How The Speed of Light Was Measured in 1676

How The Speed of Light Was Measured in 1676:

Roemer measured the speed of light by timing eclipses of Jupiter's moon Io. In this figure, S is the Sun, E1 is the Earth when closest to Jupiter (J1) and E2 is the Earth about six months later, on the opposite side of the Sun from Jupiter (J2). When the Earth is at E2, the light from the Jupiter system has to travel an extra distance represented by the diameter of the Earth's orbit. This causes a delay in the timing of the eclipses. Roemer measured the delay and, knowing approximately the diameter of the Earth's orbit, made the first good estimate of the speed of light. Illustration by Diana Kline.

In 1676, the Danish astronomer Ole Roemer (1644–1710) became the first person to measure the speed of light. Until that time, scientists assumed that the speed of light was either too fast to measure or infinite. The dominant view, vigorously argued by the French philosopher Descartes, favored an infinite speed.
Roemer, working at the Paris Observatory, was not looking for the speed of light when he found it. Instead, he was compiling extensive observations of the orbit of Io, the innermost of the four big satellites of Jupiter discovered by Galileo in 1610. By timing the eclipses of Io by Jupiter, Roemer hoped to determine a more accurate value for the satellite’s orbital period. Such observations had a practical importance in the seventeenth century. Galileo himself had suggested that tables of the orbital motion of Jupiter’s satellites would provide a kind of “clock” in the sky. Navigators and mapmakers anywhere in the world might use this clock to read the absolute time (the standard time at a place of known longitude, like the Paris Observatory). Then, by determining the local solar time, they could calculate their longitude from the time difference. This method of finding longitude eventually turned out to be impractical and was abandoned after the development of accurate seagoing timepieces. But the Io eclipse data unexpectedly solved another important scientific problem—the speed of light.
The orbital period of Io is now known to be 1.769 Earth days. The satellite is eclipsed by Jupiter once every orbit, as seen from the Earth. By timing these eclipses over many years, Roemer noticed something peculiar. The time interval between successive eclipses became steadily shorter as the Earth in its orbit moved toward Jupiter and became steadily longer as the Earth moved away from Jupiter. These differences accumulated. From his data, Roemer estimated that when the Earth was nearest to Jupiter (at E1), eclipses of Io would occur about eleven minutes earlier than predicted based on the average orbital period over many years. And 6.5 months later, when the Earth was farthest from Jupiter (at E2), the eclipses would occur about eleven minutes later than predicted.
Roemer knew that the true orbital period of Io could have nothing to do with the relative positions of the Earth and Jupiter. In a brilliant insight, he realized that the time difference must be due to the finite speed of light. That is, light from the Jupiter system has to travel farther to reach the Earth when the two planets are on opposite sides of the Sun than when they are closer together. Romer estimated that light required twenty-two minutes to cross the diameter of the Earth’s orbit. The speed of light could then be found by dividing the diameter of the Earth’s orbit by the time difference.
The Dutch scientist Christiaan Huygens, who first did the arithmetic, found a value for the speed of light equivalent to 131,000 miles per second. The correct value is 186,000 miles per second. The difference was due to errors in Roemer’s estimate for the maximum time delay (the correct value is 16.7, not 22 minutes), and also to an imprecise knowledge of the Earth’s orbital diameter. More important than the exact answer, however, was the fact that Roemer’s data provided the first quantitative estimate for the speed of light, and it was in the right ballpark.
Roemer returned to Denmark in 1681, where he pursued a distinguished career in both science and government. He designed and built the most accurate astronomical instruments of his time and made extensive observations. He later served as mayor and prefect of police of Copenhagen and ultimately as head of the State Council. Roemer is remembered today of course not for his high political office but for being the first person to measure the speed of light.