How Did Rømer Measure the Speed of Light with Io?

For most of history, people assumed light simply arrived: you open your eyes and the world is there. The first solid evidence that light takes time to travel came not from a laboratory but from a clock in the sky, Jupiter’s moon Io. Our Ole Rømer sticker sums up his insight: “Io isn’t late. Light is.” This post builds on our explainer Why Is the Speed of Light the Limit?.

Why was Io useful as a clock?

Io, the innermost of Jupiter’s four large moons, circles the planet in about 42.5 hours, and on every orbit it passes into Jupiter’s shadow. The moment Io slips into the shadow (an immersion) or reappears from it (an emersion) is sharp and can be timed with a telescope. In the 1600s astronomers studied these eclipses closely because a reliable table of them could be used to work out longitude (Bobis & Lequeux 2008^[1]).

If Io kept perfect time, the eclipses would arrive at evenly spaced intervals. They did not. When Earth was moving away from Jupiter, the eclipses ran progressively later than the tables predicted. When Earth was moving toward Jupiter, they ran early.

How does the timing argument work?

The idea is simple. Light from Io has to cross the gap between Jupiter and Earth. That gap changes through the year by up to the full width of Earth’s orbit. If light travels at a finite speed c, every extra metre adds a delay:

Δt = Δd / c

Here Δt is the extra delay in seconds, Δd is the change in Earth–Jupiter distance in metres, and c is the speed of light in metres per second. Today c is fixed by definition at exactly 299 792 458 m/s (NIST^[2]). The astronomical unit (au), roughly the average Earth–Sun distance, is fixed at exactly 149 597 870 700 m (BIPM SI Brochure^[3]).

A worked number

Light crosses one astronomical unit in

1 au / c = 149 597 870 700 m ÷ 299 792 458 m/s ≈ 499 s

That is about 8 minutes 19 seconds. The maximum extra path, the full diameter of Earth’s orbit, is 2 au, so the total swing in eclipse timing is about 998 s, roughly 16 minutes 38 seconds. That is the effect Rømer had to find in 17th-century observations, spread over months.

What did Rømer actually find in 1676?

The historical record is more interesting than the textbook version. Historians Laurence Bobis and James Lequeux reconstructed the story from the Paris Academy’s minutes and letters (Bobis & Lequeux 2008^[1]). Key points from their account:

• In August 1676, Jean-Dominique Cassini, director of the Paris Observatory, announced an irregularity in Io’s eclipses and suggested it might be because light takes “ten or eleven minutes” to cross a distance equal to the radius of Earth’s orbit. To win astronomers over, he predicted that an emersion of Io due on 16 November 1676 would come about 10 minutes later than the tables said. He soon raised objections to his own idea.
• An emersion of Io observed on 9 November 1676 came about 10 minutes late. Whether the 16 November one was observed is not known. Rømer, a young Danish astronomer working at the Observatory, took up the light-delay explanation.
• On 21 November 1676 he read an account to the Academy showing that the motion of light is not instantaneous. It was published in the Journal des Sçavans on 7 December 1676.
• An English translation appeared in the Philosophical Transactions in 1677, as “A Demonstration concerning the Motion of Light” (Phil. Trans. 1677^[4]).

So the hypothesis was first floated by Cassini, then abandoned by him, and argued for and published by Rømer. Credit stories in physics are often tidier than the facts, a theme we explore in Who Really Discovered It?.

Did Rømer calculate the speed of light?

Not in the sense of giving a number in kilometres per second. Bobis and Lequeux note that Christiaan Huygens “was the first scientist to give a numerical value for this velocity” and that “neither Cassini nor Rømer had attempted this” (Bobis & Lequeux 2008^[1]). In his 1690 Treatise on Light, Huygens combined Rømer’s timing with the size of Earth’s orbit; in modern units his figure was about 230 000 km/s.

The inputs were uncertain. Estimates of the full delay in that era varied: Bobis and Lequeux note Cassini later adopted 14 minutes 10 seconds in his tables, after 20 to 22 minutes had been announced earlier.

Textbook version vs history

Many textbooks tell a cleaner story. OpenStax’s University Physics, for example, says Rømer found Io’s period of 42.5 h and “calculated that the speed of light was 2.0 × 10⁸ m/s”, which it notes “is 33% below the value accepted today” (OpenStax University Physics, §1.1^[5]). The underlying physics in that account is right. The attribution of a specific numerical result to Rømer is not supported by the historical study cited above, so we treat it as a simplification.

How was Rømer’s idea confirmed?

Not everyone accepted the finite speed of light at once. Cassini remained unconvinced, and other irregularities in the moons’ motion made the case messy. The decisive confirmation came in 1728, when James Bradley reported the aberration of starlight: stars appear slightly shifted in the direction of Earth’s motion, an effect that only makes sense if light has a finite speed and Earth moves around the Sun (Bradley 1728^[6]). Bobis and Lequeux note that in France scientists were convinced only after Bradley’s discovery.

Today the finite speed of light is built into daily technology. Satellite navigation, for example, depends on timing light-speed signals to nanoseconds, with relativity corrections on top, as we explain in How Does GPS Correct for Relativity?. The Light, Time & Relativity sticker sheet, which includes Rømer, carries the same story.

FAQ

Was Rømer’s value of the speed of light accurate?

Rømer argued that light’s speed is finite and gave timings. The first numerical value came from Huygens, about 230 000 km/s in modern units, roughly 23% below today’s exact value.

Why does the delay depend on Earth’s position and not Jupiter’s?

Both matter, but Earth moves around the Sun much faster than Jupiter does. Over a few months the Earth–Jupiter distance changes mainly because of Earth’s motion.

What is the speed of light today?

Exactly 299 792 458 m/s. The 17th General Conference on Weights and Measures defined the metre from it in 1983 (BIPM SI Brochure^[3]), so the number is fixed rather than measured, and light takes about 499 s to cross one astronomical unit.

References

1. L. Bobis & J. Lequeux (2008), “Cassini, Rømer and the velocity of light,” Journal of Astronomical History and Heritage 11(2), 97–105. https://articles.adsabs.harvard.edu/pdf/2008JAHH...11...97B
2. NIST CODATA 2022 recommended values: speed of light in vacuum (exact). https://physics.nist.gov/cgi-bin/cuu/Value?c
3. BIPM, The International System of Units (SI Brochure), 9th edition (2019, updated). https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf
4. [O. Rømer] (1677), “A Demonstration concerning the Motion of Light, communicated from Paris, in the Journal des Sçavans,” Phil. Trans. R. Soc. Lond. 12, 893–894 (DOI 10.1098/rstl.1677.0024; metadata verified via Crossref). https://doi.org/10.1098/rstl.1677.0024
5. S. J. Ling, J. Sanny & W. Moebs, University Physics Volume 3 (OpenStax, Rice University), §1.1 “The Propagation of Light”. https://openstax.org/books/university-physics-volume-3/pages/1-1-the-propagation-of-light
6. J. Bradley (1728), letter to Dr Edmond Halley “giving an account of a new discovered motion of the fix’d stars,” Phil. Trans. R. Soc. Lond. 35, 637–661 (DOI 10.1098/rstl.1727.0064; metadata verified via Crossref). https://doi.org/10.1098/rstl.1727.0064

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.