Rømer's determination of the speed of light was the demonstration in 1676 that light has an apprehensible, measurable speed and so does not travel instantaneously. The discovery is usually attributed to Danish astronomer Ole Rømer, who was working at the Royal Observatory in Paris at the time.
By timing the eclipses of the Jovian moon Io, Rømer estimated that light would take about 22 minutes to travel a distance equal to the diameter of Earth's orbit around the Sun. Using modern orbits, this would imply a speed of light of 226,663 kilometres per second, 24.4% lower than the true value of 299,792 km/s. In his calculations Rømer used the idea and observations that the apparent time between eclipses would be greater when the Earth relatively moves away from Jupiter and lesser while moving closer.
Rømer's theory was controversial at the time that he announced it and he never convinced the director of the Paris Observatory, Giovanni Domenico Cassini, to fully accept it. However, it quickly gained support among other natural philosophers of the period such as Christiaan Huygens and Isaac Newton. It was finally confirmed nearly two decades after Rømer's death, with the explanation in 1729 of stellar aberration by the English astronomer James Bradley.
Background
The determination of east-west positioning (longitude) was a significant practical problem in cartography and navigation before the 1700s. In 1598 Philip III of Spain had offered a prize for a method to determine the longitude of a ship out of sight of land. Galileo proposed a method of establishing the time of day, and thus longitude, based on the times of the eclipses of the moons of Jupiter, in essence using the Jovian system as a cosmic clock; this method was not significantly improved until accurate mechanical clocks were developed in the eighteenth century. Galileo proposed this method to the Spanish crown in 1616–1617 but it proved to be impractical, not least because of the difficulty of observing the eclipses from a ship. However, with refinements the method could be made to work on land.
The Italian astronomer Giovanni Domenico Cassini had pioneered the use of the eclipses of the Galilean moons for longitude measurements, and published tables predicting when eclipses would be visible from a given location. He was invited to France by Louis XIV to set up the Royal Observatory, which opened in 1671 with Cassini as director, a post he would hold for the rest of his life.
One of Cassini's first projects at his new post in Paris was to send Frenchman Jean Picard to the site of Tycho Brahe's old observatory at Uraniborg, on the island of Hven near Copenhagen. Picard was to observe and time the eclipses of Jupiter's moons from Uraniborg while Cassini recorded the times they were seen in Paris. If Picard recorded the end of an eclipse at 9 hours 43 minutes 54 seconds after midday in Uraniborg, while Cassini recorded the end of the same eclipse at 9 hours 1 minute 44 seconds after midday in Paris – a difference of 42 minutes 10 seconds – the difference in longitude could be calculated to be 10° 32' 30". Picard was helped in his observations by a young Dane who had recently completed his studies at the University of Copenhagen – Ole Rømer – and he must have been impressed by his assistant's skills, as he arranged for the young man to come to Paris to work at the Royal Observatory there.
Eclipses of Io
Io is the innermost of the four moons of Jupiter discovered by Galileo in January 1610. Rømer and Cassini refer to it as the "first satellite of Jupiter". It orbits Jupiter once every 42½ hours, and the plane of its orbit is very close to the plane of Jupiter's orbit around the sun. This means that it passes some of each orbit in the shadow of Jupiter – an eclipse.
Viewed from the Earth, an eclipse of Io is seen in one of two ways. Io suddenly disappears, as it moves into the shadow of Jupiter. This is termed an immersion. Io suddenly reappears, as it moves out of the shadow of Jupiter. This is called an emergence. From the Earth, it is not possible to view both the immersion and the emergence for the same eclipse of Io, because one or the other will be hidden (occulted) by Jupiter itself. At the point of opposition (point H in the diagram below), both the immersion and the emergence would be hidden by Jupiter.