T87. Determining the Speed of Light

DETERMINING THE SPEED OF LIGHT by Fredric M. Menger, Emory University, Atlanta, GA USA

In 1675 Ole Römer, a Danish astronomer, calculated that the speed of light is 186,000 miles per second. How was he able to determine this important number? It was known at the time, from the findings of French astronomers, that the distance of the Earth from the Sun is 93 million miles. This means that the distance between the Earth’s positions from one side of the Sun to the other is 186 million miles (see points A and B in the scheme below; since the scheme is not drawn to scale, the Sun and planets are drawn much too large relative to the mileage distance). Now Jupiter, orbiting the Sun far away from Earth, has a satellite (a moon) called Io. When Io was observed from Earth in position A, Io was seen to disappear when eclipsed by Jupiter (in position C). Io then reappears gradually, only to totally disappear again 42 hours later. Thus, Römer knew that Io requires 42 hours to complete one revolution around Jupiter. But, and this is important, when observed from Earth at position B, the time for Io’s revolution was determined to be 1000 seconds longer than 42 hours. Why the time difference? It was reasoned that the time difference is related to the 1000 seconds that light reflected from Io needs to travel the extra 186 million miles to position B relative to position A. Clearly, the speed of light is 186 x 10⁶ miles/1000 seconds or 186,000 miles per second.

Scheme. Schematic showing Earth in positions A and B that are 186 million miles apart. The diameter of the Sun is insignificant relative to this long distance (the schematic, which is not to scale, portrays the Sun and Earth as much too large). Jupiter has a moon Io that rotates around Jupiter in 42 hours (as observed from Earth at position A) or 42 hours + 1000 seconds (as observed from Earth at position B). From these data one can calculate the speed of light as explained in the essay.