Time-Bound
Roemer measures light speed
Soon after the invention of the telescope, Galileo discovered the four largest moons of Jupiter. Subsequently many astronomers made careful observations of those moons, and already by the 1660's detailed tables of their movements had been developed by Borelli (1665) and Cassini (1668). Naturally these tables were based mainly on observations taken around the time when Jupiter is nearly "in opposition", which is to say, when the Earth passes directly between Jupiter and the Sun, because this is when Jupiter appears high in the night sky. The orbital periods of Jupiter's four largest moons were found to be 1.769 days, 3.551 days, 7.155 days, and 16.689 days, and these are very constant and predictable, like giant clockwork. However, by the 1670's people began to make observations of Jupiter's moons from the opposite side of the Earth's orbit, i.e., when the Earth was on the opposite side of the Sun from Jupiter. Obviously it's more difficulty to make measurements at these times, because the Jovian system is nearly in conjunction with the Sun, but at dawn and dusk it is possible to observe Jupiter even when it is fairly close to conjunction. These observations, taken about 6 months away from the optimum viewing times, revealed a puzzling phenomenon. The eclipses and passages of Jupiter's moons, which could be predicted so precisely when Jupiter is in opposition, are found to be consistently late by about 17 minutes relative to their predicted times of occurrence. This is not to say that the time intervals between successive eclipses is increased by 17 minutes, but that the absolute time of occurrence is 17 minutes later than was predicted six months earlier based on the observed orbital period at that time. For example, the moon Io has a period of 1.769 days, so it completes about 103 orbits in six months, and apparently it lost a total of 17 minutes during those 103 orbits, which is an average of about 9.9 seconds per orbit. All the other moons seemed to be late by the same amount when observed with Jupiter near conjunction. Nevertheless, at the subsequent "opposition" viewing six months later, all the moons are found to be back on schedule! It's as if a clock runs slow in the mornings and fast in the afternoons, so that on average it never loses any time from day to day. While mulling over this data in 1675 on a visit to Paris, the Danish astronomer Ole Roemer thought of a beautiful explanation based on a remarkable hypothesis: "sight" is not instantaneous. Light travels at a finite speed, which implies that when we see things we are really seeing how they were at some time in the past. The further away we are from an object, the greater the time delay in our view of that object. Applying this hypothesis to the observations of Jupiter's moons, Roemer considered the case when Jupiter was in opposition on, say, January 1, so the light from the Jovian eclipses was traveling from the orbit of Jupiter to the orbit of the Earth The intervals between successive eclipses around this time will be very uniform near the opposition point, because the eclipses themselves are uniform and the distance from Jupiter to the Earth is fairly constant during this time. However, after about six and a half months Jupiter is in conjunction, which means the Earth is on the opposite side of its orbit from Jupiter. The light from the "July 18" eclipse will still cross the Earth's orbit at the expected time, but it must then travel an additional distance, equal to the diameter of the Earth's orbit, in order to reach the Earth. Hence we should expect it to be "late" by the amount of time required for light to travel the Earth's orbital diameter. In the late 1600's there were already some rough estimates of the mean Earth-Sun distance, so this enabled Roemer to estimate the speed of light.
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