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Rømer and the Finite Speed of Light

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Fokke Tuinstra; Rømer and the Finite Speed of Light. Physics Today 1 December 2004; 57 (12): 16–17.

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Ole Rømer’s 1676 demonstration that light propagates at a finite speed must have been a revelation to the members of the French Royal Academy of Science. A young and brilliant Danish “postdoc” at the Paris Observatory, Rømer had unexpectedly answered a long-standing fundamental question. Before his discovery, the likes of René Descartes and Johannes Kepler had claimed that light was an instantaneous phenomenon, and all attempts to prove otherwise had failed.

Isaac Newton and especially Christiaan Huygens welcomed Rømer’s result; Huygens found it encouraging in the development of his wave theory of light. There were also a few ardent opponents, such as Robert Hooke and Rømer’s observatory colleague Jean Cassini.

What value of the speed of light did Rømer actually report? I found 16 references, spanning the years 1694–2003, that give values from 200 000 to 350 000 km/s. Such a range can hardly be attributed to mistakes in the conversion of measurement units.

None of the sources I found quoted an original paper or proceedings. The present French Academy of Sciences led me to proceedings of a 1976 conference marking the tricentennial of Rømer’s discovery. 1 Those proceedings include a copy of his only publication about the speed of light. 2 The sole message of that concise and tantalizing paper is that the speed of light is finite, though incredibly large. Rømer did not mention any specific value.

The first paragraph of Rømer’s paper states the question: Is light propagation an instantaneous phenomenon or does it take time? The next paragraph gives observations of Jupiter’s innermost moon (the one we now call Io) to show that light covers a distance like Earth’s diameter, “about 3000 lieues” (one lieue = 4.448 km), in less than one second. Rømer’s reasoning was as follows: If light has a finite speed, then when Earth is approaching Jupiter, Io’s period should appear shortened. Half a year later, when Earth and Jupiter move apart, the moon’s period should appear to be longer. Io’s actual period is about 42.5 hours, during which time Earth traverses “at least 210 Earth diameters.” The two periods therefore, according to Rømer, should differ by “nearly half a quarter of an hour.” But he did not observe a difference.

However, Rømer wrote, that does not mean that light travel does not take time. Comparing the time lapse of 40 successive periods of Earth’s nearing Jupiter with 40 periods while Earth is receding, he observed a perceptible difference. Therefore, he stated, light should traverse the diameter of Earth’s orbit around the Sun in 22 minutes. This retardation of light showed up in all of the observations Rømer had done at the Paris observatory since 1668.

With a good sense of dramatic timing, Rømer played his ace in the next paragraph, where he illustrated the effect of the proposed retardation of light. In early September, he had predicted that Io’s emerging from Jupiter’s shadow on 9 November would be 10 minutes late with respect to a timetable he had made up from August observations. The prediction appeared to be correct, which convinced academy members that Rømer’s idea about a finite speed of light was correct.

The final paragraph of his paper explains that none of the reasons normally used to account for irregularities in the period of a moon or planet can explain the observed deviations in the period of Jupiter’s innermost moon.

At best, the paper provides data to establish a lower limit on the speed of light. Rømer says that Earth travels in its orbit at least 210 Earth diameters in 42.5 hours. 3 If R is the radius of Earth’s circular orbit, the planet covers a distance of 2 π R per year, which puts the lower limit for the radius at 9.2 × 10 7 km; consequently, the lower limit of the speed of light is 140 000 km/s.

Probably the first person to actually calculate the speed of light was Huygens in 1678. Rømer communicated his results to Huygens in a letter before the paper was published. In his famous Traité de la Lumière , 4 Huygens wrote that Rømer’s results had not yet been published. Huygen’s book appeared in 1690, but it had been written before 1678. In that year, he presented his theory on light at the academy.

Like Rømer, Huygens seemed barely interested in the exact value of the speed of light. He estimated Earth’s diameter to be 12 750 km and the diameter of its orbit to be 24 000 Earth diameters. According to Rømer’s observations, light traverses this distance in 22 minutes. To keep things simple, Huygens rounded the speed down to 1000 diameters per minute, or 212 400 km/s. Without the rounding, his speed of light would have been 232 000 km/s. It was Edmund Halley, in 1694, who found that Rømer’s 22 minutes should instead be 17 minutes; thus Halley gave the speed of light as approximately 300 000 km/s.

The conclusion must be that Rømer is not directly responsible for any of the values of the speed of light attributed to him. He probably was aware that the data were uncertain. But he was the first one to prove that the speed of light is finite—a scientific breakthrough that is essential to modern physics. If the speed of light were not finite, we probably would have to stick to a platinum bar in Paris for the standard meter.


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1676: Ole Rømer Measures the Speed of Light

roemer's experiment failed because of his ignorance about the

Rømer spent many years observing Jupiter’s moons — the same four moons that Galileo reported having seen in 1610. By 1676 the exact orbital periods had been worked out and timed quite precisely. Using telescopes at Uraniborg on the island of Hveen, near Copenhagen, and the Paris Observatory , Rømer noticed that the time between eclipses of a given moon were not always the same. Furthermore, he noticed a pattern to these discrepancies and suspected that the difference of about 16.7 minutes over a year’s time was due to the additional time it took light to reach Earth when it was far from Jupiter than when it was closer. Given the known diameter of Earth’s orbit at the time he made a fairly good estimate of the speed of light, now known to be approximately 186,000 miles per second.

Ole Rømer and the Speed of Light

In 1676, Danish astronomer Ole Rømer predicted that an eclipse of one of Jupiter’s moons would occur ten minutes later than expected. How did he know?

Astronomical image of Alpha Capricorni

September marks two significant dates in the early history of astronomy and physics—the birthday of Danish astronomer Ole Rømer on September 25, and the anniversary of an unusual pronouncement of his, one that ultimately would revolutionize our understanding of the world.

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During a 1676 meeting of the  Paris Académie des Sciences Rømer announced that an upcoming eclipse of one of Jupiter’s moons would occur ten minutes later than expected, a curious statement from someone relatively young and unknown. Rømer wasn’t even a member of the Académie , although he did serve as assistant to some of the more prominent associates, such as astronomer Giovanni Domenico Cassini.

Sure enough, on November 9, 1676, astronomers in Paris observed the eclipse ten minutes later than originally had been predicted, causing quite the uproar. How could Rømer possibly know that this would be? He explained his methods in a paper that he read to the Académie   on November 21—after noting a pattern of variation in observations of previous eclipses, he had introduced a value for the speed of light into his calculations.

The speed of light is a quantity that eluded some of the most renowned scholars in history, including Augustine and Galileo. In fact, at the time of Rømer’s successful prediction, there was ongoing debate over whether light had a measurable speed at all , or was somehow transmitted instantaneously.  As the English translation of Rømer’s paper explains,”Philosophers have been labouring for many years to decide by some Experience, whether the action of Light be conveyed in an instance to distance places, or whether it requireth time.”

Even though the moon’s “delayed” eclipse appeared to confirm experimentally that Rømer was correct, he was attacked by well-respected, senior members of the Académie, including his sometime patron, Giovanni Domenico Cassini.

Cassini argued that Rømer’s equation did not apply to the eclipses of Jupiter’s other moons, therefore it could not represent the speed of light. Other members were convinced at once, including Isaac Newton, who made reference to Rømer and his speed of light in his 1704 treatise, Opticks .

It wouldn’t be until 1729, however, that Rømer’s claim was independently and definitively confirmed by English astronomer James Bradley, through his discovery of the aberration of light. It took fifty-three years, but Rømer’s bold assertion regarding the finite nature of light was finally rendered physical fact.

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Ole Rømer’s Discovery of the Speed Of Light

How his observations gave us the first measure of the speed of light.

John Loeffler

John Loeffler

Ole Rømer’s Discovery of the Speed Of Light

There is something about the speed of light that will always hold our fascination. Maybe it’s that human beings don’t like the idea of a universal speed limit or that something as seemingly ephemeral as light can have qualities like speed.

Whatever it is, it’s something that even the least scientifically inclined to know something about and that’s largely due to the work of Ole  Rømer , who made the first real estimate of the speed of light.

Who was Ole  Rømer ?

Olaus Roemer

Ole Rømer was the son of a modest Danish merchant in Aarhus, Denmark. Born in 1644, Rømer was sent to the University of Copenhagen at the age of 18 and studied Mathematics and Astronomy under the guidance of Rasmus Bartholin.

Rømer would go on to tutor the eldest son of the Louis XIV, king of France, and became a fixture in French scientific society of the time, regularly presenting papers on a variety of topics.

His work with machinery and mechanics was widely respected by his peers across Europe, and he lived in the then newly constructed observatory in Paris, where he stayed until leaving France in 1681 to take up a professorship at the University of Copenhagen.

His discovery of the speed of light was purely coincidental to his other work, but it is one of his lasting legacies.

What Was Known About Light in Rømer’s Time?

Speed Of Light

The exact nature of light prior to 1676 was a hotly debated topic, going all the way back, as all things scientific usually do, to the Ancient Greeks.

It was Aristotle and the philosopher and mathematician Heron who first proposed that light propagated instantaneously, making the speed of light infinite.

This began a scientific back and forth over the centuries with every famous scientific mind of both Western and Islamic societies venturing an opinion about the nature and speed of light.

Galileo was Rømer’s nearest contemporary to attempt to measure the speed of light, but was unsuccessful owing to the relatively short distance he was measuring with and the lack of a precise enough clock to measure by.

The final word on the speed of light by the time Rømer made his discovery belonged to Descartes, who argued convincingly for the instantaneous propagation of light, making the speed of light infinite and immeasurable.

Rømer’s Discovery of the Speed of Light

Io Jupiter

Rømer’s discovery came as a result of his astronomical work, building off the earlier work of Galileo. Discovered in 1610, the Galilean moon of Jupiter , Io, had been extensively studied by astronomers, so much so that it’s orbital period around Jupiter was known to astronomers at the time.

Making a complete orbit of Jupiter in only 1.759 days, Rømer made meticulous recordings of Io’s orbit around Jupiter as part of his work. It was these records that held the key to Rømer’s discovery.

Every orbital period, Jupiter would eclipse Io for several minutes to an observer on Earth. As Rømer recorded the length of each eclipse, he noticed a peculiar pattern.

Whenever the Earth was moving towards Jupiter, the start time of Io’s eclipse would come earlier and earlier until the nearest distance between the Earth and Jupiter, after which the start time of Io’s eclipse would be later and later until the Earth was at its farthest from Jupiter, at which point the pattern would repeat.

Roemer Diagram

Rømer knew that the position of the Earth had no influence on the length of Io’s orbital period, so something else had to account for the difference he was seeing the in the recorded start times of the eclipse.

It was then that Rømer realized that what he was seeing was the difference in the time it took light to travel between Io and Earth.

As Earth moved closer to Jupiter, light had less distance to travel and as Earth moved away from Jupiter, light had to travel farther. It took the extraordinary distance between Earth and Jupiter for such a discrepancy in the time it took light to travel to become observable.

Once it did, however, the speed of light could be easily calculated by taking the diameter of the Earth’s orbit and dividing it by the difference in time between the quickest and longest recorded eclipses, which Rømer calculated to be about 22 minutes.

This put the first approximation of the speed of light at around 131,000 miles per second.

Rømer’s Legacy

Roemer Telescope

While Rømer’s discovery was off by about 55,000 miles a second this was an extraordinarily accurate approximation given the imperfect data about Earth’s orbit that was available at the time as well as the slight discrepancy in Rømer’s observations and the actual difference in Io’s eclipses.

The actual difference between the earliest and latest start times for Io’s eclipse is about 17 minutes, not 22.

It would be up to others to further refine the exact measurement of the speed of light to what we know today, but Rømer’s discovery put an end to a two-thousand-year-old debate in a way that any scientist in the world could replicate for themselves.

Rømer’s discovery opened up new ways for measuring distances in the solar system. “For it is now certain,” wrote Isaac Newton in Principia, “from the phenomena of Jupiter’s satellites, confirmed by the observations of different astronomers, that light is propagated in [finite] succession and requires about seven or eight minutes to travel from the sun to the earth.”

As Europe was about the begin its Scientific Revolution in the 18th century, not a small part of that momentum is owed to Rømer’s work. By proving what was possible through application of science, Rømer helped prepare the way for the era of discovery that followed.

Rømer himself wasn’t finished, though. He went on to mentor and guide other young scientists who would become household names for centuries to come.

Rømer never stopped with work with machinery, even inventing the mercury thermometer and inspiring Fahrenheit to develop his system of temperature measurement.

Nothing will be as impressive as his discovery of the once immeasurable speed of light though. He wasn’t looking to make history, but Ole Rømer is proof that curiosity and coincidence are the essential fuel that drives scientific discovery.

Via: Isis Journal (1940) / JSTOR

Correction: An earlier version of this article incorrectly stated that the length of Io’s eclipse appeared to lengthen and shorten depending on the Earth’s relative position to Jupiter. Rømer actually observed that the times at which an eclipse would begin would come earlier or later, depending on the Earth’s position. We apologize for the error.


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John Loeffler John is a writer and programmer living in New York City. He writes about computers, gadgetry, gaming, VR/AR, and related consumer technologies. You can find him on Twitter @thisdotjohn


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Ole rømer and the speed of light.

Patricia Daukantas

While his 17th-century contemporaries were debating the nature of light, Ole Rømer was busy measuring its velocity. This little-known Danish scientist was the first to determine that light moves at a finite speed.


In the 1670s, light was a popular topic of scientific inquiry. Natural philosophers did not know what light was made of, but they knew it when they saw it. In England at that time, Royal Society members Isaac Newton and Robert Hooke were bitterly debating whether light was a stream of particles or an ethereal wave.

Meanwhile, elsewhere in Europe, another aspect of light was just beginning to be explored. A Danish astronomer working with decades of careful solar-system observations published his discovery that light—whatever its form—travels at a finite, measurable speed. Although we take that fact for granted today, it was a groundbreaking concept in the 17 th century. The prevailing view was that light did not travel at all; it simply existed.

Ole Christensen Rømer, a Dane educated at the University of Copenhagen, used the movements of Jupiter’s moons to show that that wasn’t the case. Although Rømer arrived at a highly imprecise figure—and some say that he only placed a lower limit on the velocity at which light can travel—he laid the groundwork for a major paradigm shift in the way scientists think about light and its properties.

Rømer wasn’t aiming to make a scientific breakthrough that would reverberate through the ages. He and his co-workers had a far more pedestrian goal in mind: to measure European longitudes more accurately. The discovery of the velocity of light was more or less a by-product of the effort to create better maps.

Rømer’s early life

In 1644, Ole Rømer was born in Aarhus, a trading city on the east coast of Denmark’s Jutland peninsula. (In some books and journals, Rømer is spelled Roemer, Römer or Romer.) His father, Christen Olsen Rømer, worked as a merchant and a skipper; his wife, Anna Olufsdatter Storm, was the daughter of an alderman. Historians know few details about their son Ole’s early years.

At age 18, young Rømer entered the University of Copenhagen, which was at that time the only university in Denmark. Erasmus Bartholin (1625-1698), professor of geometry and medicine, became his mentor and took him into his home. Rømer lived with Bartholin for a number of years.

Bartholin had been entrusted with the task of preparing a manuscript that contained data from the Danish nobleman Tycho Brahe (1546-1601) for publication. Brahe had made copious naked-eye astronomical observations, so Rømer was able to learn mathematics and astronomy from the finest raw data set that had been compiled to that date.

Bartholin also delved into optics. In 1668, while Rømer was still living in his home, Bartholin examined a single crystal of Iceland spar (now known as calcite) that he had brought back from an expedition to that island. He noticed the double refraction of light—birefringence—through the crystal and was the first person to explain the phenomenon in a little-noticed publication the following year. Perhaps his mentor’s experience inspired Rømer to think of light as a phenomenon worthy of study.

In 1671, Rømer accompanied Bartholin and the French astronomer Jean Picard (1620-1687) to the island of Hven, where, in the previous century, Brahe had built his magnificent, short-lived observatory of Uraniborg. Picard, whose passion was to measure the size of the Earth as accurately as possible, wanted to determine the exact position of the observatory (now in ruins) in order to calibrate Brahe’s records for the French government.

Over several months, Rømer and Picard observed about 140 eclipses of Io, the innermost of the four moons of Jupiter whose discovery by Galileo in 1610 had roiled the geocentric world view of Europe. At the same time, Giovanni Domenico Cassini (1625-1712), the newly appointed director of the Paris Observatory, was observing the same eclipses from the French capital. Later, by comparing the times of the eclipses, Cassini and Picard could calculate the difference in longitude between Paris and Uraniborg.

Picard brought the promising 28-year-old Rømer to the Paris Observatory in 1672, the year after the institute opened. The Dane threw himself into a productive round of building instruments, including planispheres (adjustable star charts) and a micrometer that, according to Rømer biographer I. Bernard Cohen, “was so superior to any designed previously, that it was speedily adopted for general use.”

Geometry and reasoning

At the time, the French Royal Academy of Sciences had a practical problem to solve: how to produce more accurate maps of Europe using a new technology, the pendulum clock invented by Christian Huygens (1629-1695). If two observers—one at a place of known longitude and the other at a location whose longitude was yet to be determined—could observe the same astronomical event, they could use their timings to calculate the difference in longitude between the two locations.

As a practical matter, the astronomical event had to recur often enough that it could be observed frequently. The motions of Io, which circles Jupiter in just under 42.5 hours, fit the bill. Cassini and others assembled timetables of the motions of Jupiter’s moons—the “immersions,” or times when the satellite disappeared behind the major planet from Earth’s viewpoint, and “emersions,” periods when it emerged. But the timetables were not always accurate.

In particular, Rømer noticed that, when the Earth was moving toward Jupiter (as from F to G in the diagram on the facing page), Io’s apparent orbital period would be shorter than predicted. Likewise, when the Earth was moving away from Jupiter (as from L to K), Io’s emergence from the shadow of the giant planet would be increasingly delayed. The only explanation Rømer could find for this anomaly was that it was taking longer for the light from Io to reach Earth when Earth was farther from Jupiter.


In December 1676, Rømer published an explanation for this mora luminis , or “delay of light,” in the Journal des Sçavans , the first scientific periodical printed in Europe. The article is pithy by modern standards—only six paragraphs—and written in the third person, a frequent 17 th -century convention.

Rømer never actually gave a value for the velocity of light—which is ironic considering he is famous for being the first to measure that speed! However, what he did put forth was the qualitative idea that light travels at a finite, though mighty fast, speed. (See box below.)

Eleven years ago, geologist James H. Shea analyzed Rømer’s report from the perspective of modern scientific publishing. He pointed out that Rømer omitted most of the details that a peer referee would need to evaluate the paper, including:

• The value he used for the synodic period of Io

• The mathematical calculations he performed

• The accuracy and precision of his timekeeping and telescopic instruments

• Dates and times of his key observations, and

• A test of his hypothesis against a mathematical model.

In the few places where Rømer did actually use numbers, he didn’t get them right. He wrote: “In a duration of 42 ½ hours, in which this satellite [Io] undergoes approximately one full revolution, the distance from the Earth to Jupiter changes, in both quadratures, by at least 210 diameters of the Earth.” As Shea noted, our home planet actually moves approximately 330 Earth diameters during one of Io’s orbits—Rømer underestimated the distance by nearly 60 percent.

In September 1676, Rømer made a stunning prediction to the Royal Academy of Sciences: that the next eclipse of Io, which was supposed to take place on November 9 at 5:25:45 a.m., would be 10 minutes late. Sure enough, on that date, Io’s eclipse was recorded at 5:35:45 a.m., in perfect confirmation of his hypothesis.

When presenting those results to the Academy on November 21, 1676, Rømer stated that it took about 22 minutes for light to cross the diameter of the Earth’s annual orbit (a value also published in the Journal des Sçavans ).

How did Rømer arrive at the 22-minute figure? Historians were unsure about that until the summer of 1913, when they discovered a manuscript folio that contained a list of jovian moon eclipses in Rømer’s handwriting from 1668 to 1677. Apparently, Rømer had intended to publish a more complete version of his work, with more data to back up his hypothesis, but he never got around to it. Huygens recorded in his own writing that Rømer presented additional results to the Academy in 1677.

In his December 30, 1677, letter to Huygens, Rømer wrote that he had collected more than 70 observations of Io, both his and Picard’s, since 1668. In calculating the moon’s orbital period, he had grouped the emersions and immersions together for study. He found, in Cohen’s words, that “the mean period is always greater when calculated on the basis of emersions than when calculated on immersions.”

Rømer and Picard made more than half of their observations from 1671 to 1673, and Rømer chose those data to come up with the 22-minute figure because Jupiter “offered, during this period, comparatively few variations in its movement and distance from the sun; this because 1672 marked the aphelion passage of Jupiter,” Cohen wrote.

Ancient Greeks debated whether light had any motion at all. Their general conclusion was that, if light did move, it did so at an infinite velocity. Only Empedocles of Acragas, who lived in the fifth century B.C.E., thought that light was an ineffable substance with a fast but finite speed. Aristotle reasoned that light has substance but no motion, and his thinking held sway with scholars for centuries.

In the 11 century, Ibn al-Haytham (Alhazen) proposed that light travels very fast but slows down in denser bodies. Christian Huygens (1629-1695) adopted the hypothesis that light had a finite speed, but he did not do much to promote the idea; he merely used the concept to account for the phenomena in which he was interested.

In France, prevailing opinion favored the view of René Descartes (1596-1650), who argued strenuously for the instantaneous transmission of light. The Dutch physicist Isaac Beeckman (1570-1637) tried to convince Descartes that light has a finite speed that could be measured experimentally, but to no avail. Educated society’s high regard for Descartes hindered the widespread acceptance of Rømer’s work for years after his death. Like Descartes, Johannes Kepler (1571-1630), who figured out the laws of planetary motion, also hypothesized that light traveled infinitely fast.

Galileo (1564-1642) proposed an experiment to measure the speed of light. Two experimenters would practice uncovering and covering their lanterns until the second could uncover his lantern the instant that the light from the first reached him. He tried this himself at a distance of roughly a mile from his assistant. Not surprisingly, he failed to notice any “observable delay.”


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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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

roemer's experiment failed because of his ignorance about the

[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.

roemer's experiment failed because of his ignorance about the

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roemer's experiment failed because of his ignorance about the

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

roemer's experiment failed because of his ignorance about the

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.

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Qmechanic's user avatar

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.


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.

Adam Zalcman's user avatar

  • 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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roemer's experiment failed because of his ignorance about the

  • 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?

Four things you may not know about the speed of light

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.

Portrait of the Danish astonomer Ole Rømer

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.

What's actually going on in today's telescopic Google Doodle

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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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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Lightspeed: The Ghostly Aether and the Race to Measure the Speed of Light

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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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  1. Ole Rømer’s Discovery of the Speed Of Light

    roemer's experiment failed because of his ignorance about the

  2. Ole Rømer’s Discovery of the Speed Of Light

    roemer's experiment failed because of his ignorance about the

  3. Dual Nature of Light

    roemer's experiment failed because of his ignorance about the

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

    roemer's experiment failed because of his ignorance about the

  5. PPT

    roemer's experiment failed because of his ignorance about the

  6. PPT

    roemer's experiment failed because of his ignorance about the


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  1. Physics Unit 5 Test Flashcards

    Roemer's experiment failed because of his ignorance of: the speed of light the dimensions of the earth's orbit the number of Saturn's moons the use of the telescope. the dimensions of the earth's orbit. In any homogeneous medium, the constant factor is a wave's: amplitude wavelength frequency velocity all of the above.

  2. Rømer and the Finite Speed of Light

    A young and brilliant Danish "postdoc" at the Paris Observatory, Rømer had unexpectedly answered a long-standing fundamental question. Before his discovery, the likes of René Descartes and Johannes Kepler had claimed that light was an instantaneous phenomenon, and all attempts to prove otherwise had failed.

  3. 1676: Ole Rømer Measures the Speed of Light

    His accomplishment was an essential step in developing an understanding of the universe. Eventually it would figure in the development of Einsteins theory of relativity, but the speed of light also defines the light year, which is the yardstick that astronomers use to measure the vast distances between stars and galaxies.

  4. Ole Rømer and the Speed of Light

    The speed of light is a quantity that eluded some of the most renowned scholars in history, including Augustine and Galileo. In fact, at the time of Rømer's successful prediction, there was ongoing debate over whether light had a measurable speed at all, or was somehow transmitted instantaneously. As the English translation of Rømer's ...

  5. Ole Rømer's Discovery of the Speed Of Light

    The final word on the speed of light by the time Rømer made his discovery belonged to Descartes, who argued convincingly for the instantaneous propagation of light, making the speed of light ...

  6. Optics & Photonics News

    While his 17th-century contemporaries were debating the nature of light, Ole Rømer was busy measuring its velocity. This little-known Danish scientist was the first to determine that light moves at a finite speed.

  7. Rømer and the Speed of Light

    Earlier, a somewhat similar phenomenon was discovered by the Dane Ole Rømer ("Roemer") in 1676. The story deserves to be told because it also led to the first determination of the velocity of light. Those were the times when the sailing ships of seafaring nations - especially, France, Spain, Britain and the Netherlands (Holland) - fought ...

  8. Ole Rømer and the Speed of Light

    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 ...

  9. Rømer's Measurement of the Speed of

    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 ...

  10. Measuring the Speed of Light

    In the early 17th century, many scientists believed that there was no such thing as the "speed of light"; they thought light could travel any distance in no time at all. Galileo disagreed, and he came up with an experiment to measure light's velocity: he and his assistant each took a shuttered lantern, and they stood on hilltops one mile apart.

  11. Ole Rømer

    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. ... ↑ In scientific literature, his name is alternatively spelt "Roemer ...

  12. experimental physics

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

  13. Roemer and the First Determination of the Velocity of Light (1676

    Paris 1676: The Discovery of the Velocity of Light and the Roles of Rømer and Cassini. It is often claimed that the 1676 discoveries at the Paris Observatory of a new irregularity in the orbit of Jupiter's first satellite and of the velocity of light were not due to Rømer alone but….

  14. Determination of the speed of light: Who is Ole Roemer and how did he

    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?

  15. Ole Rømer‬‬'s determination of the speed of light ...

    Today's Google Doodle celebrates Olaus Roemer, the Danish astronomer and scientist who was the first to successfully determine the speed of light ... he failed to quantify it. Roemer took that ...

  16. Roemer and the First Determination of the Velocity of Light

    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 ...

  17. Ole Roemer, Who Started It All

    Roemer's remarkable life story and many other achievements are told. Keywords: Roemer, Galileo, speed of light, Cassini ... He himself does not appear to have given a value for the speed in familiar units, perhaps because of the large errors in distance measurements—this was left to Huygens in 1690.

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

    THE FIRST DETERMINATION OF THE VELOCITY OF LIGHT 345. and bigotry, with which he had but slight encounter before his departure. For in I685 LouIs XIV revoked the Edict of Nantes, and ROEMER, a Protestant, would have been driven from the country, in company with that other " undesirable Protestant," CHRISTIAAN HUYGENS.

  19. Roemer's experiment failed because of his ignorance about the: the

    Roemer's experiment failed because of his ignorance about the dimensions of the Earth's orbit. Roemer was trying to determine the actual speed of light in his experiments, back in the 17th century.

  20. Roemer's experiment failed because of his ignorance about the what

    a) the speed of light. b) the dimensions of the earth´s orbit. c) the number of Saturn´s moons. d) the use of the telescope. The most probable answer would be his miscalculations about the dimensions of the Earth's orbit which is why his experiment ultimately failed. arrow right.