Until fairly recent times there was much conjecture and differing of opinions on light and its velocity, many believed such as Jonathen Kepler, a key figure in 17th century astronomical revolution, that light had an infinite speed and travelled everywhere instantly, another key figure this time in mathematics and philosophy Rene Descartes argued that if light had a finite velocity that in events such as a lunar eclipse there would an obvious misalignment. Others however perceived that it was finite, some early philosophers such as Sir Francis Bacon noted that light could have a finite speed but it was too fast to be perceived, previous to this the Iraqi scientist Al-Haytham, famous for his work on the principles of optics in the 10th and 11th century’s discovered light had a finite speed much greater than that of sound.
Galileo made the first attempts at disproving the predominate opinion at the time that light had a finite speed in 17th century by proposing an experiment, at which he would measure the time it took for a flash of light from a lantern to travel about a mile. His experiment failed, light appeared to travel instantaneously between the two points, Galileo was undeterred and maintained that the results did not mean light had an infinite speed but that it must greater than originally thought. Galileo was of course correct as the time it would of taken the light to traverse such a distance would of been in the order of 510-6 s.
The first evidence of a finite speed of light to be obtained was by Ole Rømer, the basis for which were set down by Galileo in the early 17th century who was working on a different problem at the time, the determination of longitude, especially at sea, a project that had been set forth by the king of Spain with the promise of a prize to whomever could manage such a task. He conceived the idea that using a telescope to observe the moons of Jupiter and using them in essence as a cosmological clock from which the time and hence the longitude could be calculated. Unfortunately because of the timetables created by Galileo of Jupiter’s moons eclipses and the difficulty of observing the moons from sea, his idea was impractical.
However several decades later Rømer went to an island community near to which he had studied in Copenhagen to predetermine the islands observatories longitude. There he observed Jupiter’s largest moon ‘Io’ and its eclipses with Jupiter over a period of roughly 8 months, about 140 orbits. What Rømer discovered was that the eclipses did not all last the same period of time, but instead were related to Earths position in its own orbit. It became apparent from the results that when Earths orbit was approaching Jupiter the period of eclipse became shorter and when it was travelling away it became longer. The time predicted by the mathematics involved was too early if Earth was near Jupiter and too late if Earth was far away.
Rømer attributed these discrepancies down to light having a finite speed, when Jupiter was farther away, light would take longer than predicted to travel to Earth so that Io appeared at an later time than predicted, and conversely the opposite would happen when Jupiter and Earth were close together.
The speed of light was not obtained immediately after these readings, in fact it is said in a number of sources that Rømer himself never made any formal predictions of the speed of light, instead others used his figures to create their own estimates. After making his results he joined up with Giovanni Domenico Cassini who also had observed Jupiter’s moons for two years previous to Rømer and had discovered the same discrepancies which he at first contributed to the finite speed of light, Rømer went to work with Cassini in Paris continuing to observe the moons of Saturn and collating their previous results. Strangely Cassini abandoned the idea that light had a finite velocity, Rømer fortunately didn’t and isolated the important results of observations made by him and Cassini between 1971 and 1978, presenting it to the French Academy of Sciences. Reports from the meeting are vague, but the main results are still present. These state that the 40 orbits observed as the Earth moves towards Jupiter are 22 minutes short than the 40 orbits observed when Earth is moving away from Jupiter and hence Rømer concluded that the distance from one side of the earths orbit (2AU) to the other takes 22 minutes for light to cross. Christiaan Huylens a Dutch physicist, mathematician and astronomer used these results and with the astronomical unit which was estimated to be about 140 million kilometres at the time, came up with the value of 2.210-8 .26% away from the current value 310-8 but still a much greater value than any physical phenomenon known at the time. In conclusion Rømer’s attitude towards the nature of light was ahead of is time despite the way most people of the period felt. Consequently many people were unsatisfied with Rømer’s theory and until the observations of James Bradley, an English astronomer who discovered the aberration of light many people still did not believe in Rømer’s belief of a finite speed of light. It was however a revolutionary step to finding the modern value of the speed of light.