How Was the Speed of Light First Measured?
― A Moon of Jupiter Showed Up Late
Light travels fast enough to circle the Earth seven and a half times in one second. It's so fast that, for a long time, experiments on the ground could only conclude it "arrives instantly." The first thing to actually catch light's speed wasn't a device on Earth at all. It was a small moon, far away, orbiting Jupiter — and turning up "late."
On a summer night, fireworks burst in the distance. You see the flash right away, but the boom doesn't reach you for a few seconds. Everyone knows, from experience, that sound has a speed.
But what about light? Between the instant the firework bursts and the instant it reaches your eyes, is there any gap at all? As far as you can tell, there's no way to know.
Until about 350 years ago, most scholars also believed light arrived instantly. The person who overturned that idea was an astronomer who spent years watching Jupiter through a telescope.
The key was combining two facts
Io, the innermost of Jupiter's large moons, slips into Jupiter's shadow and re-emerges roughly every 42.5 hours. This happens over and over, at almost exactly regular intervals.
Earth orbits the Sun once a year. During the part of the year when Earth was farthest from Jupiter, Io seemed to emerge from the shadow later than predicted. It wasn't Io that was late — it was the light's arrival.
In other words, for the very same event, the farther away you are, the later the "news" of it reaches you. Once you know how big that delay is, you can calculate the speed of light.
Io was an accurate clock hanging in the sky
Jupiter's four large moons were discovered by Galileo Galilei in 1610, using a telescope. Io, the closest to Jupiter, orbits in under two days. Every time round, it slips into the shadow Jupiter casts, then re-emerges a while later.
This "eclipse" happens at the same instant no matter where on Earth you watch it from. That made it attractive at the time as a clock for finding one's longitude, on land or at sea. The Paris Observatory is said to have produced tables predicting the times of Io's eclipses.
But after years of observations piled up, something troubling turned up. The predicted and actual times drifted apart depending on the season. When Earth was close to Jupiter, the eclipse came early; when Earth was far away, it came late.
Why did moving away make the clock run late?
The person who tackled this mismatch head-on was Ole Rømer, a Dane working at the Paris Observatory. In 1676, he is said to have predicted in advance that "Io's eclipse that November will be about 10 minutes later than forecast." The observation matched his prediction closely.
Figure 1 shows why. When Earth is close to Jupiter, light from Io has only a short distance to travel. About half a year later, once Earth has swung round to the far side of the Sun, the light has to cross an extra distance equal to the diameter of Earth's orbit.
Light from the instant Io leaves the shadow has to travel farther the more distant Earth is, which is why the eclipse appears late. Rømer is said to have estimated that light takes about 22 minutes to cross Earth's orbit. Today's value is about 16 minutes 40 seconds, so his very first measurement was remarkably close.
Why couldn't ground-based experiments detect it?
Galileo reportedly tried having two people stand on distant hilltops, opening and closing lamp covers, to time light's round trip. But no delay at all showed up. Light takes less than a hundred-thousandth of a second to travel one kilometre — thousands of times shorter than the lag in a person's own reaction time.
Rømer's method worked because he stretched the distance out to the scale of the solar system instead. The diameter of Earth's orbit is about 300 million km. Over a distance that large, even light takes several minutes — easily measurable with the pendulum clocks of the day.
His other trick was to let the delay "accumulate" before observing it. In the time it takes Io to complete one orbit, Earth moves away by a distance that, to light, is a difference of only about 15 seconds. But add up dozens of orbits, and it becomes a clear gap of over 10 minutes.
Cassini, the director of the Paris Observatory, is said never to have fully accepted the explanation involving the speed of light. It took about 50 more years, until 1728, for the finite speed of light to become widely accepted. That's when James Bradley in England discovered a separate phenomenon called "aberration of light" — a tiny yearly shift in the apparent direction of stars — and arrived at the same conclusion.
Summary
Light doesn't arrive instantly — it travels at a fixed speed. The first evidence for this came from observing that eclipses of Jupiter's moon Io appeared later the farther Earth was from Jupiter. Rømer turned an invisible delay into a visible one by stretching light's path — too short to measure on Earth — out to the scale of Earth's orbit.
Light wasn't instant after all.
A late-arriving moon of Jupiter was the one that told us so.
You can read about measuring Earth's size using a shadow 2,200 years ago in "How Was the Size of the Earth First Measured?", and about measuring the distance to the Moon using light's round-trip time in "How Far Away Is the Moon, Really?".
- When Jupiter is visible at night, mount binoculars on a tripod and look at it. You'll see small points of light lined up right next to Jupiter. These are the four moons Galileo discovered.
- Sketch their positions on paper every few days. The point closest to Jupiter shifts position the most from night to night. That's Io.
- Look up the predicted time of an "Io eclipse" using astronomy software or an app, then watch through a small telescope. Seeing the point suddenly appear right on schedule lets you experience the very sight Rømer once watched.
When Jupiter is visible changes from year to year — check a stargazing site, such as the National Astronomical Observatory of Japan's, to find out. Today's predictions already factor in light's delay, so you won't see any mismatch — and that, itself, is proof that Rømer's discovery is still in use today.
Want to go deeper? ― Terms, formulas, and where this fits in your studiesWe label each part by level, from middle-school science to university-level specialist courses
- MSCovered in middle-school science
- HSCovered in high-school "Physics" or "Earth Science"
- HS+Advanced high-school content, or a textbook sidebar topic
- UnivNot covered in high school — university-level specialist content (astronomy, electromagnetism, metrology)
- ResearchNot yet settled even at university level — something researchers are actively investigating
MSTerms: this phenomenon has names
- Speed of light: the speed light travels at in a vacuum. About 300,000 km per second.
- Eclipse of a moon: when a moon (satellite) passes into the shadow cast by the planet it orbits, and goes dark. For Io, this happens roughly every 42.5 hours.
- Astronomical unit: the average distance between Earth and the Sun. About 150 million km. Light takes about 8 minutes 20 seconds to cross it.
MSHSCheck it with a formula: getting the speed of light from Io's delay
Between Earth's near and far positions relative to Jupiter, the difference in the distance light must travel equals the diameter of Earth's orbit. The time it takes to cross that extra distance is the eclipse delay.
| In symbols | c = Δd ÷ Δt |
| In words | Speed of light = extra distance travelled ÷ extra time taken (the eclipse delay) |
| Where it comes from | "Speed = distance ÷ time." If light travels at a constant speed, a difference in distance shows up directly as a difference in arrival time |
Here's what each symbol and unit means.
| c | speed of light (km/s) |
| Δd | difference in light's path length between the near and far positions (km) — here, the diameter of Earth's orbit |
| Δt | the resulting delay in when the eclipse is seen (seconds) |
| Earth–Sun distance (radius) | about 150,000,000 km |
| Delay crossing the orbit (modern value) | about 1000 seconds (about 16 min 40 s) |
| Rømer's estimated delay | said to be about 22 minutes |
| Io's orbital period | about 42.5 hours |
| Earth's orbital speed | about 30 km/s |
| Difference in path length (diameter) | 150,000,000 × 2 = 300,000,000 km |
| Speed of light (using modern delay) | 300,000,000 ÷ 1000 = 300,000 km/s |
| Rømer's 22 minutes in seconds | 22 × 60 = 1320 s |
| Speed of light (using 22 min) | 300,000,000 ÷ 1320 ≈ 227,000 km/s |
| One Io orbit in seconds | 42.5 × 3600 = 153,000 s |
| Max distance Earth recedes in that time | 30 × 153,000 = 4,590,000 km |
| Delay per orbit | 4,590,000 ÷ 300,000 ≈ 15.3 s |
The speed of light comes out to about 300,000 km/s. Even Rømer's contemporary estimate of 22 minutes landed in the right ballpark of hundreds of thousands of km/s. The delay per single orbit is only about 15 seconds — barely within reach of a pendulum clock. The key to his success was stacking up dozens of orbits until the delay exceeded 10 minutes.
HSHS+How was the speed of light measured after that?
HSIn high-school physics, you learn that light is a type of electromagnetic wave, travelling at about 3.0×10⁸ m/s in a vacuum. The formula in this article is the same "speed = distance ÷ time" used for the speed of sound. The only difference is that the distance involved is on the scale of the solar system.
HS+In 1728, Bradley discovered "aberration of light." Just as rain looks like it's falling from ahead when you run through it, the ratio between Earth's orbital speed and the speed of light causes a star's apparent direction to shift slightly. In 1849, Fizeau became the first to measure the speed of light in a ground-based experiment, by sending a beam through the gaps of a spinning toothed wheel and back.
UnivToday, the speed of light isn't something we "measure"
Since 1983, the speed of light in a vacuum has been defined as exactly 299,792,458 m/s — no longer a measured value. The metre, the unit of length, is now defined as the distance light travels in 1/299,792,458 of a second. Meanwhile, the delay Rømer saw in Io's eclipses is known in astronomy as the "light-time effect," and it's still used today in observing binary stars and exoplanets — a periodic shift in eclipse timing can reveal an otherwise invisible companion star.
📖 For the derivation and further reading: Speed of light (Japanese Wikipedia) / Aberration of light (Japanese Wikipedia)
ResearchWhat's still not fully settled
- Did Rømer himself put a number on the speed of light? It's said that it was his contemporary Huygens who converted the 22-minute delay into a speed in km/s. Much of Rømer's original material was lost in a fire, so historians of science still debate exactly how far his own calculations went.
- How far can eclipse-timing shifts take us in finding hidden objects? Research is ongoing into detecting third stars or planets from tiny shifts in eclipse timing. But it's hard to distinguish these from shifts caused by the star's own activity, and some claimed detections are still being confirmed.
- Is the speed of light really the same everywhere? That light's speed doesn't depend on direction or energy has been confirmed to extremely high precision. Even so, tests at ever-finer precision continue, using light arriving from deep space.
In other words, even this article describes things "as best understood so far." A small 350-year-old case of tardiness is still, today, a working tool for exploring the universe.
Where this fits in the curriculum (by level)
| Level | Subject/Unit | Where in this article |
|---|---|---|
| MS | Science - Light and Sound / The Solar System and Planets | The gap between a firework's flash and boom; the positions of Earth and Jupiter |
| HS | Physics - Waves (speed of light) / Earth Science - Planetary Motion | Calculating the speed of light via speed = distance ÷ time |
| HS+ | Advanced Physics - History of measuring light's speed | Bradley's aberration of light, Fizeau's toothed wheel |
| Univ | Astronomy / Metrology (defining units) | Defining length via the speed of light, the light-time effect |
| Research | History of Science / Observing binaries and exoplanets | Rømer's original records, finding objects via eclipse-timing |
| ― | Everyday connections | Positioning systems using satellite radio signals rely on the speed of light being fixed |
- Wikipedia (Japanese), "Speed of light" (光速)
- Wikipedia (Japanese), "Ole Rømer" (オーレ・レーマー)
- Wikipedia (Japanese), "Aberration of light" (光行差)
- I. B. Cohen, "Roemer and the First Determination of the Velocity of Light (1676)", Isis, 31 (1940)
- National Astronomical Observatory of Japan (国立天文台), ed., Rika Nenpyo (理科年表, Chronological Scientific Tables), Maruzen Publishing (speed of light, astronomical unit, planetary orbital elements)
※This article is a general-audience science explainer. The figures given are rough estimates meant to aid understanding of the underlying mechanism. Dates and figures for historical events may vary slightly between sources.