In 1676, the Danish astronomer Ole RømerThere are several alternative spellings of Rømer's surname, including "Roemer", "Rœmer", and "Römer". The Danish "Ole" is sometimes latinized to "Olaus". demonstrated that light has a measurable speed and so does not travel instantaneously. Rømer was working at the Royal Observatory in Paris at the time.
By timing the eclipses of Jupiter's moon Io, Rømer estimated that light would take about 22 minutes to travel a distance equal to the diameter of Earth's orbit around the Sun.P. 328 of Using modern orbits, this would imply a speed of light of 226,663 kilometres per second,Calculation on WolframAlpha. 24.4% lower than the true value of 299,792 km/s.Calculation on WolframAlpha. In his calculations Rømer used the idea and observations that the apparent time between eclipses would be greater while the Earth is moving further from Jupiter and lesser while moving closer.
Rømer's theory was controversial at the time that he announced it and he never convinced the director of the Paris Observatory, Giovanni Domenico Cassini, to fully accept it. However, it quickly gained support among other natural philosophers of the period such as Christiaan Huygens and Isaac Newton. It was finally confirmed nearly two decades after Rømer's death, with the explanation in 1729 of stellar aberration by the English astronomer James Bradley.
Background The determination of east–west positioning (longitude) was a significant practical problem in cartography and navigation before the 1700s. In 1598 Philip III of Spain had offered a prize for a method to determine the longitude of a ship out of sight of land. 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 in 1616–1617 but it proved to be impractical, not least because of the difficulty of observing the eclipses from a ship. However, with refinements the method could be made to work on land.
The Italian astronomer Giovanni Domenico Cassini had pioneered the use of the eclipses of the Galilean moons for longitude measurements, and published tables predicting when eclipses would be visible from a given location. He was invited to France by Louis XIV to set up the Royal Observatory, which opened in 1671 with Cassini as director, a post he would hold for the rest of his life.
One of Cassini's first projects at his new post in Paris was to send Frenchman Jean Picard to the site of Tycho Brahe's old observatory at Uraniborg, on the island of Hven near Copenhagen. Picard was to observe and time the eclipses of Jupiter's moons from Uraniborg while Cassini recorded the times they were seen in Paris. If Picard recorded the end of an eclipse at 9 hours 43 minutes 54 seconds after midday in Uraniborg, while Cassini recorded the end of the same eclipse at 9 hours 1 minute 44 seconds after midday in Paris – a difference of 42 minutes 10 seconds – the difference in longitude could be calculated to be 10° 32' 30".The timing of the end of the eclipse comes from one of the few surviving manuscripts of Rømer, in which he records the date as 19 March 1671: see Meyer (1915). By consistency with the other timings recorded in the manuscript (written several years after the event), it has been assumed that Rømer noted the Paris time of the eclipse's end. The time difference of 42 minutes and 10 seconds between Paris and Uraniborg comes from the same manuscript: the value accepted today is 41 minutes 26 seconds. Picard was helped in his observations by a young Dane who had recently completed his studies at the University of Copenhagen – Ole Rømer – and he must have been impressed by his assistant's skills, as he arranged for the young man to come to Paris to work at the Royal Observatory there.
Eclipses of Io
Io is the innermost of the four moons of Jupiter discovered by Galileo in January 1610. Rømer and Cassini referred to it as the "first satellite of Jupiter". It orbits Jupiter once every 42½ hours, and the plane of its orbit is very close to the plane of Jupiter's orbit around the sun. This means that it passes some of each orbit in the shadow of Jupiter – an eclipse.
Viewed from the Earth, an eclipse of Io is seen in one of two ways. Io suddenly disappears, as it moves into the shadow of Jupiter. This is termed an immersion. Io suddenly reappears, as it moves out of the shadow of Jupiter. This is termed an emergence. From the Earth, the immersion and the emergence cannot be observed for the same eclipse of Io, because one or the other will be hidden (occulted) by Jupiter itself. At the point of opposition (point H in the diagram below), both the immersion and the emergence would be hidden by Jupiter.
For about four months before the opposition (from F to G), immersions of Io into Jupiter's shadow can be observed, and about four months after the opposition of Jupiter (from L to K in the diagram below), emergences of Io from its eclipses can be observed. For about five or six months of the year, around the point of conjunction, eclipses of Io cannot be observed at all, because the view of Jupiter is too close to the sun. Even during the periods before and after opposition, many eclipses of Io cannot be observed from a given location on the Earth's surface: some will occur during the daytime and some will occur while Jupiter is below the horizon (hidden by the Earth itself).
The key phenomenon that Rømer observed was that the time between eclipses was not constant, but varied slightly over the year. He was fairly confident that the orbital period of Io was not actually changing, so he deduced that change was a consequence of changes in the distance between Earth and Jupiter. The orbital paths of Earth and Jupiter were available to him, and by referring to them he noticed that during periods in which Earth and Jupiter were moving away from each other the interval between eclipses always increased, whereas when Earth and Jupiter were moving toward each other, the interval between eclipses decreased. Rømer reasoned that these observations could be explained by a constant speed of light, which he calculated.
Observations
Most of Rømer's papers were destroyed in the Copenhagen Fire of 1728, but one manuscript that survived contains a listing of about sixty observations of eclipses of Io from 1668 to 1678.Meyer (1915). In particular, it details two series of observations on either side of the oppositions of 2 March 1672 and 2 April 1673. Rømer comments in a letter to Christiaan Huygens dated 30 September 1677 that these observations from 1671 to 1673 form the basis for his calculations.Rømer (1677).
The surviving manuscript was written some time after January 1678, the date of the last recorded astronomical observation (an emergence of Io on 6 January), and so was later than Rømer's letter to Huygens. Rømer appears to have been collecting data on eclipses of the Galilean moons in the form of an aide-mémoire, possibly as he was preparing to return to Denmark in 1681. The document also records the observations around the opposition of 8 July 1676 that formed the basis for the announcement of Rømer's results.
Initial announcement On 22 August 1676,Several texts erroneously place the date of the announcement in 1685 or even in 1684. Bobis and Lequeux (2008) have convincingly demonstrated that the announcement was made on 22 August 1676, and that it was made by Cassini and not Rømer. Cassini made an announcement to the Royal Academy of Sciences in Paris that he would be changing the basis of calculation for his tables of eclipses of Io. He may also have stated the reason:Bobis and Lequeux (2008).The original record of the meeting of the Royal Academy of Sciences has been lost. The quotation comes from an unpublished manuscript in Latin preserved in the library of the Paris Observatory, probably written by Joseph-Nicolas Delisle (1688–1768) at some point before 1738. See Bobis and Lequeux (2008), which contains a facsimile of the manuscript.
Most importantly, Rømer announced the prediction that the emergence of Io on 16 November 1676 would be observed about ten minutes later than would have been calculated by the previous method. There is no record of any observation of an emergence of Io on 16 November, but an emergence was observed on 9 November. With this experimental evidence in hand, Rømer explained his new method of calculation to the Royal Academy of Sciences on 21 November.
The original record of the meeting of the Royal Academy of Sciences has been lost, but Rømer's presentation was recorded as a news report in the Journal des sçavans on 7 December.. This anonymous report was translated into English and published in Philosophical Transactions of the Royal Society in London on 25 July 1677.Bobis and Lequeux (2008) tentatively attribute the translation to Edmond Halley (1656–1742), who would become English Astronomer Royal and who is best known for his calculations concerning Halley's Comet. However, other sources – not least his own Catalogus Stellarum Australium published in 1679 – suggest that Halley was on the island of St. Helena in the South Atlantic Ocean at the time.
Rømer's reasoning
Order of magnitude Rømer starts with an order of magnitude demonstration that the speed of light must be so great that it takes much less than one second to travel a distance equal to Earth's diameter.
The point L on the diagram represents the second quadrature of Jupiter, when the angle between Jupiter and the Sun (as seen from Earth) is 90°.Although the news report doesn't make it explicit, the choice of a point of quadrature for the example is unlikely to be fortuitous. At the second quadrature, the motion of the Earth in its orbit is taking it directly away from Jupiter. As such, it is the point at which the greatest effect is expected over a single orbit of Io. Rømer assumes that an observer could see an emergence of Io at the second quadrature (L), and the emergence which occurs after one orbit of Io around Jupiter (when the Earth is taken to be at point K, the diagram not being to scale), that is 42½ hours later. During those 42½ hours, the Earth has moved farther away from Jupiter by the distance LK: this, according to Rømer, is 210 times the Earth's diameter.The figure of 210 Earth-diameters per orbit of Io for the orbital speed of the Earth relative to Jupiter is far lower than the real figure, which averages around 322 Earth-diameters per orbit of Io taking into account the orbital motion of Jupiter. Rømer appears to have believed that Jupiter is closer to the Sun (and hence moving faster along its orbit) than is really the case. If light travelled at a speed of one Earth-diameter per second, it would take 3½ minutes to travel the distance LK. And if the period of Io's orbit around Jupiter were taken as the time difference between the emergence at L and the emergence at K, the value would be 3½ minutes longer than the true value.
Rømer then applies the same logic to observations around the first quadrature (point G), when Earth is moving towards Jupiter. The time difference between an immersion seen from point F and the next immersion seen from point G should be 3½ minutes shorter than the true orbital period of Io. Hence, there should be a difference of about 7 minutes between the periods of Io measured at the first quadrature and those measured at the second quadrature. In practice, no difference is observed, from which Rømer concludes that the speed of light must be very much greater than one Earth-diameter per second.
Cumulative effect