Rømer's Speed of Light

In 1676, Danish astronomer Ole Rømer made history by showing that light has finite speed. He is often credited as supplying the first estimate for the speed of light, but this isn't really true. Based on his observation of Io, he surmised that it takes 22 minutes for light to traverse the diameter of Earth's orbit, but that's as far as he went; there's no actual number for velocity anywhere in his paper. The diameter of Earth's orbit wasn't precisely known at the time, moreover there were plenty of error factors in his measurements.

When the Doppler effect is mentioned in the context of light, it usually refers to a change in the perceived frequency of the photons, i.e. color shifting. However, the Doppler effect can be applied to _any_ periodic phenomenon. If an observer is approaching a periodic event source, the perceived interval of the event is shorter than its actual interval.

The start and stop of Io's periodic eclipse can be visualized as spherical wave fronts that emanate from the Jovian system. If an observer lies between these two wave fronts, they perceive Io to be eclipsed. This is depicted in the following applet.

Although the Doppler effect had not yet been coined, it's basically the premise of Rømer's argument. He carefully noted each time that Io enters an eclipse (which happens every other Earth day or thereabouts), then analyzed how its perceived orbital period changes throughout the year, according to whether or not Earth is approaching Jupiter.

Interestingly, tidal forces between Io and the other Galilean moons also cause quite a bit of variation in Io's orbital period, but luckily this effect did not cause enough error to make Rømer lose his place in history.

The following vignette lets you play with time in the year 2021.

• The top canvas shows how the positions of Earth, Jupiter, and Io are roughly related. Not to scale!
• The bottom canvas depicts Jupiter's moons as seen from Earth, with a built-in time delay that accounts for the speed of light. This includes Io, Europa, Ganymede, and Callisto.

@prideout
August 2024

• I used the astronomy-engine library, written by Don Cross, to determine absolute positions of various celestial bodies.
  (github link)
• English Translation of Rømer's paper, dated 1677 - 1678.
  (download pdf)
• An analysis of Rømer's paper by James H. Shea, published in 1998.
  (download pdf)