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How a moon of Jupiter measures light speed

Q: The speed of light is 300,000 km/s. How was it determined? (Jason, Kuching, Malaysia)

A: Since the 1970's (when we developed stable lasers and accurate cesium clocks), we have calculated light speed from laser measurements. In 1972, Kenneth M. Evenson et al measured its speed as 299,792.456 km/s within plus or minus 0.001 km/s. See the table below for more measurements.

Io (the black dot is Io’s shadow) as she sweeps across the face of Jupiter. [NASA]

But we first calculated light speed over three hundred years ago using a telescope, a simple clock with no minute hand (accurate at best to minutes), and planetary knowledge.

In 1676, a Danish astronomer, Ole Rrmer, meandered into the calculation while puzzling over strange data. Intent on watching Jupiter’s moon, Io, orbit around its giant planet — he noticed something odd. He clocked Io orbiting Jupiter in 42.5 hours when Earth was close to Jupiter. He knew every orbit should take the same time because the length of the orbit was always the same. So, he clocked the time from when Io last exited Jupiter’s shadow — fully expecting it would take 42.5 hours each time. But, as Earth slowly moved away from Jupiter over successive weeks and months, Io didn’t exit in 42.5 hours. Instead, Io took more time! Why?

He deduced he was seeing Io as it was at an earlier time — before light made the trip from Jupiter to his eyes on Earth. Light is the messenger bringing him the information (image) of the eclipse event and it takes time for the messenger to make the trip. If the messenger arrives late, he figured that meant the messenger had farther to go.

So far, so good, he thought, because sometimes Jupiter’s reflected light does have farther to go to reach him on Earth. Jupiter takes 12 years to complete one orbit around the Sun. So, sometimes light has to travel farther to get from Jupiter to Earth. See the figure. In fact, every 13 months, Earth is on the other side of the Sun from Jupiter (in Position 2 of the figure). Therefore, the messenger (light) from Jupiter has to travel the diameter of Earth’s orbit farther than it does when Earth is in Position 1, nearest to Jupiter.

As Earth (blue circles) travels about the Sun, light from Jupiter (colorful circle) has to go varying distances to reach an observer on Earth. Position 1 is the nearest and Position 2 is the farthest distances. Light goes a distance equal to Earth’s orbit diameter farther to reach Position 2 than to Position 1. [From Physics 2000, University of Colorado at Boulder, used with permission.]

Indeed, when Earth was farthest from Jupiter (one orbit diameter away), he recorded his longest time. From this information, Rrmer deduced the time it took light to travel across Earth’s orbit must be about 22 minutes. (Modern measurements give less than 17 minutes.) Dividing an Earth-orbit diameter by the transit time across Earth’s orbit gave him the first measurement of light speed — about 137,000 miles per second (220,000 km/s).

This value was far from the one we use today because nobody knew Earth’s orbit diameter accurately back then. But his technique was good. In September 1676, he predicted that an eclipse on November 9 would be 10 minutes late. Sure enough! His skeptical colleagues at the Royal Observatory in Paris were surprised and victory was sweet.

"One of the great things about Rrmer's work is how it used simple equipment to solve a problem that defeated many of his predecessors," says Robert Massey, astronomer of the Royal Observatory Greenwich in London.

Speaking of Jupiter’s moons, "when Galileo saw them moving he got into trouble with the Catholic church as it directly contradicted the idea that the Earth was the center of movement for the Universe.

"And later in the 17th century, navigators used timings of the moon's eclipses as a celestial clock - by comparing them with local time they could find their longitude."