In the seventeenth century, as Europeans stepped up their exploration of the distant regions of the globe, the determination of longitude at sea was a major problem. King Philip II of Spain had offered a prize as far back as 1567 to anyone who could provide a solution, and in 1598 his successor Philip III increased the reward to 6,000 ducats and a pension.
In 1617, Galileo Galilei proposed a method based on observations of the moons of Jupiter. By observing the eclipses of the moon Io by the planet (Jupiter), it was possible to work out the position of the Earth in its daily rotation, thus the time of day, and from this the longitude. (Io orbits Jupiter very 42.5 hours, or just under four times per week.)
But Galileo's timetables weren't very accurate, and this, combined with the difficulties of making observations from a ship, meant that Galileo's method proved impracticable. In the meantime, however, while making observations along these lines, the Italian astronomer Giovanni Cassini (working at the French Royal Observatory in Paris) noticed that when the Earth was moving towards Jupiter, the intervals between the eclipses got shorter; and vice versa. He suspected that this was because the light from Jupiter (and Io) was taking a finite time to reach the Earth; but rather oddly, he didn't follow it up.
The Danish astronomer Ole Rømer (sometimes known as Olaus Rømer) made similar observations to Cassini's, from near Copenhagen. By comparing their observations, Cassini and Rømer were able to calculate the difference in longitude between their respective observatories. But it was Rømer who used his figures to calculate that light took approximately 22 minutes to cross the diameter of Earth's orbit around the Sun.
Rømer published his findings in 1677, and the strict result of his observations was that the speed of light is 7,600 times faster than the speed at which Earth orbits the Sun. The actual figure is 10,100. Rømer was aware that his figure was only an approximation, as the distance from Earth to Jupiter was not known accurately at the time.
Rather oddly, Rømer made no attempt to translate this into standard units. This was left to the Dutch scientist Christiaan Huygens who, using Rømer's figures (very soon after they were published), calculated the speed of light to be 220,000 metres per second.
In 1728, the English astronomer James Bradley was investigating what he termed the 'aberration of light', which causes stars to appear to change their positions through the year. He correctly theorised that this was due to the variation in the angle at which the light from the star falls on Earth, due to Earth's own movement in space. Using his observations, Bradley calculated the speed of light to be 301,000 metres per second.
The actual value is a fraction under 300,000 metres per second (or 186,000 miles per hour).
The mathematics behind all this theory is quite complicated. Wikipedia attempts to explain it, but the most readable explanation that I have found is here.
(Neither Galileo, Cassini nor Rømer was able to claim Philip III's prize. As readers of this website will no doubt be aware, it was the English horologist John Harrison who effectively solved the problem of longitude by inventing the marine chronometer. He was grudgingly awarded various sums by the Board of Longitude, and Wikipedia reckons that he and his family received a total of £23,065 between 1737 and 1773.)
© Macclesfield Quiz League 2017