The moons of Jupiter and the speed of light

Recently, I was setting up my telescope to image the great planet Jupiter. I was interested in capturing an eclipse of one its largest moons, Io. Everything was ready, all the batteries were charged, the telescope was aligned and tracking the planet, but there was a problem. The eclipse just wasn’t happening. My computer programme predicted it to start at 21:10 on the 12th March 2017, but nothing happened. I was more than surprised, my computer is normally accurate to the second. So I checked the settings, the time is internet controlled so no problem there, the computer showed other stars in their correct positions so I knew it was not having problems with other parts of the sky. Then at about 21:48, Io started to cast a dark circle on Jupiter. I was amazed, I have never seen a total eclipse on Earth but I can now see one on Jupiter. But why was it more than 30 minutes late? It turns out that my confusion was shared by astronomers in the 17th century and, in an effort to explain the discrepancies of Io’s eclipse times, they inadvertently measured the speed of light.

It was the 17th century astronomers Giovanni Domenico Cassini, Ole Rømer and Jean Picard (not from Star Trek) who first studied the eclipses of Io on Jupiter whilst trying to solve the famous longitude problem: before the invention of accurate clocks, there was little way of knowing how far east or west you were sailing from a given location (normally Paris or London). Galileo himself proposed to use the predicable orbits of Jupiter’s moons to calculate the time on Earth, which can then be used to calculate longitude.

Ole Rømer (left) and Giovanni Cassini (right). Along with Jean Picard these pioneering 17th century astronomers observed and studied hundreds of Jovian eclipses. (Wikipedia Commons)

Unsurprisingly, this proved too difficult a task to do on a moving ship with the primitive optical equipment available at the time. On land, however, this method could be used to improve maps and navigation. So Cassini and Rømer set to work. They observed hundreds of Jovian eclipses over several months and were able to determine the difference in longitude between Paris and their location. Unfortunately, there was a problem; after accurately calculating the orbit of Io, Cassini found that sometimes during the year, eclipses were occurring earlier while at other times eclipses  happened later than predicted. Cassini logically surmised that light had to travel at a finite speed instead of instantaneously spanning the distance from Jupiter to Earth. For instance, when the Earth and Jupiter are on near opposite sides of the Sun, the light traveling from Jupiter will take longer to reach Earth (around 54 minutes). This causes the Io eclipses to appear delayed. When the Earth is between the Sun and Jupiter (a period called Opposition), then light from Jupiter takes only about 37 minutes to reach Earth making eclipses of Io happen earlier than expected.

An eclipse of Io imaged by my myself on 12-13/03/2017. The Io eclipse cases a dark spot on Jupiters northern cloud band. The delay of this event caused by the speed of light prompted me to write this post! (My own work)

Strangely, Cassini never followed up his discovery, Rømer continued observing and recording Io eclipses and defined an equation that related the delay caused by the speed of light to the angle between Earth and Jupiter. However, it would not have been possible to publish an actual speed of light because the distances between the planets were not known then. Interestingly, Rømer could have shown the speed of light as a ratio of Earth’s orbital speed…but for some reason he didn’t. It was another famous astronomer, Christian Huygens, who took that credit. He used Rømer’s detailed observations and formula to define the speed of light as 7600 times faster than Earth’s orbital speed.  This equates to a speed of 226328 km/s which is only 25% lower than the true value of light speed.

Christian Huygens, a leader in 17th century science. He was the first person to define the speed of light using the eclipses of Io. (Wikipedia commons)

This was the first time a universal constant had been calculated quantitatively and since then the speed of light has played a huge role in James Clerk Maxwell’s theory of electromagnetism and Einstein’s theories of relativity. But for anyone peering into the night sky, the work of these great men more than 300 years ago shows us that starlight is old…and by looking at it we are looking back in time. We see Jupiter as it was 40-50 minutes ago, the nearest star 4 years ago and the relatively nearby Andromeda galaxy 2.56 million years ago. Not bad for 17th century science.

I think next time I’m sitting by my telescope waiting for an Io eclipse, I’ll be a bit more appreciative of the significance that 30 minute delay had on our understanding of the universe.

Post by: Dan Elijah.

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