[Galileo Galilei|Galileo]] proposed a method of establishing the time of day, and thus longitude, based on the times of the eclipses of the moons of [[Jupiter]], in essence using the Jovian system as a cosmic clock; this method was not significantly improved until accurate mechanical clocks were developed in the eighteenth century. Galileo proposed this method to the Spanish crown (1616–1617) but it proved to be impractical, because of the inaccuracies of Galileo's timetables and the difficulty of observing the eclipses on a ship. However, with refinements, the method could be made to work on land.

After studies in Copenhagen, Rømer joined [[Jean Picard]] in 1671 to observe about 140 eclipses of Jupiter's moon [[Io (moon)|Io]] on the island of [[Hven]] at the former location of [[Tycho Brahe]]’s observatory of [[Uraniborg]], near Copenhagen, over a period of several months, while in Paris [[Giovanni Domenico Cassini]] observed the same eclipses. By comparing the times of the eclipses, the difference in longitude of Paris to Uraniborg was calculated.

Cassini had observed the moons of Jupiter between 1666 and 1668, and discovered discrepancies in his measurements that, at first, he attributed to light having a finite speed. In 1672 Rømer went to Paris and continued observing the satellites of Jupiter as Cassini's assistant. Rømer added his own observations to Cassini's and observed that times between eclipses (particularly those of Io) got shorter as Earth approached Jupiter, and longer as Earth moved farther away. Cassini made an announcement to the Academy of Sciences on 22 August 1676:

<blockquote>''This second inequality appears to be due to light taking some time to reach us from the satellite; light seems to take about ten to eleven minutes [to cross] a distance equal to the half-diameter of the terrestrial orbit''.<ref>{{cite journal
| first1      = Laurence
| last1       = Bobis
| first2      = James
| last2       = Lequeux
| title       = Cassini, Rømer and the velocity of light
| url         = https://articles.adsabs.harvard.edu/pdf/2008JAHH...11...97B
| journal     = J. Astron. Hist. Herit.
| volume      = 11
| issue       = 2
| pages       = 97–105
| date        = 2008
| doi = 10.3724/SP.J.1440-2807.2008.02.02
| bibcode     = 2008JAHH...11...97B
| s2cid = 115455540
}}</ref></blockquote>

[[File:Illustration from 1676 article on Ole Rømer's measurement of the speed of light.png|thumb|Illustration from the 1676 article on Rømer's [[Speed of light#Astronomical measurements|measurement of the speed of light]]. Rømer compared the duration of Io's orbits as Earth moved towards Jupiter (F to G) and as Earth moved away from Jupiter (L to K).]]
Oddly, Cassini seems to have abandoned this reasoning, which Rømer adopted and set about buttressing in an irrefutable manner, using a selected number of observations performed by Picard and himself between 1671 and 1677. Rømer presented his results to the [[French Academy of Sciences]], and it was summarised soon after by an anonymous reporter in a short paper, ''{{lang|fr|Démonstration touchant le mouvement de la lumière trouvé par M. Roemer de l'Académie des sciences}}'', published 7 December 1676 in the ''[[Journal des sçavans]]''.<ref>{{cite journal |last1=Romer |title=Démonstration touchant le mouvement de la lumière trouvé par M. Roemer de l'Académie des sciences |journal=Le Journal des Sçavans |date=1676 |pages=233–236 |url=https://gallica.bnf.fr/ark:/12148/bpt6k56527v/f234.image |trans-title=Demonstration concerning the movement of light found by Mr. Romer of the Academy of Sciences |language=fr}}</ref> Unfortunately, the reporter, possibly in order to hide his lack of understanding, resorted to cryptic phrasing, obfuscating Rømer's reasoning in the process. Rømer himself never published his results.<ref name="Teuber218">{{cite book
| last            = Teuber
| first           = Jan
| display-editors = 4
| editor          = Friedrichsen, Per
| editor2         = Henningsen, Ole
| editor3         = Olsen, Olaf
| editor4         = Thykier, Claus
| editor5         = Tortzen, Chr. Gorm
| title           = Ole Rømer&nbsp;– videnskabsmand og samfundstjener
| date            = 2004
| publisher       = Gads Forlag
| location        = Copenhagen
| language        = da
| isbn            = 87-12-04139-4
| page            = 218
| chapter         = Ole Rømer og den bevægede Jord&nbsp;– en dansk førsteplads?
}}</ref>

Rømer's reasoning was as follows. Referring to the illustration, assume the Earth is at point ''L'', and Io emerges from Jupiter's shadow at point ''D''. After several orbits of Io, at 42.5 hours per orbit, the Earth is at point ''K''. If light is not propagated instantaneously, the additional time it takes to reach ''K'', which he reckoned about 3½ minutes, would explain the observed delay. Rømer observed ''immersions'' at point ''C'' from positions ''F'' and ''G'', to avoid confusion with [[eclipse]]s (Io shadowed by Jupiter from ''C'' to ''D'') and [[occultation]]s (Io hidden behind Jupiter at various angles). In the table below, his observations in 1676, including the one on 7 August, believed to be at the opposition point ''H'',<ref>Point ''H'' had occurred about one month earlier, according to {{cite web
 |url          = http://math-ed.com/Resources/GIS/Geometry_In_Space/java1/Temp/TLVisPOrbit.html
 |title        = Visualize Solar System at a given Epoch
 |access-date  = 9 March 2009
 |author       = Dieter Egger
 |date         = 24 February 1997
 |url-status   = dead
 |archive-url  = https://web.archive.org/web/20090322002132/http://math-ed.com/Resources/GIS/Geometry_In_Space/java1/Temp/TLVisPOrbit.html
 |archive-date = 22 March 2009
 }}</ref> and the one observed at [[Paris Observatory]] to be 10 minutes late, on 9 November.<ref name="Saito">{{cite journal
| last    = Saito
| first   = Yoshio
| title   = A Discussion of Roemer's Discovery concerning the Speed of Light
| journal = AAPPS Bulletin
| volume  = 15
| issue   = 3
| pages   = 9–17
| date    = June 2005
}}</ref>

{| class="wikitable" style="text-align:right; margin:1em auto 1em auto;"
|+ The eclipses of Io recorded by Rømer in 1676<br /><span style="font-weight:500; font-size:80%; line-height:80%;">Time is normalized (hours since midnight rather than since noon); values on even rows are calculated from the original data.</span>
|-
! Month
! Day
! Time
! Tide
! orbits
! average (hours)
|-
| May
| 12
| 2:49:42
| '''C'''
| colspan="2" | 
|-
| colspan="3" | <small>2,837,189s</small>
|
| 18
| 41.48
|-
| June
| 13
| 22:56:11
| '''C'''
| colspan="2" | 
|-
| colspan="3" | <small>4,748,019s</small>
|
| 31
| 42.54
|-
| Aug
|  7
| 21:49:50
| '''D'''
| colspan="2" | 
|-
| colspan="3" | <small>611,765s</small>
|
| 4
| 42.48
|-
| Aug
| 14
| 23:45:55
| '''D'''
| colspan="2" | 
|-
| colspan="3" | <small>764,718s</small>
|
| 5
| 42.48
|-
| Aug
| 23
| 20:11:13
| '''D'''
| colspan="2" | 
|-
| colspan="3" | <small>6,729,872s</small>
|
| 44
| 42.49
|-
| Nov
|  9
| 17:35:45
| '''D'''
| colspan="2" | 
|}

By [[trial and error]], during eight years of observations Rømer worked out how to account for ''the retardation of light'' when reckoning the [[ephemeris]] of Io. He calculated the delay as a proportion of the angle corresponding to a given Earth's position with respect to Jupiter, ''Δt''&nbsp;=&nbsp;22·({{frac|α|180°}})<nowiki>[minutes]</nowiki>. When the angle α is 180° the delay becomes 22 minutes, which may be interpreted as the time necessary for the light to cross a distance equal to the diameter of the Earth's orbit, '''H''' to '''E'''.<ref name="Saito" /> (Actually, Jupiter is not visible from the conjunction point '''E'''.) That interpretation makes it possible to calculate the strict result of Rømer's observations: The ratio of the speed of light to the speed with which Earth orbits the sun, which is the ratio of
the duration of a year divided by pi as compared to the 22 minutes

{{frac|365·24·60|''π''·22}} ≈ 7,600.

In comparison, the modern value is circa {{frac|299,792&nbsp;km&nbsp;s<sup>−1</sup>|29.8&nbsp;km&nbsp;s<sup>−1</sup>}} ≈ 10,100.<ref>{{cite book
| last      = Knudsen
| first     = Jens Martin
| author2   = Hjorth, Poul G.
| title     = Elements of Newtonian Mechanics
| orig-year  = 1995
| edition   = 2nd
| date      = 1996
| publisher = Springer Verlag
| location  = Berlin
| isbn      = 3-540-60841-9
| page      = 367
}}</ref>

Rømer neither calculated this ratio, nor did he give a value for the speed of light. However, many others calculated a speed from his data, the first being [[Christiaan Huygens]]; after corresponding with Rømer and eliciting more data, Huygens deduced that light travelled {{frac|16|2|3}} Earth diameters per second,<ref>[[Christiaan Huygens|Huygens, Christiaan]] (8 January 1690) ''[http://www.gutenberg.org/catalog/world/readfile?fk_files=164378 Treatise on Light]''. Translated into English by Silvanus P. Thompson, [[Project Gutenberg]] etext, [http://www.gutenberg.org/catalog/world/readfile?fk_files=164378&pageno=11 p. 11]. Retrieved on 29 April 2007.</ref> which is approximately 212,000&nbsp;km/s.

Rømer's view that the velocity of light was finite was not fully accepted until measurements of the so-called [[aberration of light]] were made by [[James Bradley]] in 1727.

In 1809, again making use of observations of Io, but this time with the benefit of more than a century of increasingly precise observations, the astronomer [[Jean Baptiste Joseph Delambre]] reported the time for light to travel from the Sun to the Earth as 8 minutes and 12 seconds. Depending on the value assumed for the astronomical unit, this yields the speed of light as just a little more than 300,000 kilometres per second. The modern value is 8 minutes and 19 seconds, and a speed of 299,792.458&nbsp;km/s.

A plaque at the Observatory of Paris, where the Danish astronomer happened to be working, commemorates what was, in effect, the first measurement of a universal quantity made on this planet.