How we found the speed of light: it's not infinite!

“Nothing in the universe can travel at the speed of light, they say, forgetful of the shadow’s speed.” -Howard Nemerov

I know many of you are still mad at the night sky because of the full Moon preventing you from seeing the recent, close-by supernova in the Pinwheel Galaxy, at least until the end of the week.

(Image credit: Original source unknown, retrieved from the Rose City Astronomers.)

With the full Moon brightly illuminating your sky (and filling it with light pollution), only the brightest, most compact objects are visible at most locations on Earth.

But there is one object — rising at about 9:30 PM each night, these days — that’s not only visible to the naked eye, but one of the night sky’s grandest sights through any telescope, large or small.

(Image credit: David Richards.)

The planet Jupiter! In fact, those of you with the extraordinary patience to track our Solar System’s largest planet over the course of a few hours will not only have the chance to see Jupiter and its four Galilean moons, you’ll get to see them in action!

(Video credit: YouTube user armichael.)

In particular, the innermost of Jupiter’s Moons, Io, completes one revolution around Jupiter in an incredibly precise 42 hours, 27 minutes, and 33.5047 seconds. (Yes, we really do know it to that accuracy!) Every time Io passes in front of Jupiter — and it does this about four times every week — it casts a shadow onto Jupiter’s surface, creating a solar eclipse.

(Image credit: John Spencer (Lowell Observatory) and NASA.)

But what’s more interesting for our purposes is that every time Io heads behind Jupiter, the gas giant’s mightly shadow plunges its satellites into darkness, causing a lunar eclipse.

This can result, depending on where Earth in is its orbit relative to Jupiter and the Sun, in one of Jupiter’s moon’s seeming to eerily “appear” out of nowhere, some distance away from the edge of Jupiter itself.

(Animation credit: Robert J. Modic, over a mere 10-minute timespan! Apologies to those with slow connections; this is a 3.2 MB animation.)

This is just geometry at work here, of course. By time the 1670s came around, it was universally recognized (among astronomers, at any rate) that the planets of our Solar System all orbited the Sun, with the Earth being an inner (and hence faster) planet as compared to Jupiter.

(Image credit: Ole Rømer’s notebook, sketch from 1676!)

During six months out of the year, the Earth would be approaching Jupiter (at point B), for example, at the points F and G. When this happens, whenever one of Jupiter’s moons reaches point C, above, it disappears into Jupiter’s shadow.

During the other six months, the Earth recedes away from Jupiter, for example, at points L and K. During this time, whenever one of Jupiter’s moons reaches point D, it appears to emerge from Jupiter’s shadow.

However — and here’s the interesting part — it appears to take longer for a moon, like Io, to emerge from Jupiter’s shadow when you’re at point K as compared to point L! And by the same token, it appears to take longer for a moon to plunge into Jupiter’s shadow when you’re at point F as compared to point G! What gives?

In the early 1600s, it was known that the speed of light was very, very fast, but it wasn’t known whether it was infinitely fast or not. The only experiment done to measure it was Galileo’s experiment in 1638, which I call the Beacon of Gondor experiment.

(Image credit: Flickr user fallen petals.)

One night, Galileo sent his assistant out far across the fields, and ordered him to stand at the crest of a hill. Galileo would be atop a distant hill. Galileo would unveil his lantern, so that his light would shine brightly atop the hill, and as soon as the assistant saw the light, he would then unveil his lantern. Galileo reasoned that he would be able to measure the distance between his assistant and himself, as well as the time it took for the light to travel round-trip, and hence he’d be able to figure out the speed of light.

Well, considering that the speed of light is around 300,000 kilometers per second, you can imagine what the results of this experiment, conducted from two hills across a field, were.

Very, very fast, was Galileo’s conclusion. But was it infinitely fast, or was it simply too fast to measure between two humans on Earth?

For a couple of generations, the question was unsettled. But in the 1670s, Danish astronomer Ole Rømer not only settled it, he became the first person to measure what the speed of light actually was. All you need to know is where the Earth, Jupiter, and the Sun are positioned, which we knew in great detail thanks to the work of Kepler and Brahe nearly a century prior. Here’s what you do.

Above is where the Earth, Jupiter, and the Sun were positioned back in June of this year; this corresponds to point “F” in Rømer’s diagram from his sketchbook. What you can do is measure when Io appears to complete its transit of Jupiter (when it finishes passing in front of it), and accurately time how long it takes before it plunges into Jupiter’s shadow.

(Image credit: Jim Ferreira.)

Then, wait a few months, until the Earth is at a closer position to Jupiter, but still makes the same angle it did all those months ago when you made your earlier observation. Today, for example, could correspond to point “G” in Rømer’s diagram.

(Above image made from a screen capture using this orrery application.)

Do the exact same thing; time how long from the end of Io’s transit until it plunges into Jupiter’s shadow. If you’ve done your measurements accurately and correctly, you will find — this time — that it was several minutes shorter than it was a few months ago!

Why would this happen? Let’s go back to Rømer’s sketch.

The light emitted by Io, at point C, is the last bit of light we’ll be able to see from it before the lunar eclipse begins. If that light traveled infinitely fast, then someone at point G would get the light at the same time as someone at point F, and there would be no difference.

But if the speed of light were finite, that last bit of emitted light would arrive at point G earlier than at point F! If you can determine the distance between point F and point G, and you can measure the time difference between when the moon plunges into shadow (at point C), you can measure the speed of light!

(Of course, you can do it just as easily with the moon re-emerging from Jupiter’s shadow — at point D — during the other six months of the year.)

In the centuries since, of course, we’ve refined our measurements of the speed of light, and we’ve even measured the speed of gravity, which turns out to be the same. It turns out that the original, 1676 measurement was low by about 25%, mostly due to errors in the Earth-Sun distance.

(Image credit: Steve Hamilton.)

You can do this yourself, with any of Jupiter’s four Galilean satellites, with simply a telescope and a clock, and some careful observations over the course of a year. If you’d like to get started, tomorrow night, September 13th, at about 11:24 PM Pacific Daylight Time (sorry folks, it’s my time zone), you can see Jupiter’s moon Europa plunge into shadow off of its eastern limb.

And that’s how we found that the speed of light is not only finite, but were able to measure what it actually was! Not bad for 300 years ago! Read the comments on this post…

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