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Ole Rømer Sticker

Io Isn’t Late. Light Is. | Physics

\[\Delta t = \frac{\Delta d}{c}\]
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Jupiter’s moon Io kept missing its schedule, and that was the clue. In 1676 Ole Rømer saw Io’s eclipses run late when Earth was farther from Jupiter: light takes time to travel. A pixel-art portrait on a 3" × 3" sticker; the physics panel below has the equation, every symbol and the sources.

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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The physics

Io's eclipses behind Jupiter ran later when Earth was farther from Jupiter, because the light had farther to travel. Rømer used that delay to show that light has a finite speed, crossing the width of Earth's orbit in a matter of minutes.

The sticker says Io Isn’t Late. Light Is. Ole Rømer worked that out in 1676.

Io circles Jupiter every 42½ hours and slips into Jupiter's shadow on a steady schedule, which made it a clock that astronomers anywhere could read. At the Paris Observatory, Rømer found that the timings drifted with the seasons, running behind the tables when Earth was moving away from Jupiter.

From the beginning of September he predicted that Io's emergence from the shadow on 9 November 1676 would come about ten minutes later than expected, and it did. The moon wasn't slow. Earth was farther from Jupiter, and the light carrying the news had farther to go. His account, read to the Académie that month and printed in English the next year, put light's crossing of Earth's whole orbit at about 22 minutes.

Who first put the light explanation forward is still an open question. Giovanni Domenico Cassini, the observatory's director, floated it in an August 1676 announcement and then backed away from it. Rømer kept it. Rømer never published a speed: Christiaan Huygens turned the timing into one in 1690, about 230,000 kilometres per second in modern units. The idea was not widely accepted until James Bradley found the aberration of starlight in 1729.

The modern figure for that crossing is about 16.6 minutes. Rømer's 22 was the first good evidence that light takes time to travel at all.

Io was on time. The message was in transit.

Equations

\[\Delta t = \frac{\Delta d}{c}\]
\[\begin{gathered} \frac{2\,\text{AU}}{c} \approx 998\ \text{s} \approx 16.6\ \text{min} \\ (\text{R\o mer's estimate} \approx 22\ \text{min}) \end{gathered}\]
\[c = 299\,792\,458\ \text{m/s (exact)}\]
Symbols
SymbolMeaningUnit
\(\Delta t\) extra light travel time \(\mathrm{s}\)
\(\Delta d\) extra distance light must travel \(\mathrm{m}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)
\(\text{AU}\) astronomical unit, about the mean Earth–Sun distance (exactly 149 597 870 700 m since 2012) \(\mathrm{m}\)

Source Rømer, O. (1677). A demonstration concerning the motion of light, communicated from Paris, in the Journal des Sçavans, and here made English. Philosophical Transactions of the Royal Society of London 12, 893–894.doi.org/10.1098/rstl.1677.0024 (opens in a new tab)