Speed of Light | The Eclipses of Io

The Speed of Light series consist of five parts. Quick access links are here.

Part 1 | Earliest Ideas

Part 2 | The Eclipses of Io

Part 3 | Chopping Light Beams

Part 4 | Done With Mirrors

Part 5 | Michelson and Morley

In this post, the first successful calculation of the speed of light is described. It is an interesting story of astronomy.


Galileo and the Moons of Jupiter

Wikimedia Commons

Galileo Galilei was the first to record observations of Jupiter and its four largest moons through a telescope. This set the stage for later efforts by the Danish Astronomer Ole Christensen Rømer to measure the motions of Io, the closest of the moons to Jupiter. This post is about those efforts by Rømer and how they ultimately led to the realization that light had a finite and incredibly fast speed.

The telescope first appeared in the Netherlands in October 1608. The national government in The Hague received patent applications by Hans Lipperhey of Middelburg. Later, one was received from Jacob Metius of Alkmaar. He called it a device for “seeing faraway things as though nearby.” The telescopes had a convex and concave lens in a slender tube two to three feet long. Objects were magnified three or four times. Lenses of this type were in common use in eyeglasses.

News spread rapidly about the telescope. Soon, they appeared in many cities. Low powered versions could be purchased in Paris and cities in Italy. Thomas Harriot used a 6x telescope to view the Moon in August 1609. Galileo made his first 3x telescope in June or July 1609. He made an 8x one in August. His 20x version was used the first times in October or November 1609. This 20x telescope was used to discover the four moons of Jupiter. This short video uses a desktop software program to explain how the view might have appeared to Galileo. It should help you get a better sense of perspective on the rest of this post.

Latitude and Longitude

One of the huge challenges of the time was to know the correct longitude and time when sailing the seas. Time was used, along with the sextant, to navigate the seas. The sextant could accurately establish your position north or south by the locations in the sky of familiar objects such as the Moon, Sun, and stars. If Polaris, the north star, is directly overhead, you are at the north pole latitude. If it is near the horizon, you are near the equatorial latitude.

Where you are east or west is a more difficult question to answer. That is only determined by knowing the precise time. The time determines your longitude. Navigators and astronomers in the 1600s were trying to build a clock mechanism that would work accurately for long periods of time at sea. They also wanted a way to view some object in the heavens in order to know the exact time. That is why the Galilean moon Io is important. Astronomers hoped the consistent and regular orbit of Io might be useful as a clock. This brief video illustrates that idea and specifically what value Rømer measured.

Accidental Discovery by Rømer

Rømer set out to measure as accurately as possible the time between consecutive eclipses of Io by Jupiter. Sometimes, people set out to study something and end up re-directed in an unplanned direction leading to new insights and discoveries that are extremely important. Such was the case for Rømer.

He was at the Paris Observatory beginning in 1672 specifically to time the Io eclipse dates and times. During the time of closest approach of Earth to Jupiter, Io would have been larger and more easily seen and timed through a telescope. This short video shows the relative distances of the orbits of the two planets. The orbit of Io is too small to see in this simulated view. The video covers slightly more than a year of Earth time.

These two snapshots two months apart in time show Earth nearest to Jupiter and in the process of passing it. Two months of time would allow many orbits of Io to be timed. Rømer found the orbit time between Io eclipses to be 42.456 hours, less than two days between them. He potentially could have witnessed nearly 30 eclipses if clear skies always prevailed. Not likely at Paris.

Earth nearing closest distance from Jupiter

Two months later

It was hoped his data would allow accurate predictions of specific eclipse times at future dates in the year. Ships at sea would carry the ephemeris of eclipse times as seen from the Paris longitude on their journey. When they needed to know their own longitude, an observation of eclipse of Io would be made telescopically. Reference to the ephemeris for Paris time would be compared to the local time of the ship. If the ship saw the Io eclipse at 8 pm, and the Paris ephemeris said 12 pm, the 4 hour difference translates into 60˚ west of Paris longitude. Earth rotates 360˚ in 24 hours. That is 15˚ per hour toward the east. Paris would be more advanced in time than points west.

The key was to use the regular period of time of Io eclipses in order to predict the times on future dates throughout the year. Rømer could calculate 42.456 hours ahead from each one of the eclipses and predict all future dates in the year.

Also key was the ability to carry an accurate clock on a ship in order to know the correct time of a local place. Shipboard spring wound clocks were subject to large errors. That problem was solved 100 years later.

As Rømer worked to make the accurate eclipse timings he noticed something strange about his values. As the Earth moved in orbit to the distances farther from Jupiter as in these next two snapshots, observed eclipse times didn’t match the predicted eclipse times. The observations were several minutes later than the predictions as the dates increased. They reached a maximum of 22 minutes late when Earth was farthest away as in the second image, compared to when Earth was closest to Jupiter shown above.

Earth moving away from Jupiter and Io

Earth farthest away from Jupiter and Io

The following is based upon notes from the web site of the Round Tower at the Univ. of Copenhagen, Europe’s oldest functioning astronomy observatory. Details about Ole Rømer are found at this link.

Rømer announced his results to the French Academie of des Sciences in September 1676.

The extra distance of travel of the light from the Io eclipse by Jupiter was taking longer to arrive because of the additional distance it must travel to reach Earth. He predicted an eclipse on November 9 would be delayed 10 minutes, which it was.

Enter Christiaan Huygens of Holland

Huygens read Rømer’s paper in September 1677. He wrote a letter to Rømer asking for more information. Huygens apparently understood the concept that light traveled across the diameter of the Earth’s orbit in 22 minutes. It had a finite speed.

In 1678, Huygens spoke to the Academie des Sciences and presented a paper called “Traite de lumiere“. In that treatise, he used the diameter of Earth’s orbit known at the time and Rømer’s value for the 22 minutes of light delay as it crossed the orbit diameter in order to calculate the speed of light. Ole Rømer is credited with the measurements leading to the concept that light had finite speed. Huygens did the arithmetic. He was the first person known to publish a value for the speed of light calculated from those measurements. His calculation was expressed in unusual terrestrial units as 16 2/3 earth-diameters/second, as well as others not used today.

Using today’s value for the diameter of the Earth of 12,742 km, the speed converts to 212,400 km/sec. The accepted value for the speed of light is 299,800 km/sec. The value calculated by Huygens from Rømer’s measurements was remarkably close to the correct value. It was wrong only because the diameter of the orbit of Earth was not known with sufficient accuracy.

Rømer went back to Denmark in 1681. He continued his career in science and government. He served as mayor and prefect of police of Copenhagen. He also served as head of the State Council. He is not remembered for his political offices. He is remembered for being the first person to measure the speed of light.


24 thoughts on “Speed of Light | The Eclipses of Io

  1. @ Jim in IA,

    Outstanding job here on the speed of light and Jupiter’s moons, Jim. I can’t imagine it being presented more clearly than this. You previously mentioned Dava Sobel and I noted with interest the comments made on the John Harrison Wikipedia page about her book, Latitude which I read with great interest soon after it was published. This fascinating story is, I submit, just further evidence that people haven’t gotten smarter in the last few centuries, but that we collectively continue to benefit from the work of those who have gone before. And it’s because of the scientific method.

    • Clear thinking and the scientific method take great creative ideas and help us make big strides forward.

      I’m glad you already know about Dava Sobel. She is an excellent writer. The books are packed with information.

      I also watched the PBS Nova program Search for Longitude. It was a good dramatization.

      Thanks for stopping by and those kind words.

    • You remind me of an Isaac Newton quotation (though Bernard of Chartres apparently expressed the idea first, in the 1100s):

      “If I have seen further it is by standing on the shoulders of Giants.”

      And that in turn triggers another Isaac Newton quotation:

      “I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”

      • Those are two great quotes. He was quite an interesting person with interests in many areas. He dabbled in religion and alchemy.


  2. I love the math involved, at least as much as the science. Chug chug chug…. keep calculating… you’ll get there…

    Very well written, both of them. I think I understand the story pretty well now.

  3. Everything has a history … and the evolution form 3X to 20X was huge …. and simply part of the steps necessary to allow us to see what we can today.

  4. Great example of using large scale to be able to perceive small things, in this case the distance across the solar system to measure small differences in the time light travels, unmeasurable directly. Astronomy really benefits from that, like using parallax 6 months apart. Really quite remarkable these guys were able to abstract out what is happening physically so far from earth and our human scale. Exciting time of discovery.

    • A trait I’ve noticed in the ones who made big discoveries is the ability to have a vast 3-D perspective on space. Most of us live our days experiencing a pretty limited world view.

      I agree. It is an exciting time. Only a few weeks ago we saw the discovery of events only trillionths of trillionths of trillionths of a second into the age of our universe. Now that is something else.

  5. You mention that Huygens read Rømer’s paper in September 1677. Five and four years earlier, in 1672 and 1673, Huygens met in Paris with a young Leibniz. At that time Leibniz hadn’t studied much mathematics and asked Huygens to guide him on what to read, which Huygens did. Leibniz was a quick study and before long he’d learned enough to begin making discoveries of his own, including that of the basic principles of calculus.

    • Leibniz and Newton disagreed on who invented calculus. Is that right? Huygens seemed to know a lot of influential thinkers of the time. He was one himself.


      • Yes, it was quite a conflict, and it went on for decades. The substance of their discoveries is the same, but Leibniz’s notation won out and is still largely in use.

        Huygens is important in the history of science; I wonder why he’s not presented in American science classes (at least I don’t remember him from any classes I had in elementary or secondary school).

      • I think it is a common story. Many important advances in human history get attached to a person(s) who were in the right place at the right time and got some sort of recognition. It is usually a much larger group that needs to be acknowledged for laying the foundation that one person gets to stand upon. Those make for some very interesting stories in themselves.

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