In the snap of a finger, light manages to circumnavigate the globe 7 times. Light is fast, very fast, but at the same time light is not infinitely fast. In a remarkable experiment performed in the 1670s, the speed of light was measured by the Danish astronomer Ole Romer.
He and others were charged with the seemingly tedious task of writing accurate tables of the orbits of the Galilean moons. These 4 close-in moons of Jupiter are not new, having first been discovered by Galileo about 150 years before Romer arrived on the scene.
Romer, Cassini, and others measured the time it took for a moon to disappear behind Jupiter, or to be eclipsed, and then to emerge again on the other side. The measurements were carried many times when Earth was moving towards Jupiter in its orbit near to a configuration called opposition, and again when Earth was moving away from Jupiter near to the conjunction configuration. Note the measurement near conjunction was much harder to make as it had to be done against a brighter sky. Nevertheless, the astronomers at the time managed somewhat heroically to make such measurements.
When they did, somewhat surprisingly Romer found that the time Io spent in eclipse at opposition was not the same as the time for Io to be in eclipse at conjunction. In fact Io emerged from behind Jupiter sooner at opposition. Romer realized that this difference in the duration of eclipses measured at different locations in Earth’s orbit would have no physical impact on Io, so how could the difference be explained?
In a brilliant insight, he surmised that the difference is owing to the longer travel time for light at greater distances, such that near to conjunction there would be a delay in the duration of the eclipse. He measured this difference in the eclipse duration on the near and far side of Earth's orbit to be 17 minutes (close compared to the 22 minutes we measure today), and from that was able to make the first computation of the speed of light. Remarkably, all this happened more than 130 years before Einstein postulated that the speed of light is a constant.