Everyone knows the speed of light in a vacuum is approximately 186,000 miles per second, but how did physicists figure this out?
From here.
I’d known about the first quote in Q.E.D.'s post – the man’s name is also given as Ole Romer, with the second o sometimes umlauted. Interestingly, since the Earth’s orbit is 93,000,000 miles in radius, and therefore 186,000,000 miles in diameter, Jupiter is almost exactly 1,000 light-seconds closer at opposition (when we’re lined up Sun-Earth-Jupiter) than at conjunction with the Sun (when we’re lined up Earth-Sun-Jupiter).
The Moon is 1.33 light-seconds from Earth – which produced brief delays of 2.67 seconds in radio communications with the Apollo astronauts.
http://physics.about.com/cs/opticsexperiments/a/290903_2.htm
Now anyone can measure this speed - with chocolate and a microwave oven!
The only equipment you need for this experiment is a microwave, a ruler and chocolate, cheese or any other food that melts. Remove the turntable from the microwave and replace with chocolate on a plate (so the plate does not rotate), and heat until it just starts to melt - about 20 seconds, depending on the power of the oven. There will be some melted hot spots and some cold solid spots in the chocolate. The distance between the hot spots is half the wavelength of the microwaves, and the frequency of the microwaves will often be printed on the back of the oven. The speed of light is equal to the wavelength multiplied by the frequency of an electromagnetic wave (microwaves and visible light are both examples of electromagnetic waves). So from this simple experiment, and some easy math, you can work out the speed of light from Milky Way Magic Stars®!
Even easier, any oven you’re likely to come into contact with will run at 2450 MHz. There are commercial microwave ovens, used for such things as curing epoxy, that run at 915 MHz, but you’ll never see these outside of an industrial setting.
I alternately see Roemer’s experiment given as a measure of the speed of light or as a measure of the AU (the distance from the Sun to the Earth). Today’s value for the AU is determined using the speed of light, so it wouldn’t do all that much good. (Polycarp mentions that it’s almost exactly 500 light-seconds. In fact, it’s almost exactly 499 light-seconds, if you like that sort of thing.)
Here’s my question. In order to get c from Roemer’s Method you need to know the AU, and Q.E.D.'s link suggests they did, to an order of magnitude, anyway. Does anyone know how they did that? According to my research, Cassini was working around the same time (1670s) to determine the AU via Martian parallax, but this method did not prove fruitful until photographic observations were carried out in 1879.
Over a year, the Earth’s distance to the Sun varies by about 3 percent–so that would be about 15 light-seconds difference from aphelion to perihelion.
That’s true, but that wouldn’t be hard to correct for, even if Roemer’s time, if you were willing to sit down with pen and paper and spend a few hours at it.
Here is some information on this, as well as some links to explore.
About 15-20 years ago there was very interesting article in American Journal of Physics. It surveyed several physics texts, looking for the value of the speed of light determined by Roemer. There was quite a confusion of values. So they went back to Roemer’s own work and found…
…that Roemer never actually declared a value for the speed of light. The article claimed that Roemer wanted to prove that the speed was finite, but didn’t actually determine a value. It sounds a little squirrely (why not actually measure the value, once you’re set up? Or at least declare a range of values?), but the AJP isn’t a crank publication.
We measured it by using a very quickly spinning mirrored thing, (modified drill?), and a laser beam. We measured the angle of reflection and worked backwards w/ the speed of rotation.
Ever heard of the Michelson-Morley Experiment to detect the
speed of light?
Actually, this link is much nicer: Michelson-Morley Experiment
It is amazing that they could measure time with any kind of accuracy in 1676. What type of time piece did he use?
Quote:
The first successful measurement of c was made by Olaus Roemer in 1676. He noticed that the time between the eclipses of the moons of Jupiter was less as the distance away from Earth is decreasing than when it is increasing.
Well, I already knew all of that, except for the actual value that Cassini got. I was skeptical that Cassini could have measured the parallax to Mars accurately without a camera - in ideal conditions it’s only 34 arcsec, and there’s a lot of room for error - but since he got a pretty good value, I guess I can’t doubt it. Anyway, it sounds like, before 1672, there was no real value for the AU, and it was only four years later that Roemer did his thing.
Read Longitude by Dava Sobel. Clocks were pretty precise at that time, allready!
Especially when you had the luxury of a big, bulky clock sitting in one place on terra firma (which an astronomer would have). The challenge was just in making precise clocks that you could put on a ship.
T. Mehr, the Michelson-Morley experiment didn’t measure the speed of light, it compared the speed of light in different directions. But Michelson working without Morley did do several experiments to measure the speed of light, which were (at the time) the most precise ever. If I remember correctly, he used the spinning mirror method.
As for the microwaved chocolate method, I wouldn’t call it an experimental determination, since you have to look up the frequency of the microwave. Surely, there was an experiment of some sort done by the microwave manufacturer to calibrate that, but that experiment is not of the home kitchen variety, and in fact probably used prior knowledge of the speed of light.
Another method to determine the speed of light is to separately measure the constants epsilon[sub]0[/sub] and mu[sub]0[/sub], which describe the strength of the electric and magnetic forces. Then, you can use Maxwell’s equations to show that c = 1 / sqrt(epsilon[sub]0[/sub]*mu[sub]0[/sub]).
Cal’s on the right track for an answer to Achernar’s question, but the history is a little bit more surprising than he remembers. While the textbook mythology would have us believe that Romer was proving that the speed of light was finite, the actual point of his paper was that it was very large. For it was already a widely accepted idea that light wasn’t infinitely fast. Once you realise that, while superficially instantaneous, sound takes a measurable time to get from place to place, it’s fairly natural to conclude that light might do so as well. So you have Galileo with guys and lanterns on hilltops trying to measure that speed. Romer’s point is that you’ll have to do a lot better than that.
Both his original 1676 paper (in French) and the 1677 translated reprint are available from here. The main conclusion is that light can cross the diameter of the Earth in no more than a second. That’s much faster than anybody in the period could hope to measure on the ground.
To get this far, he still has to have some minimum estimate for how large an A.U. is. He could have appealed to Cassini and Flamsteed’s measurements of parallax during the opposition of Mars in 1672, but it looks as if he didn’t. But he didn’t need to. Writing in his 1712 paper proposing using transits of Venus, Halley begins by nicely reviewing previous estimates of the A.U. Interestingly, he doesn’t mention Cassini or Flamsteed either. Instead, he describes the pretty neat arguments people had been using to guess plausible values. Halley’s own guess by these methods is not bad: it’s about 70% of the actual answer.
Back of the envelope suggests Romer is assuming one of the older, smaller estimates. Possibly even Ptolemy’s.
Huygens does turn the issue round in his Treatise on Light (1690; Dover, 1962), pointing out that Romer’s paper, which he quotes almost verbatim in its entirity, implies that light must have a finite speed.