Rømer's determination of the speed of light
Encyclopedia
Rømer's determination of the speed of light was the demonstration in 1676 that light has a finite speed
, and so doesn't travel instantaneously. The discovery is usually attributed to Danish
astronomer Ole Rømer (1644–1710),There are several alternative spellings of Rømer's surname: Roemer, Rœmer, Römer etc. The Danish Ole is sometimes latinized to Olaus. who was working at the Royal Observatory
in Paris
at the time.
Rømer estimated that light would take about 22 minutes to travel a distance equal to the diameter
of Earth's orbit
around the Sun: this is equivalent to about 220,000 kilometres per second
in modern units, about 26% lower than the true value. While the exact details of Rømer's calculations have been lost, the error is probably due to an error in the orbital elements
of Jupiter
, leading Rømer to believe that Jupiter was closer to the Sun than is actually the case.
Rømer's theory was controversial at the time he announced it, and he never convinced the director of the Royal 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
.
was a significant practical problem in cartography
and navigation
. Philip III of Spain
had offered a prize for a method to determine the longitude of a ship out of sight of land, and 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 (1616–17) but it proved to be impractical, not least because of the difficulty of observing the eclipses on 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 in 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 emergence 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 emergence. The time difference of 42 minutes and 10 seconds between Paris and Uraniborg comes from the same manuscript: the modern value 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.
is the innermost of the four moons of Jupiter discovered by Galileo
in January 1610. Rømer and Cassini refer 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 much 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.
From the Earth, it is not possible to view both the immersion and the emergence 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 after the opposition of Jupiter (from L to K in the diagram below), it is possible to view emergences of Io from its eclipses, while for about four months before the opposition (from F to G), it is possible to view immersions of Io into Jupiter's shadow. For about five or six months of the year, around the point of conjunction, it is impossible to observe the eclipses of Io at all because Jupiter is too close (in the sky) to the sun. Even during the periods before and after opposition, not all of the eclipses of Io can be observed from a given location on the Earth's surface: some eclipses will occur during the daytime for a given location, while other eclipses will occur while Jupiter is below the horizon (hidden by the Earth itself).
, but one manuscript that survived contains a listing of about sixty observations of eclipses of Io from 1668 to 1678. 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 1671–73 form the basis for his calculations.
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 is posterior to Rømer's letter to Huygens. Rømer appears to be 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.
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: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, Cassini 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 22 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.
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 90º.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 also 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 further 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 at all, from which Rømer concludes that the speed of light must be very much greater than one Earth-diameter per second.
Jupiter was in opposition on 2 March 1672: the first observations of emergences were on 7 March (at 07:58:25) and 14 March (at 09:52:30). Between the two observations, Io had completed four orbits of Jupiter, giving an orbital period of 42 hours 28 minutes 31¼ seconds.
The last emergence observed in the series was on 29 April (at 10:30:06). By this time, Io had completed thirty orbits around Jupiter since 7 March: the apparent orbital period is 42 hours 29 minutes 3 seconds. The difference seems minute – 32 seconds – but it meant that the emergence on 29 April was occurring a quarter-hour after it would have been predicted. The only alternative explanation was that the observations on 7 and 14 March were wrong by two minutes.
Cassini announced that the new tables would
Hence Cassini and Rømer appear to have been calculating the times of each eclipse based on the approximation of circular orbits, and then applying three successive corrections to estimate the time that the eclipse would be observed in Paris.
The three "inequalities" (or irregularities) listed by Cassini were not the only ones known, but they were the ones that could be corrected for by calculation. The orbit of Io is also slightly irregular because of orbital resonance
with Europa
and Ganymede
, two of the other Galilean moons
of Jupiter, but this would not be fully explained for another century. The only solution available to Cassini and to other astronomers of his time was to issue periodic corrections to the tables of eclipses of Io to take account of its irregular orbital motion: periodically resetting the clock, as it were. The obvious time to reset the clock was just after the opposition of Jupiter to the Sun, when Jupiter is at its closest to Earth and so most easily observable.
The opposition of Jupiter to the Sun occurred on or around 8 July 1676. Rømer's aide-mémoire lists two observation of emergences of Io after this opposition but before Cassini's announcement: on 7 August at 09:44:50 and on 14 August at 11:45:55. With these data, and knowing the orbital period of Io, Cassini could calculate the times of each of the eclipses over the next four to five months.
The next step in applying Rømer's correction would be to calculate the position of Earth and Jupiter in their orbits for each of the eclipses. This sort of coordinate transformation was commonplace in preparing tables of positions of the planets for both astronomy and astrology
: it is equivalent to finding each of the positions L (or K) for the various eclipses which might be observable.
Finally, the distance between Earth and Jupiter can be calculated using standard trigonometry
, in particular the law of cosines
, knowing two sides (distance between the Sun and Earth; distance between the Sun and Jupiter) and one angle (the angle between Jupiter and Earth as formed at the Sun) of a triangle. The distance from the Sun to Earth was not well known at the time, but taking it as a fixed value a, the distance from the Sun to Jupiter can be calculated as some multiple of a from Kepler's third law
.
This model left just one adjustable parameter – the time taken for light to travel a distance equal to a, the radius of Earth's orbit. Rømer had about thirty observations of eclipses of Io from 1671–73 that he used to find the value which fitted best: eleven minutes. With that value, he could calculate the extra time it would take light to reach Earth from Jupiter in November 1676 compared to August 1676: about ten minutes.
, and wrote to the French Controller-General of Finances
Jean-Baptiste Colbert
in Rømer's defence. However Cassini
, Rømer's superior at the Royal Observatory, was an early and tenacious opponent of Rømer's ideas, and it seems that Picard
, Rømer's mentor, shared many of Cassini's doubts.
Cassini's practical objections took up many debates at the Royal Academy of Sciences (with Huygens participating by letter from London). Cassini noted that the other three Galilean moons
did not seem to show the same effect as seen for Io, and that there were other irregularities which could not be explained by Rømer's theory. Rømer replied that it was much more difficult to accurately observe the eclipses of the other moons, and that the unexplained effects were much smaller (for Io) than the effect of the speed of light: however, he admitted to Huygens that the unexplained "irregularities" in the other satellites were larger than the effect of the speed of light. The dispute had something of a philosophical note: Rømer claimed that he had discovered a simple solution to an important practical problem, while Cassini rejected the theory as flawed as it could not explain all the observations.This last point is put quite clearly as late as 1707 by Cassini's nephew, Giacomo Filippo Maraldi
(1665–1729), who also worked at the Royal Observatory: "In order for an hypothesis to be accepted, it is not enough that it agrees with some observations, it must also be consistent with the other phenomena." Quoted in Bobis and Lequeux (2008). Cassini was forced to include "empirical corrections" in his 1693 tables of eclipses, but never accepted the theoretical basis: indeed, he chose different correction values for the different moons of Jupiter, in direct contradiction with Rømer's theory.
Rømer's ideas received a much warmer reception in England. Although Robert Hooke
(1635–1703) dismissed the supposed speed of light as so large as to be virtually instantaneous, the Astronomer Royal
John Flamsteed
(1646–1719) accepted Rømer's hypothesis in his ephemerides
of eclipses of Io. Edmond Halley
(1656–1742), a future Astronomer Royal, was also an early and enthusiastic supporter. Isaac Newton
(1643–1727) also appears to have accepted Rømer's ideas, and gives a value of "seven or eight minutes" for light to travel from the Sun to Earth in his 1704 book Opticks
. Newton also notes that Rømer's observations had been confirmed by others, presumably by Flamsteed and Halley in Greenwich
at the very least: the value of 7–8 minutes is closer to the true value (8 minutes 19 seconds) than Rømer's initial estimate of 11 minutes.
While it was obviously difficult for many (such as Hooke) to conceive of the enormous speed of light, Rømer's idea suffered a second handicap in that they were based on Kepler's
model of the planets orbiting the Sun in elliptical
orbits. While Kepler's model had widespread acceptance by the late seventeenth century, it was still considered sufficiently controversial for Newton to spend several pages discussing the observational evidence in favour in his Philosophiæ Naturalis Principia Mathematica (1687).
Rømer's view that the velocity of light was finite was not fully accepted until measurements of stellar aberration
were made in 1727 by James Bradley
(1693–1762). Bradley, who would be Halley's successor as Astronomer Royal, calculated a value of 8 minutes 13 seconds for light to travel from the Sun to Earth. Ironically, stellar aberration had first been observed by Cassini and (independently) by Picard in 1671, but neither astronomer was able to give an explanation for the phenomenon. Bradley's work also laid to rest any remaining serious objections to the Keplerian model of the Solar System.
(1717–83) used Rømer's method in the preparation of his ephemerides of Jupiter's moons (1746), as did Giovanni Domenico Maraldi
working in Paris. The remaining irregularities in the orbits of the Galilean moons
would not be satisfactorily explained until the work of Joseph Louis Lagrange
(1736–1813) and Pierre-Simon Laplace
(1749–1827) on orbital resonance
.
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 (1749–1822) reported the time for light to travel from the Sun to the Earth as 8 minutes 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 first measurements of the speed of light using completely terrestrial apparatus were published in 1849 by Hippolyte Fizeau
(1819–96). Compared to modern values, Fizeau's result (about 313,000 kilometres per second) was too high, and less accurate than those obtained by Rømer's method. It would be another thirty years before A. A. Michelson
in the United States published his more precise results (299,910±50 km/s) and Simon Newcomb
confirmed the agreement with astronomical measurements, almost exactly two centuries after Rømer's announcement.
Huygens' estimate was a value of 110,000,000 toise
s per second: as the toise was later determined to be just under two metres,The exact ratio is 1 toise = metres, or approximately 1.949 m: French law of 19 frimaire An VIII
(10 December 1799). Huygens was using Picard's
value (1669) of the circumference of the Earth as 360×25×2282 toises, while the 1799 legal conversion uses the more precise results of Delambre and Méchain
. this gives the value in modern units.
However, Huygens' estimate was not a precise calculation but rather an illustration at an order of magnitude
level. The relevant passage from Treatise sur la lumière reads:
Huygens was obviously not concerned about the 9% difference between his preferred value for the distance from the Sun to Earth and the one he uses in his calculation. Nor was there any doubt in Huygens' mind as to Rømer's achievement, as he wrote to Colbert
(emphasis added):
Neither Newton nor Bradley bothered to calculate the speed of light in Earth-based units. The next recorded calculation was probably made by Fontenelle
: claiming to work from Rømer's results, the historical account of Rømer's work written some time after 1707 gives a value of 48203 leagues
per second. This is 16.826 Earth-diameters per second.
, and this 166 years before Christian Doppler's
1842 discovery. The Doppler effect is the change in observed frequency of an oscillator (in this case, Io orbiting around Jupiter) when the observer (in this case, on Earth's surface) is moving: the frequency is higher when the observer is moving towards the oscillator and lower when the observer is moving away from the oscillator. This apparently anachronistic analysis implies that Rømer was measuring the ratio , where c is the speed of light and v is the Earth's orbital velocity (strictly, the component of the Earth's orbital velocity parallel to the Earth–Jupiter vector), and indicates that the major inaccuracy of Rømer's calculations was his poor knowledge of the orbit of Jupiter.
There is no evidence that Rømer thought that he was measuring : he gives his result as the time of 22 minutes for light to travel a distance equal to the diameter of Earth's orbit or, equivalently, 11 minutes for light to travel from the Sun to Earth. It can be readily shown that the two measurements are equivalent: if we give τ as the time taken for light to cross the radius of an orbit (e.g. from the Sun to Earth) and P as the orbital period (the time for one complete rotation), thenThe expression is given for the approximation to a circular orbit. The derivation is as follows:
(1) express the orbital velocity in terms of the orbital radius r and the orbital period P: v =
(2) substitute τ = → v =
(3) rearrange to find .
Bradley
, who was measuring in his studies of aberration in 1729, was well aware of this relation as he converts his results for into a value for τ without any comment.
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
, and so doesn't travel instantaneously. The discovery is usually attributed to Danish
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
astronomer Ole Rømer (1644–1710),There are several alternative spellings of Rømer's surname: Roemer, Rœmer, Römer etc. The Danish Ole is sometimes latinized to Olaus. who was working at the Royal Observatory
Paris Observatory
The Paris Observatory is the foremost astronomical observatory of France, and one of the largest astronomical centres in the world...
in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
at the time.
Rømer estimated that light would take about 22 minutes to travel a distance equal to the diameter
Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...
of Earth's orbit
Earth's orbit
In astronomy, the Earth's orbit is the motion of the Earth around the Sun, at an average distance of about 150 million kilometers, every 365.256363 mean solar days .A solar day is on average 24 hours; it takes 365.256363 of these to orbit the sun once in the sense of returning...
around the Sun: this is equivalent to about 220,000 kilometres per second
Metre per second
Metre per second is an SI derived unit of both speed and velocity , defined by distance in metres divided by time in seconds....
in modern units, about 26% lower than the true value. While the exact details of Rømer's calculations have been lost, the error is probably due to an error in the orbital elements
Orbital elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are generally considered in classical two-body systems, where a Kepler orbit is used...
of Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...
, leading Rømer to believe that Jupiter was closer to the Sun than is actually the case.
Rømer's theory was controversial at the time he announced it, and he never convinced the director of the Royal Observatory, Giovanni Domenico Cassini
Giovanni Domenico Cassini
This article is about the Italian-born astronomer. For his French-born great-grandson, see Jean-Dominique Cassini.Giovanni Domenico Cassini was an Italian/French mathematician, astronomer, engineer, and astrologer...
, to fully accept it. However, it quickly gained support among other natural philosophers
Natural philosophy
Natural philosophy or the philosophy of nature , is a term applied to the study of nature and the physical universe that was dominant before the development of modern science...
of the period, such as Christiaan Huygens and Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
. It was finally confirmed nearly two decades after Rømer's death, with the explanation in 1729 of stellar aberration
Aberration of light
The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations...
by the English astronomer James Bradley
James Bradley
James Bradley FRS was an English astronomer and served as Astronomer Royal from 1742, succeeding Edmund Halley. He is best known for two fundamental discoveries in astronomy, the aberration of light , and the nutation of the Earth's axis...
.
Background
The determination of longitudeLongitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
was a significant practical problem in cartography
Cartography
Cartography is the study and practice of making maps. Combining science, aesthetics, and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively.The fundamental problems of traditional cartography are to:*Set the map's...
and navigation
Navigation
Navigation is the process of monitoring and controlling the movement of a craft or vehicle from one place to another. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks...
. Philip III of Spain
Philip III of Spain
Philip III , also known as Philip the Pious, was the King of Spain and King of Portugal and the Algarves, where he ruled as Philip II , from 1598 until his death...
had offered a prize for a method to determine the longitude of a ship out of sight of land, and Galileo
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...
proposed a method of establishing the time of day, and thus longitude, based on the times of the eclipses of the moons of Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...
, 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 (1616–17) but it proved to be impractical, not least because of the difficulty of observing the eclipses on a ship. However, with refinements the method could be made to work on land.
The Italian
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
astronomer Giovanni Domenico Cassini
Giovanni Domenico Cassini
This article is about the Italian-born astronomer. For his French-born great-grandson, see Jean-Dominique Cassini.Giovanni Domenico Cassini was an Italian/French mathematician, astronomer, engineer, and astrologer...
had pioneered the use of the eclipses of the Galilean moons
Galilean moons
The Galilean moons are the four moons of Jupiter discovered by Galileo Galilei in January 1610. They are the largest of the many moons of Jupiter and derive their names from the lovers of Zeus: Io, Europa, Ganymede and Callisto. Ganymede, Europa and Io participate in a 1:2:4 orbital resonance...
for longitude measurements, and published tables predicting when eclipses would be visible from a given location. He was invited to France by Louis XIV
Louis XIV of France
Louis XIV , known as Louis the Great or the Sun King , was a Bourbon monarch who ruled as King of France and Navarre. His reign, from 1643 to his death in 1715, began at the age of four and lasted seventy-two years, three months, and eighteen days...
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 in his new post in Paris was to send Frenchman Jean Picard
Jean Picard
Jean-Felix Picard was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand. He was the first person to measure the size of the Earth to a reasonable degree of accuracy in a survey conducted in 1669–70, for which he is honored with a...
to the site of Tycho Brahe
Tycho Brahe
Tycho Brahe , born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...
's old observatory at Uraniborg
Uraniborg
Uranienborg was a Danish astronomical observatory operated by Tycho Brahe; built circa 1576-1580 on Hven, an island in the Øresund between Zealand and Scania, which at that time was part of Denmark. The observatory was shortly after its construction expanded with an underground facility,...
, on the island of Hven near Copenhagen
Copenhagen
Copenhagen is the capital and largest city of Denmark, with an urban population of 1,199,224 and a metropolitan population of 1,930,260 . With the completion of the transnational Øresund Bridge in 2000, Copenhagen has become the centre of the increasingly integrating Øresund Region...
. 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 emergence 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 emergence. The time difference of 42 minutes and 10 seconds between Paris and Uraniborg comes from the same manuscript: the modern value 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
University of Copenhagen
The University of Copenhagen is the oldest and largest university and research institution in Denmark. Founded in 1479, it has more than 37,000 students, the majority of whom are female , and more than 7,000 employees. The university has several campuses located in and around Copenhagen, with the...
– 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
IoIo (moon)
Io ) is the innermost of the four Galilean moons of the planet Jupiter and, with a diameter of , the fourth-largest moon in the Solar System. It was named after the mythological character of Io, a priestess of Hera who became one of the lovers of Zeus....
is the innermost of the four moons of Jupiter discovered by Galileo
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...
in January 1610. Rømer and Cassini refer 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 much of each orbit in the shadow of Jupiter – an eclipse
Eclipse
An eclipse is an astronomical event that occurs when an astronomical object is temporarily obscured, either by passing into the shadow of another body or by having another body pass between it and the viewer...
.
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 called an emergence.
From the Earth, it is not possible to view both the immersion and the emergence for the same eclipse of Io, because one or the other will be hidden (occulted
Occultation
An occultation is an event that occurs when one object is hidden by another object that passes between it and the observer. The word is used in astronomy . It can also refer to any situation wherein an object in the foreground blocks from view an object in the background...
) 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 after the opposition of Jupiter (from L to K in the diagram below), it is possible to view emergences of Io from its eclipses, while for about four months before the opposition (from F to G), it is possible to view immersions of Io into Jupiter's shadow. For about five or six months of the year, around the point of conjunction, it is impossible to observe the eclipses of Io at all because Jupiter is too close (in the sky) to the sun. Even during the periods before and after opposition, not all of the eclipses of Io can be observed from a given location on the Earth's surface: some eclipses will occur during the daytime for a given location, while other eclipses will occur while Jupiter is below the horizon (hidden by the Earth itself).
Observations
Most of Rømer's papers were destroyed in the Copenhagen Fire of 1728Copenhagen Fire of 1728
The Copenhagen Fire of 1728 was the largest fire in the history of Copenhagen, Denmark. It began on the evening of October 20, 1728, and continued to burn until the morning of October 23. It destroyed approximately 28% of the city , left 20% of the population homeless, and the reconstruction lasted...
, but one manuscript that survived contains a listing of about sixty observations of eclipses of Io from 1668 to 1678. 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 1671–73 form the basis for his calculations.
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 is posterior to Rømer's letter to Huygens. Rømer appears to be collecting data on eclipses of the Galilean moons
Galilean moons
The Galilean moons are the four moons of Jupiter discovered by Galileo Galilei in January 1610. They are the largest of the many moons of Jupiter and derive their names from the lovers of Zeus: Io, Europa, Ganymede and Callisto. Ganymede, Europa and Io participate in a 1:2:4 orbital resonance...
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
French Academy of Sciences
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
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: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
Joseph-Nicolas Delisle
Joseph-Nicolas Delisle was a French astronomer.-Life:He was one of the 11 sons of Claude Delisle . Like many of his brothers, among them Guillaume Delisle, he initially followed classical studies. Soon however, he moved to astronomy under the supervision of Joseph Lieutaud and Jacques Cassini...
(1688–1768) at some point before 1738. See Bobis and Lequeux (2008), which contains a facsimile of the manuscript.
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.
Most importantly, Cassini 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 22 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
Journal des sçavans
The Journal des sçavans , founded by Denis de Sallo, was the earliest academic journal published in Europe, that from the beginning also carried a proportion of material that would not now be considered scientific, such as obituaries of famous men, church history, and legal reports...
on 7 December. This anonymous report was translated into English and published in Philosophical Transactions of the Royal Society
Philosophical Transactions of the Royal Society
The Philosophical Transactions of the Royal Society is a scientific journal published by the Royal Society of London. It was established in 1665, making it the first journal in the world exclusively devoted to science, and it has remained in continuous publication ever since, making it the world's...
in London on 25 July 1677.Bobis and Lequeux (2008) tentatively attribute the translation to Edmond Halley
Edmond Halley
Edmond Halley FRS was an English astronomer, geophysicist, mathematician, meteorologist, and physicist who is best known for computing the orbit of the eponymous Halley's Comet. He was the second Astronomer Royal in Britain, following in the footsteps of John Flamsteed.-Biography and career:Halley...
(1656–1742), who would become English Astronomer Royal
Astronomer Royal
Astronomer Royal is a senior post in the Royal Household of the Sovereign of the United Kingdom. There are two officers, the senior being the Astronomer Royal dating from 22 June 1675; the second is the Astronomer Royal for Scotland dating from 1834....
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.
Order of magnitude
Rømer starts with an order of magnitudeOrder of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...
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
Quadrature (astronomy)
In astronomy, quadrature is that aspect of a heavenly body in which it makes a right angle with the direction of the Sun. It is applied especially to the apparent position of a superior planet, or of the Moon at first and last quarters....
of Jupiter, when the angle between Jupiter and the Sun (as seen from Earth) is 90º.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 also 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 further 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 at all, from which Rømer concludes that the speed of light must be very much greater than one Earth-diameter per second.
Cumulative effect
However Rømer also realised that any effect of the finite speed of light would add up over a long series of observations, and it is this cumulative effect that he announced to the Royal Academy of Sciences in Paris. The effect can be illustrated with Rømer's observations from spring 1672.Jupiter was in opposition on 2 March 1672: the first observations of emergences were on 7 March (at 07:58:25) and 14 March (at 09:52:30). Between the two observations, Io had completed four orbits of Jupiter, giving an orbital period of 42 hours 28 minutes 31¼ seconds.
The last emergence observed in the series was on 29 April (at 10:30:06). By this time, Io had completed thirty orbits around Jupiter since 7 March: the apparent orbital period is 42 hours 29 minutes 3 seconds. The difference seems minute – 32 seconds – but it meant that the emergence on 29 April was occurring a quarter-hour after it would have been predicted. The only alternative explanation was that the observations on 7 and 14 March were wrong by two minutes.
Prediction
Rømer never published the formal description of his method, possibly because of the opposition of Cassini and Picard to his ideas (see below).The Royal Academy of Sciences had instructed Rømer to publish a joint paper with his colleagues. However, the general nature of his calculation can be inferred from the news report in the Journal de sçavans and from Cassini's announcement on 22 August 1676.Cassini announced that the new tables would
contain the inequality of the days or the true motion of the Sun [i.e. the inequality due to the eccentricity of the Earth’s orbit], the eccentric motion of Jupiter [i.e. the inequality due to the eccentricity of the orbit of Jupiter] and this new, not previously detected, inequality [i.e. due to the finite speed of light].
Hence Cassini and Rømer appear to have been calculating the times of each eclipse based on the approximation of circular orbits, and then applying three successive corrections to estimate the time that the eclipse would be observed in Paris.
The three "inequalities" (or irregularities) listed by Cassini were not the only ones known, but they were the ones that could be corrected for by calculation. The orbit of Io is also slightly irregular because of orbital resonance
Orbital resonance
In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...
with Europa
Europa (moon)
Europa Slightly smaller than Earth's Moon, Europa is primarily made of silicate rock and probably has an iron core. It has a tenuous atmosphere composed primarily of oxygen. Its surface is composed of ice and is one of the smoothest in the Solar System. This surface is striated by cracks and...
and Ganymede
Ganymede (moon)
Ganymede is a satellite of Jupiter and the largest moon in the Solar System. It is the seventh moon and third Galilean satellite outward from Jupiter. Completing an orbit in roughly seven days, Ganymede participates in a 1:2:4 orbital resonance with the moons Europa and Io, respectively...
, two of the other Galilean moons
Galilean moons
The Galilean moons are the four moons of Jupiter discovered by Galileo Galilei in January 1610. They are the largest of the many moons of Jupiter and derive their names from the lovers of Zeus: Io, Europa, Ganymede and Callisto. Ganymede, Europa and Io participate in a 1:2:4 orbital resonance...
of Jupiter, but this would not be fully explained for another century. The only solution available to Cassini and to other astronomers of his time was to issue periodic corrections to the tables of eclipses of Io to take account of its irregular orbital motion: periodically resetting the clock, as it were. The obvious time to reset the clock was just after the opposition of Jupiter to the Sun, when Jupiter is at its closest to Earth and so most easily observable.
The opposition of Jupiter to the Sun occurred on or around 8 July 1676. Rømer's aide-mémoire lists two observation of emergences of Io after this opposition but before Cassini's announcement: on 7 August at 09:44:50 and on 14 August at 11:45:55. With these data, and knowing the orbital period of Io, Cassini could calculate the times of each of the eclipses over the next four to five months.
The next step in applying Rømer's correction would be to calculate the position of Earth and Jupiter in their orbits for each of the eclipses. This sort of coordinate transformation was commonplace in preparing tables of positions of the planets for both astronomy and astrology
Astrology
Astrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...
: it is equivalent to finding each of the positions L (or K) for the various eclipses which might be observable.
Finally, the distance between Earth and Jupiter can be calculated using standard trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
, in particular the law of cosines
Law of cosines
In trigonometry, the law of cosines relates the lengths of the sides of a plane triangle to the cosine of one of its angles. Using notation as in Fig...
, knowing two sides (distance between the Sun and Earth; distance between the Sun and Jupiter) and one angle (the angle between Jupiter and Earth as formed at the Sun) of a triangle. The distance from the Sun to Earth was not well known at the time, but taking it as a fixed value a, the distance from the Sun to Jupiter can be calculated as some multiple of a from Kepler's third law
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....
.
This model left just one adjustable parameter – the time taken for light to travel a distance equal to a, the radius of Earth's orbit. Rømer had about thirty observations of eclipses of Io from 1671–73 that he used to find the value which fitted best: eleven minutes. With that value, he could calculate the extra time it would take light to reach Earth from Jupiter in November 1676 compared to August 1676: about ten minutes.
Initial reactions
Rømer's explanation of the difference between predicted and observed timings of Io's eclipses was widely, but far from universally, accepted. Huygens was an early supporter, especially as it supported his ideas about refractionRefraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
, and wrote to the French Controller-General of Finances
Controller-General of Finances
The Controller-General of Finances was the name of the minister in charge of finances in France from 1661 to 1791. The position replaced the former position of Superintendent of Finances , which was abolished with the downfall of Nicolas Fouquet.- History :The term "contrôleur général" in...
Jean-Baptiste Colbert
Jean-Baptiste Colbert
Jean-Baptiste Colbert was a French politician who served as the Minister of Finances of France from 1665 to 1683 under the rule of King Louis XIV. His relentless hard work and thrift made him an esteemed minister. He achieved a reputation for his work of improving the state of French manufacturing...
in Rømer's defence. However Cassini
Giovanni Domenico Cassini
This article is about the Italian-born astronomer. For his French-born great-grandson, see Jean-Dominique Cassini.Giovanni Domenico Cassini was an Italian/French mathematician, astronomer, engineer, and astrologer...
, Rømer's superior at the Royal Observatory, was an early and tenacious opponent of Rømer's ideas, and it seems that Picard
Jean Picard
Jean-Felix Picard was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand. He was the first person to measure the size of the Earth to a reasonable degree of accuracy in a survey conducted in 1669–70, for which he is honored with a...
, Rømer's mentor, shared many of Cassini's doubts.
Cassini's practical objections took up many debates at the Royal Academy of Sciences (with Huygens participating by letter from London). Cassini noted that the other three Galilean moons
Galilean moons
The Galilean moons are the four moons of Jupiter discovered by Galileo Galilei in January 1610. They are the largest of the many moons of Jupiter and derive their names from the lovers of Zeus: Io, Europa, Ganymede and Callisto. Ganymede, Europa and Io participate in a 1:2:4 orbital resonance...
did not seem to show the same effect as seen for Io, and that there were other irregularities which could not be explained by Rømer's theory. Rømer replied that it was much more difficult to accurately observe the eclipses of the other moons, and that the unexplained effects were much smaller (for Io) than the effect of the speed of light: however, he admitted to Huygens that the unexplained "irregularities" in the other satellites were larger than the effect of the speed of light. The dispute had something of a philosophical note: Rømer claimed that he had discovered a simple solution to an important practical problem, while Cassini rejected the theory as flawed as it could not explain all the observations.This last point is put quite clearly as late as 1707 by Cassini's nephew, Giacomo Filippo Maraldi
Giacomo F. Maraldi
Giacomo Filippo Maraldi was an French-Italian astronomer and mathematician. His name is also given as Jacques Philippe Maraldi....
(1665–1729), who also worked at the Royal Observatory: "In order for an hypothesis to be accepted, it is not enough that it agrees with some observations, it must also be consistent with the other phenomena." Quoted in Bobis and Lequeux (2008). Cassini was forced to include "empirical corrections" in his 1693 tables of eclipses, but never accepted the theoretical basis: indeed, he chose different correction values for the different moons of Jupiter, in direct contradiction with Rømer's theory.
Rømer's ideas received a much warmer reception in England. Although Robert Hooke
Robert Hooke
Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...
(1635–1703) dismissed the supposed speed of light as so large as to be virtually instantaneous, the Astronomer Royal
Astronomer Royal
Astronomer Royal is a senior post in the Royal Household of the Sovereign of the United Kingdom. There are two officers, the senior being the Astronomer Royal dating from 22 June 1675; the second is the Astronomer Royal for Scotland dating from 1834....
John Flamsteed
John Flamsteed
Sir John Flamsteed FRS was an English astronomer and the first Astronomer Royal. He catalogued over 3000 stars.- Life :Flamsteed was born in Denby, Derbyshire, England, the only son of Stephen Flamsteed...
(1646–1719) accepted Rømer's hypothesis in his ephemerides
Ephemeris
An ephemeris is a table of values that gives the positions of astronomical objects in the sky at a given time or times. Different kinds of ephemerides are used for astronomy and astrology...
of eclipses of Io. Edmond Halley
Edmond Halley
Edmond Halley FRS was an English astronomer, geophysicist, mathematician, meteorologist, and physicist who is best known for computing the orbit of the eponymous Halley's Comet. He was the second Astronomer Royal in Britain, following in the footsteps of John Flamsteed.-Biography and career:Halley...
(1656–1742), a future Astronomer Royal, was also an early and enthusiastic supporter. Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
(1643–1727) also appears to have accepted Rømer's ideas, and gives a value of "seven or eight minutes" for light to travel from the Sun to Earth in his 1704 book Opticks
Opticks
Opticks is a book written by English physicist Isaac Newton that was released to the public in 1704. It is about optics and the refraction of light, and is considered one of the great works of science in history...
. Newton also notes that Rømer's observations had been confirmed by others, presumably by Flamsteed and Halley in Greenwich
Royal Observatory, Greenwich
The Royal Observatory, Greenwich , in London, England played a major role in the history of astronomy and navigation, and is best known as the location of the prime meridian...
at the very least: the value of 7–8 minutes is closer to the true value (8 minutes 19 seconds) than Rømer's initial estimate of 11 minutes.
While it was obviously difficult for many (such as Hooke) to conceive of the enormous speed of light, Rømer's idea suffered a second handicap in that they were based on Kepler's
Johannes Kepler
Johannes Kepler was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican...
model of the planets orbiting the Sun in elliptical
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...
orbits. While Kepler's model had widespread acceptance by the late seventeenth century, it was still considered sufficiently controversial for Newton to spend several pages discussing the observational evidence in favour in his Philosophiæ Naturalis Principia Mathematica (1687).
Rømer's view that the velocity of light was finite was not fully accepted until measurements of stellar aberration
Aberration of light
The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations...
were made in 1727 by James Bradley
James Bradley
James Bradley FRS was an English astronomer and served as Astronomer Royal from 1742, succeeding Edmund Halley. He is best known for two fundamental discoveries in astronomy, the aberration of light , and the nutation of the Earth's axis...
(1693–1762). Bradley, who would be Halley's successor as Astronomer Royal, calculated a value of 8 minutes 13 seconds for light to travel from the Sun to Earth. Ironically, stellar aberration had first been observed by Cassini and (independently) by Picard in 1671, but neither astronomer was able to give an explanation for the phenomenon. Bradley's work also laid to rest any remaining serious objections to the Keplerian model of the Solar System.
Later measurements
Swedish astronomer Pehr Wilhelm WargentinPehr Wilhelm Wargentin
Pehr Wilhelm Wargentin , Swedish astronomer and demographer....
(1717–83) used Rømer's method in the preparation of his ephemerides of Jupiter's moons (1746), as did Giovanni Domenico Maraldi
Giovanni Domenico Maraldi
Giovanni Domenico Maraldi was an Italian-born astronomer, nephew of Giacomo F. Maraldi.Born at Perinaldo, Liguria, Maraldi came to Paris in 1727 and became a member of the French Academy of Sciences in 1731...
working in Paris. The remaining irregularities in the orbits of the Galilean moons
Galilean moons
The Galilean moons are the four moons of Jupiter discovered by Galileo Galilei in January 1610. They are the largest of the many moons of Jupiter and derive their names from the lovers of Zeus: Io, Europa, Ganymede and Callisto. Ganymede, Europa and Io participate in a 1:2:4 orbital resonance...
would not be satisfactorily explained until the work of Joseph Louis Lagrange
Joseph Louis Lagrange
Joseph-Louis Lagrange , born Giuseppe Lodovico Lagrangia, was a mathematician and astronomer, who was born in Turin, Piedmont, lived part of his life in Prussia and part in France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics...
(1736–1813) and Pierre-Simon Laplace
Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He summarized and extended the work of his predecessors in his five volume Mécanique Céleste...
(1749–1827) on orbital resonance
Orbital resonance
In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...
.
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 (1749–1822) reported the time for light to travel from the Sun to the Earth as 8 minutes 12 seconds. Depending on the value assumed for the astronomical unit
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....
, this yields the speed of light as just a little more than 300,000 kilometres per second.
The first measurements of the speed of light using completely terrestrial apparatus were published in 1849 by Hippolyte Fizeau
Hippolyte Fizeau
Armand Hippolyte Louis Fizeau was a French physicist.-Biography:Fizeau was born in Paris. His earliest work was concerned with improvements in photographic processes. Following suggestions by François Arago, Léon Foucault and Fizeau collaborated in a series of investigations on the interference of...
(1819–96). Compared to modern values, Fizeau's result (about 313,000 kilometres per second) was too high, and less accurate than those obtained by Rømer's method. It would be another thirty years before A. A. Michelson
Albert Abraham Michelson
Albert Abraham Michelson was an American physicist known for his work on the measurement of the speed of light and especially for the Michelson-Morley experiment. In 1907 he received the Nobel Prize in Physics...
in the United States published his more precise results (299,910±50 km/s) and Simon Newcomb
Simon Newcomb
Simon Newcomb was a Canadian-American astronomer and mathematician. Though he had little conventional schooling, he made important contributions to timekeeping as well as writing on economics and statistics and authoring a science fiction novel.-Early life:Simon Newcomb was born in the town of...
confirmed the agreement with astronomical measurements, almost exactly two centuries after Rømer's announcement.
Did Rømer measure the speed of light?
Several modern discussions have suggested that Rømer should not be credited with the measurement of the speed of light, as he never gave a value in Earth-based units. These authors credit Huygens with the first calculation of the speed of light.Huygens' estimate was a value of 110,000,000 toise
Toise
A toise is a unit of measure for length, area and volume originating in pre-revolutionary France. In North America, it was used in colonial French establishments in early New France, French Louisiana , and Quebec...
s per second: as the toise was later determined to be just under two metres,The exact ratio is 1 toise = metres, or approximately 1.949 m: French law of 19 frimaire An VIII
French Republican Calendar
The French Republican Calendar or French Revolutionary Calendar was a calendar created and implemented during the French Revolution, and used by the French government for about 12 years from late 1793 to 1805, and for 18 days by the Paris Commune in 1871...
(10 December 1799). Huygens was using Picard's
Jean Picard
Jean-Felix Picard was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand. He was the first person to measure the size of the Earth to a reasonable degree of accuracy in a survey conducted in 1669–70, for which he is honored with a...
value (1669) of the circumference of the Earth as 360×25×2282 toises, while the 1799 legal conversion uses the more precise results of Delambre and Méchain
Pierre Méchain
Pierre François André Méchain was a French astronomer and surveyor who, with Charles Messier, was a major contributor to the early study of deep sky objects and comets.-Life:...
. this gives the value in modern units.
However, Huygens' estimate was not a precise calculation but rather an illustration at an order of magnitude
Order of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...
level. The relevant passage from Treatise sur la lumière reads:
If one considers the vast size of the diameter KL, which according to me is some 24 thousand diameters of the Earth, one will acknowledge the extreme velocity of Light. For, supposing that KL is no more than 22 thousand of these diameters, it appears that being traversed in 22 minutes this makes the speed a thousand diameters in one minute, that is 16-2/3 diameters in one second or in one beat of the pulse, which makes more than 11 hundred times a hundred thousand toises;
Huygens was obviously not concerned about the 9% difference between his preferred value for the distance from the Sun to Earth and the one he uses in his calculation. Nor was there any doubt in Huygens' mind as to Rømer's achievement, as he wrote to Colbert
Jean-Baptiste Colbert
Jean-Baptiste Colbert was a French politician who served as the Minister of Finances of France from 1665 to 1683 under the rule of King Louis XIV. His relentless hard work and thrift made him an esteemed minister. He achieved a reputation for his work of improving the state of French manufacturing...
(emphasis added):
I have seen recently, with much pleasure, the beautiful discovery of Mr. Romer, to demonstrate that light takes time in propagating, and even to measure this time;
Neither Newton nor Bradley bothered to calculate the speed of light in Earth-based units. The next recorded calculation was probably made by Fontenelle
Bernard le Bovier de Fontenelle
Bernard Le Bovier de Fontenelle , also called Bernard Le Bouyer de Fontenelle, was a French author.Fontenelle was born in Rouen, France and died in Paris just one month before his 100th birthday. His mother was the sister of great French dramatists Pierre and Thomas Corneille...
: claiming to work from Rømer's results, the historical account of Rømer's work written some time after 1707 gives a value of 48203 leagues
League (unit)
A league is a unit of length . It was long common in Europe and Latin America, but it is no longer an official unit in any nation. The league originally referred to the distance a person or a horse could walk in an hour...
per second. This is 16.826 Earth-diameters per second.
Doppler method
It has also been suggested that Rømer was measuring a Doppler effectDoppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...
, and this 166 years before Christian Doppler's
Christian Doppler
Christian Andreas Doppler was an Austrian mathematician and physicist.-Life and work:Christian Doppler was raised in Salzburg, Austria, the son of a stonemason. Doppler could not work in his father's business because of his generally weak physical condition...
1842 discovery. The Doppler effect is the change in observed frequency of an oscillator (in this case, Io orbiting around Jupiter) when the observer (in this case, on Earth's surface) is moving: the frequency is higher when the observer is moving towards the oscillator and lower when the observer is moving away from the oscillator. This apparently anachronistic analysis implies that Rømer was measuring the ratio , where c is the speed of light and v is the Earth's orbital velocity (strictly, the component of the Earth's orbital velocity parallel to the Earth–Jupiter vector), and indicates that the major inaccuracy of Rømer's calculations was his poor knowledge of the orbit of Jupiter.
There is no evidence that Rømer thought that he was measuring : he gives his result as the time of 22 minutes for light to travel a distance equal to the diameter of Earth's orbit or, equivalently, 11 minutes for light to travel from the Sun to Earth. It can be readily shown that the two measurements are equivalent: if we give τ as the time taken for light to cross the radius of an orbit (e.g. from the Sun to Earth) and P as the orbital period (the time for one complete rotation), thenThe expression is given for the approximation to a circular orbit. The derivation is as follows:
(1) express the orbital velocity in terms of the orbital radius r and the orbital period P: v =
(2) substitute τ = → v =
(3) rearrange to find .
Bradley
James Bradley
James Bradley FRS was an English astronomer and served as Astronomer Royal from 1742, succeeding Edmund Halley. He is best known for two fundamental discoveries in astronomy, the aberration of light , and the nutation of the Earth's axis...
, who was measuring in his studies of aberration in 1729, was well aware of this relation as he converts his results for into a value for τ without any comment.
External links
- Visualize Solar System at a given Epoch
- The history of a velocity
- Rømer and the Doppler principle
- Proceeding of a Rømer Experiment for Schools from EAAE Summer SchoolSummer schoolSummer school is a school, or a program generally sponsored by a school or a school district, that teaches students during the summer vacation....
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