roemer's experiment failed because of his ignorance about the

The Cassini controversy

Initially, Rømer’s hypothesis about the velocity of light was met with resistance among the French scientific elite. The opposition was led by Cassini, who refused to accept that light had a finite speed, despite having flirted with the idea earlier in his career. Instead, he attributed the irregularities in the eclipse timings, which he had noticed while compiling his tables, to irregular motions of the planets or other causes that were yet to be revealed.

In an interesting twist, some modern researchers, including Laurence Bobis and James Lequeux of the Paris Observatory, have asserted that it was actually Cassini, and not Rømer, who first proposed the “successive motion” of light. At the very least, these scholars contend, the hypothesis was a joint effort.

According to Suzanne Débarbat, a historian of science at the Paris Observatory, Cassini briefly believed in the finite velocity of light, but he changed his mind when no one could detect such a delay in the eclipses of the other three Galilean moons of Jupiter. He could not admit that a hypothesis that was valid for one of the four moons did not work for the other three. (Remember, nothing was known about the nature of the jovian system at that time or the gravitational attraction among the bodies.)

The Royal Academy’s meeting records are missing the minutes from mid-July to mid-November 1676. However, the institution’s first secretary, Jean-Baptiste Du Hamel (1624-1706), wrote in 1698 that Cassini had warned the Academy in August 1676 that the tables of the jovian satellites’ motions were inaccurate and that the eclipse of November 16 would be delayed by about 10 minutes.

Could the 75-year-old Du Hamel have been mixed up, especially given the 22-year lag between the warning and the account of it? In a never-published history of the Paris Observatory, Joseph Nicolas Delisle (1688-1768) and his collaborators used some of the now-missing minutes to credit Cassini with the warning of the delayed eclipse—and the attribution of the delay in time it took for light to travel to Earth

The existing minutes for 1676 note for November 21 that “Rømer read to the Company an account where he shows that the motion of light is not instantaneous…. He will confer with Messieurs Cassini and Picard in order to insert this report in the first Journal.” The minutes also state that Academy members discussed the findings on November 28 and allowed Cassini to present his views on the subject on December 5.

In an obscure 1862 text, Urbain Le Verrier, a Paris mathematician, wrote: “This is Roemer’s discovery. Its extreme simplicity does not decrease its value. The contemporaries have first dismissed it; later, they attempted to divert a part of the merit to Cassini. It seems that in this respect the scientific habits are the same today as they were in that time.”

Gaining acceptance

Hooke, that early champion of the wave nature of light, maintained that Rømer’s estimation was not conclusive. In his 1680 “Lectures on Light,” the English physicist called the Dane’s idea of light speed “so exceeding swift that ’tis beyond Imagination” and added, “and if so, why it may not be as well instantaneous I know no reason.”

Except for Hooke, English scientists proved receptive to Rømer’s work, especially after Rømer visited England in 1679. Rømer explained his findings to John Flamsteed, the first Astronomer Royal, who accepted them and started correcting his tables of the eclipses of Jupiter’s satellites.

Huygens, another wave theorist, and Isaac Newton (1642-1727), a proponent of his corpuscular theory of light, both embraced Rømer’s finding. In the early pages of his classic 1704 treatise Opticks , Newton seemed to present both sides of the light-velocity issue:

Mathematicians usually consider the Rays of Light to be Lines reaching from the luminous Body to the Body illuminated, and the refraction of those Rays to be the bending or breaking of those lines in their passing out of one Medium into another. And thus may Rays and Refractions be considered, if Light be propagated in an instant. But by an Argument taken from the Equations of the times of the Eclipses of Jupiter’s Satellites , it seems that Light is propagated in time, spending in its passage from the Sun to us about seven Minutes of time: And therefore I have chosen to define Rays and Refractions in such general terms as may agree to Light in both cases.

As Cohen noted dryly, “It will be remembered with what dread Newton viewed controversies.” However, late in the second volume of Opticks , the English physicist credited Rømer with the proposition that “Light is propagated from luminous Bodies in time, and spends about seven or eight Minutes of an Hour in passing from the Sun to the Earth.”

It was another English astronomer, James Bradley (1693-1762), who drove the nail into the coffin of the instantaneous-light theory a half-century after Rømer’s work. While searching—fruitlessly—to measure stellar parallax, Bradley ended up discovering the aberration of light from the stars.

Just as raindrops appear to fall straight down when one is standing still but at a slight angle when one is walking forward, the apparent position of the stars is dependent on the velocity of the observer, Bradley reasoned. When the effect happens to light, it is only about 1/200 of a degree of arc—a very small angle—but one that Bradley was able to measure with the instruments available to him in 1728.

In conducting his research, Bradley came up with a new value for the speed of light: 298,000 km/s in modern units. Amazingly, he was within 1percent of the currently accepted value of 299,742.458 km/s in a vacuum! Certain details of the matter were still not settled—notably, the presence or absence of a “lumiferous ether.” However, from 1728 onward, the question of light’s velocity became about just how accurately we could measure the speed of light, not whether light traveled at all.

Rømer’s legacy

By 1728, Rømer had been dead for 18 years; he passed away a few days before his 66 th birthday in 1710. He made his final observation of Io in January 1678, returned to his homeland in 1681 and busied himself with other scientific and civic activities thereafter.

Physicists continued to make ever-more precise measurements of the speed of light. In 1809, French astronomer Jean Baptiste Joseph Delambre used a century’s worth of increasingly precise observations of Io’s eclipses to revisit the topic. He calculated that light travels from the sun to the Earth in 8 minutes and 12 seconds. Depending on the value of the astronomical unit, Delambre’s work placed the speed of light at just over 300,000 km/s.

In the middle of the 19 th century, Hippolyte Fizeau and Leon Foucault devised earthbound instruments to measure light’s velocity, and James Clerk Maxwell combined the astronomical and earthbound speed calculations to bolster his argument that light was an electromagnetic wave. Cavity resonator wavemeters took light-speed accuracy to new heights in the 20 th century, culminating with the definition of c as exactly 299,792.458 km/s in a vacuum.

As the biographer Cohen wrote: “That Rømer’s figure [for the transit time of light between the sun and Earth] was too large, a little less than a third larger than the most recent value, is of little or no discredit. At a time when the general belief was that the velocity of light was instantaneous, he offered a means of contradicting that belief that convinced the major portion of the scientists of his time. If his figure was a little large, it was, in any case, of the right order of magnitude.”

With the question of whether light travels at a finite speed settled, the great minds of the 18th and 19th centuries moved onward to investigate diffraction, interference, polarization and other phenomena that laid the foundation for the study of optics as we know it today.

Patricia Daukantas is the senior writer/editor of Optics & Photonics News .

References and Resources

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Publish Date: 01 July 2009

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Ole Rømer and the Speed of Light

Ole Rømer (1644-1710)

On October 5 , 1644 (or according to the old julian calendar September 25 ),  Danish astronomer Ole Christensen Rømer was born. He became known by the first proof published in 1676 that the speed of light is finite and not infinite, respectively by the guidance, how the speed of light can be calculated by observation of the Jupiter moons.

Ole Rømer – Early Years

Ole  Rømer was born in Århus, Denmark, to merchant and skipper Christen Pedersen (died 1663), and Anna Olufsdatter Storm (c. 1610 – 1690), daughter of a well-to-do alderman. From 1662 Rømer studied astronomy with Erasmus Bartholin in Copenhagen and worked with him until 1671, including the publication of Tycho Brahe ‘s writings.[ 3 ] In 1671, the astronomer Jean Picard came to Copenhagen on behalf of the Paris Académie des Sciences to determine the geographical longitude of the old Tycho Brahe observatory on the island of Hven, Øresund.[ 8 ] With the determination of the difference of the length between Hven and Paris (longitude problem) the exact tables of Tycho Brahe could also be used in Paris. The orbit of the Jupiter moons had to be observed. The assistant Ole Rømer helped so skilfully with this work that he was invited to come to Paris with Picard at the end of the measurement series in April 1672. Rømer agreed and worked as a member of the Academy with Giovanni Domenico Cassini at the Paris Observatory.[ 4 ] In 1672 he developed a micrometer for telescopes and built mechanical models for planetary orbits ( Jovilabium (1677), Saturnarium (1678), Lunarium (1680)). He developed a novel epicyclic gear for this purpose. These planetariums were designed to facilitate long astronomical observations.

Royal Danish Astronomer

In 1676 Rømer was appointed royal Danish astronomer and went from Paris to the University of Copenhagen in 1681. There he became professor of mathematics. In 1681 he married the daughter of Bartholin, who died in 1694 (he married her sister in 1698). In 1683 he introduced in the Kingdom of Denmark a nationwide uniform system of measures of length and weights. Around 1700 Rømer developed an accurate measuring instrument for star positions, the meridian circle . With it he wanted to provide conclusive proof for the model of the solar system by Nicolaus Copernicus by measuring star parallaxes of Sirius. The proof succeeded only in 1838 by Friedrich Wilhelm Bessel .[ 7 ] On 1 March 1700 Denmark introduced the Gregorian calendar at Rømer’s suggestion.[ 6 ] In 1702 he built the first thermometer with two fixed points (Rømer scale), which Fahrenheit further developed after a visit to him (1708). About 1705 Rømer derived a measuring error formula for his meridian instrument in his Adversaria . Today this measuring error formula is attributed to Tobias Mayer, who found it 51 years later, i.e. 1756, without knowing Rømer’s derivation. Through his precise observation, Rømer succeeded in proving that the star Castor in the constellation of twins is a double star system. Finally he took part in the observation action of Mercury’s transit in front of the Sun on 5 May 1707 and evaluated it.

Ole Rømer at work

After Rømer had held various political offices since 1688, he became mayor of Copenhagen in 1705, head of the police and senator. In these functions he introduced far-reaching improvements, including the first street lighting (using oil lamps), renovation of water supply and sewerage. He held these posts until his death on September 19, 1710. He was buried in Copenhagen Cathedral.

Measuring the Speed of Light

The question of whether the speed at which light propagates is finite or infinite has been the subject of controversial debate for centuries. Supporters of Aristotle , among them René Descartes , pleaded for infinite speed of light. In 1668 Cassini had published his first tables in Bologna, which gave a timetable for the eclipses of the four Jupiter moons. The times given there helped with the longitude problem. Already from 1668 he had noticed deviations between timetable and observation. From 1672 Rømer continued his observations in Paris. Not only systematic deviations were confirmed, but the assumption that the eclipses – in comparison to the prediction – occurred earlier when the Earth approaches Jupiter (B) on its annual orbit around the Sun (A) on the circular arc from E via F and G to the opposition position H (see drawing by Rømer below), and later than predicted by the timetable, when the Earth departs from Jupiter from H via L and K to the conjunction position E, was confirmed.

A diagram of Jupiter (B) eclipsing its moon Io (DC) as viewed from different points in earth’s orbit around the sun. From Olaf (Ole) Roemer, “Demonstration tovchant le mouvement de la lumiere trouvé par M. Römer de l’ Academie Royale des Sciences,” December 7, 1676.

The reason for this is that the path of light between Jupiter and Earth changes, and thus – if the speed of light is a finite quantity – also the transit time of light. On 23 August 1676 Rømer dared to predict that the eclipse of the moon Io (DC) on 9 November 1676 would be visible “too late” by ten minutes. When this delay actually occurred, he presented his statement to the Royal Academy of Sciences in Paris on 21 November 1676 and published it on 7 December 1676 in the Journal des sçavans under the title Démonstration touchant le mouvement de la lumière trouvé par M. Roemer de l’Académie des sciences .

How Fast Is It?

References and Further Reading:

• [1] Ole Rømer, the speed of light, the apparent period of Io, the Doppler effect,and the dynamics of Earth and Jupiter
• [2] Ole Rømer at Britannica Online
• [3] Tycho Brahe – The Man with the Golden Nose , SciHi Blog
• [4] Giovanni Cassini and Saturn Moon Rhea
• [5] Christiaan Huygens and the Discovery of Saturn Moon Titan
• [6] The Days That Never Happened – The Gregorian Calendar , SciHi Blog
• [7]  Friedrich Bessel and the Distances of Stars , SciHi Blog
• [8]  Jean Picard and his Love for Accuracy , SciHi Blog
• [8] Ole Rømer at Wikidata
• [9]  How the Speed of Light Was First Measured ,  Educational Video Library  @ youtube
• [10]  Bobis, Laurence; Lequeux, James (2008).  “Cassini, Rømer and the velocity of light” .  J. Astron. Hist. Herit .  11  (2): 97–105. 
• [11]  MacKay, R. Jock; Oldford, R. Wayne (2000).  “Scientific Method, Statistical Method and the Speed of Light” .  Statistical Science .  15  (3): 254–278.
• [12] Timeline of 17th Century Danish Scientists via DBpedia and Wikidata

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Rømer's measurement of the speed of light.

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Ole Rømer, a Danish astronomer, calculated the speed of light by observing the eclipses of Jupiter's moon during the years 1668–1674. A discrepancy was observed for the time between the eclipses, increasing when the Earth was moving away from Jupiter and decreasing when the Earth was approaching. In half a year, there are a total of 102 eclipses of Io, giving a maximum delay of 16.5 minutes (shown in the bottom-right plot). Rømer interpreted this as the difference in the times needed for the light to travel between Jupiter and Earth. He obtained a value of 214,000 km/s compared to the current value 299,792 km/s. The diameter of the Earth's orbit was not accurately known and there was also an error in the measurement of the delay. Nevertheless, it was a first confirmation that the speed of light is finite.

Contributed by: Enrique Zeleny   (April 2010) Open content licensed under CC BY-NC-SA

The time delay of an eclipse of Io is given by

[1] J. H. Shea, "Ole R\:01ffmer, the Speed of Light, the Apparent Period of Io, the Doppler Effect, and the Dynamics of Earth and Jupiter," Am. J. Phys. , 66 (7), 1988 pp. 561–569.

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• Speed of Light  ( Wolfram ScienceWorld )
• Eclipse  ( Wolfram ScienceWorld )
• Roemer, Olaf (1644–1710)  ( Wolfram ScienceWorld )

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Enrique Zeleny "Rømer's Measurement of the Speed of Light" http://demonstrations.wolfram.com/RomersMeasurementOfTheSpeedOfLight/ Wolfram Demonstrations Project Published: April 15 2010

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Ole Christensen Rømer [1] (September 25, 1644, Århus – September 19, 1710, Copenhagen ) was a Danish astronomer who demonstrated that light had a finite speed by measuring apparent changes in the periods of the revolution of Jupiter 's moon, Io. Rømer also developed a temperature scale showing the temperature between two fixed points, namely the points at which water respectively boils and freezes. This was later adjusted by Daniel Gabriel Fahrenheit to the Fahrenheit scale in use today.

• 1.1 Professional life
• 1.2 The speed of light
• 1.3 Return to Denmark
• 1.4 Public appointments
• 1.5 Temperature measurement
• 1.6 Later years
• 2.1 The problem of measuring longitude
• 2.2 Rømer's observations
• 2.3 Effect calculated, but not light's speed
• 2.4 Acceptance of Rømer's findings
• 3 Inventions
• 4 The Ole Rømer Museum
• 6 References
• 7 External links

General biography

Rømer was born on September 25, 1644, in Århus, Denmark, to a merchant and skipper, Christen Pedersen, and his wife, Anna Olufsdatter Storm, daughter of an alderman. Christen Pedersen had taken to using the name Rømer, which means that he was from Rømø, to disambiguate himself from some other people named Christen Pedersen. [2] There are few sources on Ole Rømer until his matriculation in 1662 at the University of Copenhagen, where his mentors were Thomas and Rasmus Bartholin, the later having published his discovery of the double refraction of a light ray by Iceland spar ( calcite ) in 1668 while Rømer was living in his home.

Professional life

Rasmus Bartholin had been given the task of preparing Tycho Brahe 's observations for publication, and enlisted Rømer's help from 1664 to 1670. [3] Rømer joined the observatory of Uraniborg on the island of Hven, near Copenhagen , in 1671.

The speed of light

In 1671, the French astronomer Jean Picard was dispatched to Denmark to examine Brahe's observations and compare them with those of Giovanni Domenico Cassini in Paris. Rømer assisted him in this task, and then accompanied him the following year to Paris, where Rømer entered the employ of the French government. Louis XIV made him teacher for the Dauphin, and he also took part in the construction of the magnificent fountains at Versailles . Rømer became the first foreign member of the French Academy of Sciences in 1672. It was during this period that Rømer conducted observations of the moons of Jupiter . Unexplained but regular variations in the times of their revolution, which should have been uniform, led Rømer to speculate that there was a limit to the speed of light. This premise enabled Rømer to predict changes in the orbital periods. Rømer announced his findings in 1676.

Return to Denmark

In 1677, Rømer returned to Denmark and was appointed professor of astronomy at the University of Copenhagen. In that same year he married Anne Marie Bartholin, the daughter of Rasmus Bartholin. He was active also as an observer, both at the University Observatory at Rundetårn and in his home, using improved instruments of his own construction. Unfortunately, his observations have not survived. They were lost in the great Copenhagen Fire of 1728. However, a former assistant (and later an astronomer in his own right), Peder Horrebow, loyally described and wrote about Rømer's observations in a work published in 1735 under the title Basis Astronomiae.

Public appointments

Rømer was appointed royal mathematician in 1681, and in 1683, he introduced the first national system for weights and measures in Denmark. Initially based on the Rhine foot, a more accurate national standard was adopted in 1698. Later measurements of the standards fabricated for length and volume show an excellent degree of accuracy. His goal was to achieve a definition based on astronomical constants, using a pendulum. This would happen after his death, practicalities making it too inaccurate at the time. Notable also is his definition of the new Danish mile. It was 24,000 Danish feet, which corresponds to 4 minutes of arc latitude, thus making navigation easier.

Temperature measurement

Rømer had developed a thermometer so that he could monitor the temperature and its effect on astronomical instruments. He was among the first to develop a temperature scale, dividing the temperature between freezing water and boiling water into sixty degrees. In 1708, Daniel Gabriel Fahrenheit paid Rømer a visit to see first-hand how he made his thermometers. Fahrenheit then developed his own thermometers and the Fahrenheit scale, which is used to the present day.

In 1700, Rømer managed to get the king to introduce the Gregorian calendar in Denmark-Norway — something that Tycho Brahe had argued for in vain a hundred years earlier. This calendar, originally introduced by the Catholic Church in the sixteenth century primarily for liturgical purposes, was a correction to the Julian Calendar that had been followed virtually unchanged since the time of Julius Caesar .

Rømer also established several navigation schools in many Danish cities.

Later years

In 1705, Rømer was made the second Chief of the Copenhagen Police , a position he kept until his death in 1710. As one of his first acts, he fired the entire force, being convinced that the morale was alarmingly low. He was the inventor of the first street lights (oil lamps) in Copenhagen, and worked hard to try to control the beggars, poor people, unemployed, and prostitutes of Copenhagen.

In Copenhagen, Rømer made rules for building new houses, got the city's water supply and sewers back in order, ensured that the city's fire department got new and better equipment, and was the moving force behind the planning and making of new pavement in the streets and on the city squares.

Rømer died on September 19, 1710 in Copenhagen.

Rømer and the speed of light

The problem of measuring longitude.

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 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.

The reason why synchronized time is important in measuring longitude is that two observers, if they know they are making measurements at the same time, can measure the position of the stars with respect to the horizon, the difference in the angle between the two measurements of the same star with respect to a plane passing through the poles of the earth equaling the difference in the longitude of their positions on the earth's surface. Some additional data such as the diameter of the earth would yield the distance between the two positions as well. Conversely, if the distance between the two positions could be accurately supplied, the earth's diameter could be calculated from the data.

Rømer's observations

After his studies in Copenhagen, Rømer joined the observatory of Uraniborg on the island of Hven, near Copenhagen, in 1671. Over a period of several months, Jean Picard and Rømer observed about 140 eclipses of Jupiter 's moon Io, while in Paris Giovanni Domenico Cassini observed the same eclipses. By comparing the times of the eclipses, the difference in the longitudes of Paris and Uranienborg was calculated.

Rømer noticed upon examination of the data that he collected along with the observations of Cassini that the times at which the satellite Io emerges from the shadow of Jupiter in each of its revolutions about the planet are continually lengthened as the earth recedes from Jupiter, while in a similar but reverse manner, the times between emergences are shortened as the earth approaches Jupiter. More specifically, Rømer reported to the French Academy of Sciences in September of 1676 that between early September and the 16th of November of that year, a delay of about 10 minutes should accrue. His prediction was verified, and reported in a memoir published in December in the Journal des Savants. Because of the periodic nature of the variations, and the reversal of the phenomenon when the earth approached Jupiter, Rømer put forward the hypothesis that light had a finite velocity, and that variations in the time light took to reach the earth over changing distances between the earth and Jupiter accounted for the changes in the observed times of the revolution of Io.

Effect calculated, but not light's speed

Rømer did not actually calculate the speed of light from his observations. At the time, the distance between the sun and the earth was still only a roughly calculated quantity, while the earth's elliptical path around the sun meant that the distances between the earth and Jupiter did not accrue uniformly, but varied in a complex manner according to the time of year and the position of the earth in its orbit. It would be left to later investigators to pin down an actual speed of light based on these phenomena. Rømer appears to have been more interested in correcting tables of the revolution of Jupiter's moons for the sake of measuring longitude than he was in fixing the speed of light. His important contribution was that he recognized the true nature of the phenomenon, and quantified and predicted the observed effect on the observations of Jupiter's moons.

That light had a finite speed was a finding that the scientific community resisted accepting, even though two thousand years earlier, Aristotle had contemplated the possibility of a finite speed of light in analogy to sound and even suggested a way of measuring it. Still, the predominant view was that the speed of light was infinite.

The first scientist who attempted to calculate the speed of light based on Rømer's observations was Christiaan Huygens . [4]

Acceptance of Rømer's findings

In his Mathematical Principles of Natural Philosophy (1713), Isaac Newton credits Rømer as the first to observe the velocity of light through observations of Jupiter's moons. (G. G. and J. Robinson 1798) However, Rømer's views were not fully accepted until measurements of the so-called aberration of light were made by James Bradley in 1727. Bradley's observations and analysis depend on the fact that the velocity of the earth in its orbit around the sun distorts the actual position of any luminous body in the heavens, the distortion depending on the ratio of the velocities of the earth to that of light. This causes each star to appear to transcribe a small ellipse in the sky over a period of a year. Measuring this distortion yields a value for the speed of light. Bradley's measurements were in harmony with Rømer's observations, resulting in almost universal acceptance of Rømer's original conjecture.

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 kilometers per second.

A plaque at the Observatory of Paris, where Rømer was working at the time of his conjecture, commemorates what was, in effect, the first measurement of a universal quantity made on this planet.

In addition to inventing the first street lights in Copenhagen, Rømer also invented the transit instrument in 1690. This instrument is used primarily to measure the position of stars. [5]

The Ole Rømer Museum

The Ole Rømer Museum is located in the municipality of Høje-Taastrup, Denmark , at the excavated site of Rømer's observatory, Observatorium Tusculanum, at Vridsløsemagle. The observatory operated until about 1716 when the remaining instruments were moved to Rundetårn in Copenhagen. There is a large collection of ancient and more recent astronomical instruments on display at the museum. Since 2002 this exhibition is a part of the museum Kroppedal at the same location.

• ↑ In scientific literature, his name is alternatively spelt "Roemer," "Römer," or "Romer."
• ↑ Per Friedrichsen and Chr. Gorm Tortzen, Ole Rømer - Korrespondance og afhandlinger samt et udvalg af dokumenter (Copenhagen: C. A. Reitzels, 2001), 16.
• ↑ Friedrichsen and Tortzen 2001, 19–20.
• ↑ Christiaan Huygens, Treatise on Light (Pinnacle Press, 2017, 978-1374841383).
• ↑ William Somerville Orr, George Gore, Marcus Sparling, and J. Scoffern, Orr's Circle of the Sciences: A Series of Treatises on the Principles of Science with Their Application to Practical Pursuits, Practical Chemistry (London: Houlston and Stoneman, 1856), p. 391.

References ISBN links support NWE through referral fees

• Caes, Charles J. How Do We Know the Speed of Light. Great scientific questions and the scientists who answered them. New York: Rosen Pub. Group, 2001. ISBN 0823933873
• Catteau-Calleville, J.-P. Tableau des états danois envisagés sous les rapports du mécanisme social. Paris: Chez Treuttel et Würtz, 1802.
• Huygens, Christiaan. Treatise on Light . Pinnacle Press, 2017. 978-1374841383
• MacKay, R.J., and R.W. Oldford. "Scientific Method, Statistical Method and the Speed of Light." Statistical Science 15(3) (2000):254–278.
• Moran, Jeffrey B. How Do We Know the Laws of Thermodynamics. Great scientific questions and the scientists who answered them. New York: Rosen Pub. Group, 2001. ISBN 0823933849
• Orr, William Somerville, George Gore, Marcus Sparling, and J. Scoffern. Orr's Circle of the Sciences: A Series of Treatises on the Principles of Science with Their Application to Practical Pursuits . Nabu Press, 2010. ISBN 978-1148124131
• Robinson, G.G., and J. Robinson. A New and General Biographical Dictionary; containing an historical and critical account of the lives and writings of the most eminent persons in every nation; particularly the British and Irish; from the earliest accounts of time to the present period. London: Paternoster Row, 1798.
• Smithsonian Institution. Annual Report of the Board of Regents of the Smithsonian Institution. Washington: A.O.P. Nicholson, public printer, 1855.

External links

All links retrieved November 17, 2022.

• Roemer, Ole Christensen The Galileo Project .
• Kroppedal Museum .
• Ole Rømer on the 50 Danish Kroner banknote .

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How did Rømer measure the speed of light by observing Jupiter's moons, centuries ago?

I am interested in the practical method and I like to discover if it is cheap enough to be done as an experiment in a high school.

• experimental-physics
• speed-of-light
• measurements

The method is based on measuring variations in perceived revolution time of Io around Jupiter. Io is the innermost of the four Galilean moons of Jupiter and it takes around 42.5 hours to orbit Jupiter.

The revolution time can be measured by calculating the time interval between the moments Io enters or leaves Jupiter's shadow. Depending on the relative position of Earth and Jupiter, you will either be able to see Io entering the shadow but not leaving it or you will be able to see it leaving the shadow, but not entering. This is because Jupiter will obstruct the view in one of the cases.

You might expect that if you keep looking at Io for a few weeks or months you will see it enter/leave Jupiter's shadow at roughly regular intervals matching Io's revolution around Jupiter.

However, even after introducing corrections for Earth's and Jupiter's orbit eccentricity, you still notice that for a few weeks as Earth moves away from Jupiter the time between observations becomes longer (eventually by a few minutes). At other time of year, you notice that for a few weeks as Earth moves towards Jupiter the time between observations becomes shorter (again, eventually by a few minutes). This few minutes difference comes from the fact that when Earth is further away from Jupiter it takes light more time to reach you than when Earth is closer to Jupiter.

Say you have made two consecutive observations of Io entering Jupiter's shadow at t 0 and t 1 separated by n Io's revolutions about Jupiter T . If the speed of light was infinite, one would expect

\begin{equation} t_1 = t_0 + nT \end{equation}

This is however not the case and the difference

\begin{equation} \Delta t = t_1 - t_0 - nT \end{equation}

can be used to measure the speed of light since it is the extra time that light needs to travel the distance equal to the difference in the separation of Earth and Jupiter at t 1 and t 0 :

\begin{equation} c = \frac{\Delta d}{\Delta t} = \frac{d_{EJ}(t_1)-d_{EJ}(t_0)}{\Delta t} \end{equation}

(both numerator and denominator can be negative representing Earth approaching or receding from Jupiter)

In reality more than two observations are needed since T isn't known. It can be approximated by averaging observations equally distributed around Earth's orbit accounting for eccentricity or simply solved for as another variable.

Practical considerations

Note that you will not manage to see Io enter/leave Jupiter's shadow every Io's orbit (i.e. roughly every 42.5 hours) since some of your observation times will fall on a day or will be made impossible by weather conditions. This is of no concern however. You should simply number all Io's revolutions around Jupiter (timed by Io entering/leaving Jupiter's shadow) and note which ones you managed to observe. For successful observations you should record precise time. It might be good to use UTC to avoid problems with daylight saving time changes. After a few weeks you will notice cumulative effect of the speed of light in that the average intervals between Io entering/leaving Jupiter's shadow will become longer or shorter. Cumulative effect is easier to notice. At minimum you should try to make two observations relatively close to each other (separated by just a few Io revolutions) and then at least one more observation a few weeks or months later (a few dozens of Io revolutions). This will let you calculate the average time interval between observations within a short and long time period by dividing the length of the time period by the number of revolutions Io has made around Jupiter in that period. The average computed over the long time period will exhibit cumulative effect of the speed of light by being noticeably longer or shorter than the average computed over the short time period. More observations will help you make a more accurate determination of the speed of light. You must plan all of the observations ahead since you can't make the observations when Earth and Jupiter are close to conjunction or opposition.

Calculations

Once you collected the observations you should determine the position of Earth and Jupiter at the times of the observations (for example using JPL's Horizons system ). You can then use the positions to determine the distance between the planets at the time the observations were made. Finally, you can use the distance and the variation in Io's perceived revolution period to compute the speed of light.

You will notice that roughly every 18 millions kms change in the distance of Earth and Jupiter makes an observation happen 1 minute earlier or later.

The cost of the experiment is largely the cost of buying a telescope that allows you to see Io. Note that the experiment takes a few months and requires measuring time of the observations with the accuracy of seconds.

See this wikipedia article for historical account of the determination of the speed of light by Rømer using Io.

• 2 $\begingroup$ @Zalcman, so you confirm it is feasible?. I guess an 8 inches telescope is enough. $\endgroup$ –  user6090 Dec 19, 2011 at 9:45
• $\begingroup$ Yes, it is feasible. 8 inches should be enough, but if you're buying a new telescope for this, be sure to confirm it can view Io before you buy. $\endgroup$ –  Adam Zalcman Dec 19, 2011 at 9:54
• 2 $\begingroup$ You can see the Galilean satellites easily in 7x50 binoculars. I've never tried, but I strongly suspect you could do daylight observations of the moon if the weather is clear. IF you try this you probably will want a goto telescope (aligned the night before). For safety reasons make sure something is obstructing your line of sight to the sun. $\endgroup$ –  Dan Is Fiddling By Firelight Dec 19, 2011 at 13:49
• 1 $\begingroup$ If anything I'd think the lower magnifications from a smaller scope would make it easier. Unless you push the magnification up to hundred times (and have a scope and seeing capable of supporting it), the moons are effectively point sources. Unless you magnify them to the point they show a disk, at which point the shadow moving across the moon might be visible (not sure how fast it moves) you've just got a point source blinking out. $\endgroup$ –  Dan Is Fiddling By Firelight Dec 19, 2011 at 14:54
• 3 $\begingroup$ The Astronomy site may be a good source of information about what kinds of telescopes would be useful for this sort of project, and how to set them up. $\endgroup$ –  David Z Dec 19, 2011 at 17:53

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• DOI: 10.1086/347594
• Corpus ID: 145428377

Roemer and the First Determination of the Velocity of Light (1676)

• M. Romer , I. Cohen
• Published in Isis 1 April 1940

35 Citations

Römer, flamsteed, cassini and the speed of light, paris 1676: the discovery of the velocity of light and the roles of rømer and cassini, conjunctions in paris: interactions between rømer and huygens, the search for stellar parallaxes and the discovery of the aberration of light: the observational proofs of the earth's revolution, eustachio manfredi, and the ‘bologna case’, the satellites of jupiter, from galileo to bradley, on the speed of lights, christian doppler and the doppler effect, roemer, jupiter's satellites and the velocity of light, ole rømer's method still on the stage: the study of two bound eclipsing binaries in quintuple system v994 her, scientific method, statistical method and the speed of light, 14 references, the origin of fahrenheit's thermometric scale, related papers.

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Determination of the speed of light: Who is Ole Roemer and how did he make his discovery?

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The 340th anniversary of Ole Roemer's experiment to demonstrate the speed of light has been celebrated in a Google doodle . But who is the astronomer and how did he make this significant discovery?

Ole Roemer was a Danish astronomer who calculated the speed of light. He was born in Denmark in 1644, studied in Copenhagen and was mentored by Rasmus Bartholin who discovered the double refraction of a light ray, and later worked for French government and Louis XIV as the tutor of the Dauphin. He became a professor of astronomy at the University of Copenhagen and in later life had an instrumental role in policing the city as well as creating a system of measurements. But he is deservedly most famous for determinig the speed of light, which is one of the most imortant discoveries in the history of science.

How did he make his discovery?

According to the American Museum of Natural History , Roemer was not trying to determine the speed of light when he discovered it. Roemer had instead been conducting his own work at the Paris Observatory into how to better measure the orbital period of Io, one of Jupiter’s four big moons, around its planet. He studied the orbit of Io in relation to Saturn's orbit of the sun over a number of years, marking the time that the moon became eclipsed by Jupiter when observed from the Earth.

He noticed that when Earth's own orbit of the sun brought it closer to Jupiter, the time between Io's eclipses of Jupiter became shorter, instead of occuring at a predicted moment based on the time it took for the moon to orbit the planet. Equally, when the Earth moved further away from Jupiter, the time between Io's eclipses of the planet became longer. This time difference was measured at around eleven minutes.

Roemer realised there could not be a difference in the length of time it took for Io to orbit Jupiter and that the difference in time recorded between the eclipses must be due to the speed of light. He was then able to roughly calculate how long it took for light to travel across Earth's orbit, which he worked out was around 22 minutes, and determined the speed of light by dividing the diameter of the Earth's orbit by the time difference. Roemer's calculations were later refined, with modern measurements calculating the time it takes for light to cross Earth's orbit at around 17 minutes.

Science news in pictures

What else did he do?

Roemer achieved more than just determining the speed of light. He developed a temperature scale that divided the measurements between freezing water and boiling water into 60 degrees. He invented the mercury thermometer and in 1708 Daniel Gabriel Fahrenheit visited Roemer to see how he constructed his thermometers before creating his own and the Fahrenheit scale.

In Denmark, Roemer introduced the first national system of weights and measures, managed to persuade the King to introduce the Gregorian calendar and invented the first street lamps in in Copenhagen.

That’s quite an achievement – anything else?

In later life Roemer was appointed the second Chief of the Copenhagen Police and was instrumental in controlling the poor, beggars, the unemployed and prostitutes in the city, in addition to sorting out the water supply and sewers. He planned new pavements for the streets, worked to obtain new equipment for the fire department and planned new pavements. One of his first acts upon being appointed to the position was to fire the entire police force because he believed morale was alarmingly low.

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Victoria Woollaston-Webber

Google Doodle celebrates Olaus Roemer and his determination of the speed of light

Today’s Google Doodle celebrates Olaus Roemer, also known as ‪‪Ole Rømer‬‬, the Danish astronomer and scientist who was the first to successfully determine the speed of light.

Read more: How to measure the speed of light using chocolate and a microwave

Although Galileo Galilei is attributed as the first person to propose the idea that light has a specific speed , he failed to quantify it. Roemer took that honour in 1676 when he determined the speed while observing the eclipses of the moons of Jupiter .

In the animated Doodle , Roemer is shown pacing the floor and occasionally peering through a telescope. The first 'O' of the word Google shows the Sun connected to the second 'O', which represents Jupiter and its moon Io.

Roemer observed there was around a seven-minute interval between the successive eclipses when seen from Earth , which itself is affected by its own orbit in relation to Jupiter's. From this, Roemer theorised that as Earth moved away from Jupiter the interval increased, due to the extra distance the light was travelling.

Read more: The best Google Doodles celebrating tech, science and culture

He also used Galileo's initial findings that the speed of light was ten times faster than the speed of sound, as well as Galileo's discovery of Io, which led to the calculations in the first place.

By using the speed of the Earth and its orbit as a guide, the distance the Earth travelled between eclipses could be calculated, which led to the first estimate for the speed of light, to account for the intervals. This initial estimate listed the speed of light at around 140,000 miles/second.

It wasn't until 1975 that the more accurate speed (299,792,458 metres/second) was determined.

Explore all of the WIRED's favourite Google Doodles celebrating science, tech and culture

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• Books Received
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Roemer and the First Determination of the Velocity of Light

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Nature volume  157 ,  page 390 ( 1946 ) Cite this article

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AT a time when it was generally believed that light was propagated instantaneously, Roemer's observations on the first satellite of Jupiter convinced most contemporary men of science that the velocity of light was finite. Mr. Cohen surveys the earlier views on the subject, and describes the immediate background of Roemer's discovery. The reception accorded to the work is given in some detail. Roemer's paper in the Journal des Scavans (1676), and its English translation in the Philosophical Transactions (1677), are reproduced in facsimile, together with a holograph manuscript of some of his observations, from which it is shown how he must have arrived at the high value of 22 minutes for the time taken by light to traverse the diameter of the earth's orbit. The last chapter gives a brief outline of Roemer's distinguished and varied later career, both as public official and as man of science.

By I. Bernard Cohen. (History of Science Series, No. 1.) Pp. 64. (New York: Burndy Library, Inc., 1944.) 1 dollar.

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NOAKES, G. Roemer and the First Determination of the Velocity of Light. Nature 157 , 390 (1946). https://doi.org/10.1038/157390c0

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2 Ole Roemer, Who Started It All

• Published: October 2019
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The story of the first measurement of the speed of light by Ole Roemer in 1676. Galileo had discovered the moons of Jupiter with his new telescope, and proposed using observations of their eclipse every forty-two hours as a universal clock for our planet, since they could be seen from practically anywhere. This would keep track of the time at home, and so give a traveller his or her local longitude. (The King of Spain had offered a prize for longitude determination to avoid disasterous shipwrecks.) Roemer noticed that the eclipses were sometimes a little late, which he concluded was due to the time it took light to get from Saturn to Earth and the movement of the Earth between eclipses. His estimate of the time for light to travel from the Sun to Earth was quite accurate. Roemer’s remarkable life story and many other achievements are told.

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