How to Measure the Speed of Light With Lanterns, Wheels, and Planets

lasers-ftLIGHT TRAVELS REALLY fast. It’s so fast that it’s quite difficult to determine a value for the speed of light. But it’s not just the speed of light that is important: This value also appears in other places like the energy to mass equivalence principle (E = mc2). Here are three different methods that have been used to calculate this constant.
Hills and Lanterns

When Galileo’s name comes up, most people think about his contributions to observational astronomy. However, he did lots of other stuff including investigating the speed of light. During his time, many people considered light just to be some instantaneous thing that didn’t have a speed.

Here is Galileo’s method to measure the speed of light. Take two lanterns at night and separate them by a large distance but not too far that you can’t see them. The two lanterns are held by two different people and they have a shutter so that you can essentially turn them on and off.

Of course, this isn’t a very useful method to measure the speed of light. Let’s say that I can put a lantern 1 kilometer from the observer and it can still be seen. The time it takes light to travel there and back is insignificant compared to the human reaction time at the other end. Oh, add to this the problem of keeping accurate time. This method might work to measure the speed of sound, but not for light. In the end, Galileo’s value for the speed of light was “at least really fast.”
Moons of Jupiter

Of Jupiter’s many moons, it has four large ones that you can actually see with a nice pair of binoculars. Even better is the fact that these moons have very regular and predictable orbits. In fact, you can use the motion of the moons of Jupiter to measure the speed of light.

This is exactly what Ole Roemer did in 1676. In particular, he looked at the moon Io in an effort to possibly use the moon’s orbit as a sort of navigational clock (accurate clocks weren’t so easy to build). Roemer measured the orbit by looking at the time it takes from one Jupiter eclipse to the next eclipse. He found that the orbit of Io around Jupiter took less time when the Earth was closer to Jupiter.

If you look at the difference in distance between the Earth when it is closest to Jupiter and when it is farthest, the distance is equal to the diameter of the Earth’s orbit. When the Earth is farther away, it takes light from Io longer to get to Earth resulting in a longer apparent orbital period of Io. So, just measuring the change in apparent period and the change in distance gives an estimate for the speed of light. This is exactly how Roemer estimated the speed of light.

Jupiter is much farther away than two hills with lanterns, such that you can get a noticeable time difference. Still, this depends on an accurate value for the Earth’s orbit and a nice clock. Roemer’s value for the speed of light was still a bit off of the accepted value.
Rotating Toothed Wheel

What the heck is a toothed wheel? It’s a wheel with little squares sticking out of it that look like teeth. Here’s how it works. You set up the wheel so that it is vertical and spinning. Next shine a light through one side of the wheel and aim it at a distant mirror. The light reflects off this mirror and back to the opposite side of the wheel where you can look at the reflection.

The idea is to adjust the speed of the spinning wheel until you can’t see the reflected light at all. Perhaps this is easier to see if I replace the wheel with a long linear strip of teeth.

Now imagine that the teeth let a short pulse of light through before blocking it again. This light travels all the way to the mirror and back to the teeth. What if in that time, the teeth have moved down enough to block the eye? Then then when the tooth is no longer blocking the eye, it is blocking the light. So by knowing the speed of the teeth and the size of the teeth, you can get a value for the blocking time. With the distance to the mirror and back you can calculate the speed of light.

This is essentially what Hippolyte Fizeau did in 1848. His value for the speed of light was only about 5 percent too high (compared to the current accepted value of 3.0 x 108m/s). Leon Foucault later went on to make a better version of this that used a spinning mirror, but I think Fizeau’s apparatus is a little bit easier to understand.

Of course there are still other methods for measuring the speed of light, but these are my three favorite

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