Centuries ago, how could scientists even begin to estimate the speed of light, and be so accurate?

Answer 1

Measurement of the speed of light
Isaac Beeckman proposed an experiment (1629) in which one would observe the flash of a cannon reflecting off a mirror about one mile away. Galileo proposed an experiment (1638), with an apparent claim to having performed it some years earlier, to measure the speed of light by observing the delay between uncovering a lantern and its perception some distance away. This experiment was carried out by the Accademia del Cimento of Florence in 1667, with the lanterns separated by about one mile. No delay was observed. Robert Hooke explained the negative results as Galileo had: by pointing out that such observations did not establish the infinite speed of light, but only that the speed must be very great. Descartes criticised this experiment as superfluous, in that the observation of eclipses, which had more power to detect a finite speed, gave a negative result.

Rømer's observations of the occultations of Io from Earth.The first quantitative estimate of the speed of light was made in 1676 by Ole Rømer, who was studying the motions of Jupiter's satellite Io with a telescope. It is possible to time the orbital revolution of Io because it enters and exits Jupiter's shadow at regular intervals (at C or D). Rømer observed that Io revolved around Jupiter once every 42.5 hours when Earth was closest to Jupiter. He also observed that, as Earth and Jupiter moved apart (as from L to K), Io's exit from the shadow would begin progressively later than predicted. It was clear that these exit "signals" took longer to reach Earth, as Earth and Jupiter moved further apart. As a result of the extra time it took for light to cross the extra distance between the planets, which had accumulated in the interval between one signal and the next. Quite as in the familiar Doppler effect. The opposite is the case when they are approaching (as from F (not shown but opposite of K) to G). On the basis of his observations, Rømer estimated that it would take light 22 minutes to cross the diameter of the orbit of the Earth (that is, twice the astronomical unit); the modern estimate is closer to 16 minutes and 40 seconds.

Around the same time, the astronomical unit was estimated to be about 140 million kilometres. The astronomical unit and Rømer's time estimate were combined by Christiaan Huygens, who estimated the speed of light to be 1000 Earth diameters per minute. This is about 220,000 kilometres per second (136,000 miles per second), well below the currently accepted value, but still very much faster than any physical phenomenon then known.

Isaac Newton also accepted the finite speed. In his book "Opticks" he, in fact, reports the more accurate value of 16.6 Earth diameters per second, which it seems he inferred for himself (whether from Rømer's data, or otherwise, is not known). The same effect was subsequently observed by Rømer for a "spot" rotating with the surface of Jupiter. And later observations also showed the effect with the three other Galilean moons, where it was more difficult to observe, thus laying to rest some further objections that had been raised.

Even if, by these observations, the finite speed of light may not have been established to everyone's satisfaction (notably Jean-Dominique Cassini's), after the observations of James Bradley (1728), the hypothesis of infinite speed was considered discredited. Bradley deduced that starlight falling on the Earth should appear to come from a slight angle, which could be calculated by comparing the speed of the Earth in its orbit to the speed of light. This "aberration of light", as it is called, was observed to be about 1/200 of a degree. Bradley calculated the speed of light as about 298,000 kilometres per second (185,000 miles per second). This is only slightly less than the currently accepted value. The aberration effect has been studied extensively over the succeeding centuries, notably by Friedrich Georg Wilhelm Struve and Magnus Nyren.

Diagram of the Fizeau-Foucault apparatus.The first successful measurement of the speed of light using an earthbound apparatus was carried out by Hippolyte Fizeau in 1849. Fizeau's experiment was conceptually similar to those proposed by Beeckman and Galileo. A beam of light was directed at a mirror several thousand metres away. On the way from the source to the mirror, the beam passed through a rotating cog wheel. At a certain rate of rotation, the beam could pass through one gap on the way out and another on the way back. But at slightly higher or lower rates, the beam would strike a tooth and not pass through the wheel. Knowing the distance to the mirror, the number of teeth on the wheel, and the rate of rotation, the speed of light could be calculated. Fizeau reported the speed of light as 313,000 kilometres per second. Fizeau's method was later refined by Marie Alfred Cornu (1872) and Joseph Perrotin (1900).

Leon Foucault improved on Fizeau's method by replacing the cogwheel with a rotating mirror. Foucault's estimate, published in 1862, was 298,000 kilometres per second. Foucault's method was also used by Simon Newcomb and Albert A. Michelson. Michelson began his lengthy career by replicating and improving on Foucault's method.

In 1926, Michelson used a rotating prism to measure the time it took light to make a round trip from Mount Wilson to Mount San Antonio in California. The precise measurements yielded a speed of 186,285 miles per second (299,796 kilometres per second).

Answer 2

Hi. The moons of Jupiter were in orbits that were well observed. It was noticed that the moons were in the wrong place when the planet was near us as opposed to when it was far away ( nearly opposite the sun). By calculating the time and realizing that the change in time was due to the extra distance the light had to travel, they were able to get a good estimate of light's speed.

Answer 3

there are some ways using geometry. by it won't give u the exact value

Answer 4

my opinion, is as long as mankind exsists, science will always be wrong. everything we r learning now will be wrong in 4000 years cuz of scientific development

Answer 5

part of the answer is that they were (and still 'are') very smart people ...