# Conjunctions @ The Speed Of Light

Rømer's determination of the speed of light was the demonstration in 1676 that light has an apprehensible, measurable speed and so does not travel instantaneously. The discovery is usually attributed to Danish astronomer Ole Rømer,[note 1] who was working at the Royal Observatory in Paris at the time.

## Conjunctions @ The Speed of Light

**Download File: **__https://www.google.com/url?q=https%3A%2F%2Furlcod.com%2F2ufTTj&sa=D&sntz=1&usg=AOvVaw3-xJcD5u6COwIJS84UOFVP__

By timing the eclipses of the Jovian moon Io, Rømer estimated that light would take about 22 minutes to travel a distance equal to the diameter of Earth's orbit around the Sun.[1] Using modern orbits, this would imply a speed of light of 226,663 kilometres per second,[2] 24.4% lower than the true value of 299,792 km/s.[3] In his calculations Rømer used the idea and observations that the apparent time between eclipses would be greater when the Earth relatively moves away from Jupiter and lesser while moving closer.

The key phenomenon that Rømer observed was that the time elapsed between eclipses was not constant. Rather, it varied slightly at different times of year. Since he was fairly confident that the orbital period of Io was not actually changing, he deduced that this was an observational effect. The orbital paths of Earth and Jupiter being available to him, he noticed that periods in which Earth and Jupiter were moving away from each other always corresponded to a longer interval between eclipses. Conversely, the times when Earth and Jupiter were moving closer together were always accompanied by a decrease in the eclipse interval. This, Rømer reasoned, could be satisfactorily explained if light possessed a finite speed, which he went on to calculate.

This second inequality appears to be due to light taking some time to reach us from the satellite; light seems to take about ten to eleven minutes [to cross] a distance equal to the half-diameter of the terrestrial orbit.[6]

The point L on the diagram represents the second quadrature of Jupiter, when the angle between Jupiter and the Sun (as seen from Earth) is 90.[note 6] Rømer assumes that an observer could see an emergence of Io at the second quadrature (L), and the emergence which occurs after one orbit of Io around Jupiter (when the Earth is taken to be at point K, the diagram not being to scale), that is 42 hours later. During those 42 hours, the Earth has moved farther away from Jupiter by the distance LK: this, according to Rømer, is 210 times the Earth's diameter.[note 7] If light travelled at a speed of one Earth-diameter per second, it would take 3 minutes to travel the distance LK. And if the period of Io's orbit around Jupiter were taken as the time difference between the emergence at L and the emergence at K, the value would be 3 minutes longer than the true value.

Rømer then applies the same logic to observations around the first quadrature (point G), when Earth is moving towards Jupiter. The time difference between an immersion seen from point F and the next immersion seen from point G should be 3 minutes shorter than the true orbital period of Io. Hence, there should be a difference of about 7 minutes between the periods of Io measured at the first quadrature and those measured at the second quadrature. In practice, no difference is observed, from which Rømer concludes that the speed of light must be very much greater than one Earth-diameter per second.[8]

Rømer realised that any effect of the finite speed of light would add up over a long series of observations, and it is this cumulative effect that he announced to the Royal Academy of Sciences in Paris. The effect can be illustrated with Rømer's observations from spring 1672.

The three "inequalities" (or irregularities) listed by Cassini were not the only ones known, but they were the ones that could be corrected for by calculation. The orbit of Io is also slightly irregular because of orbital resonance with Europa and Ganymede, two of the other Galilean moons of Jupiter, but this would not be fully explained for another century. The only solution available to Cassini and to other astronomers of his time was to issue periodic corrections to the tables of eclipses of Io to take account of its irregular orbital motion: periodically resetting the clock, as it were. The obvious time to reset the clock was just after the opposition of Jupiter to the Sun, when Jupiter is at its closest to Earth and so most easily observable.

Cassini's practical objections stimulated much debate at the Royal Academy of Sciences (with Huygens participating by letter from London).[13] Cassini noted that the other three Galilean moons did not seem to show the same effect as seen for Io, and that there were other irregularities which could not be explained by Rømer's theory. Rømer replied that it was much more difficult to accurately observe the eclipses of the other moons, and that the unexplained effects were much smaller (for Io) than the effect of the speed of light: however, he admitted to Huygens[5] that the unexplained "irregularities" in the other satellites were larger than the effect of the speed of light. The dispute had something of a philosophical note: Rømer claimed that he had discovered a simple solution to an important practical problem, while Cassini rejected the theory as flawed as it could not explain all the observations.[note 9] Cassini was forced to include "empirical corrections" in his 1693 tables of eclipses, but never accepted the theoretical basis: indeed, he chose different correction values for the different moons of Jupiter, in direct contradiction with Rømer's theory.[6]

While it was difficult for people such as Hooke to conceive of the enormous speed of light, acceptance of Rømer's idea suffered a second handicap in that it was based on Kepler's model of the planets orbiting the Sun in elliptical orbits. While Kepler's model had widespread acceptance by the late seventeenth century, it was still considered sufficiently controversial for Newton to spend several pages discussing the observational evidence in favour of that model in his Philosophiæ Naturalis Principia Mathematica (1687).

Several discussions have suggested that Rømer should not be credited with the measurement of the speed of light, as he never gave a value in Earth-based units.[18] These authors credit Huygens with the first calculation of the speed of light.[19]

If one considers the vast size of the diameter KL, which according to me is some 24 thousand diameters of the Earth, one will acknowledge the extreme velocity of Light. For, supposing that KL is no more than 22 thousand of these diameters, it appears that being traversed in 22 minutes this makes the speed a thousand diameters in one minute, that is 16-2/3 diameters in one second or in one beat of the pulse, which makes more than 11 hundred times a hundred thousand toises;[20]

Neither Newton nor Bradley bothered to calculate the speed of light in Earth-based units. The next recorded calculation was probably made by Fontenelle: claiming to work from Rømer's results, the historical account of Rømer's work written some time after 1707 gives a value of 48203 leagues per second.[21] This is 16.826 Earth-diameters (214,636 km) per second.

05 If a traffic control signal is not justified under the signal warrants of Chapter 4C and if gaps in traffic are not adequate to permit pedestrians to cross, or if the speed for vehicles approaching on the major street is too high to permit pedestrians to cross, or if pedestrian delay is excessive, the need for a pedestrian hybrid beacon should be considered on the basis of an engineering study that considers major-street volumes, speeds, widths, and gaps in conjunction with pedestrian volumes, walking speeds, and delay.

06 For a major street where the posted or statutory speed limit or the 85th-percentile speed is 35 mph or less, the need for a pedestrian hybrid beacon should be considered if the engineering study finds that the plotted point representing the vehicles per hour on the major street (total of both approaches) and the corresponding total of all pedestrians crossing the major street for 1 hour (any four consecutive 15-minute periods) of an average day falls above the applicable curve in Figure 4F-1 for the length of the crosswalk.

07 For a major street where the posted or statutory speed limit or the 85th-percentile speed exceeds 35 mph, the need for a pedestrian hybrid beacon should be considered if the engineering study finds that the plotted point representing the vehicles per hour on the major street (total of both approaches) and the corresponding total of all pedestrians crossing the major street for 1 hour (any four consecutive 15-minute periods) of an average day falls above the applicable curve in Figure 4F-2 for the length of the crosswalk.

05 On approaches having posted or statutory speed limits or 85th-percentile speeds in excess of 35 mph and on approaches having traffic or operating conditions that would tend to obscure visibility of roadside hybrid beacon face locations, both of the minimum of two pedestrian hybrid beacon faces should be installed over the roadway.

06 On multi-lane approaches having a posted or statutory speed limits or 85th-percentile speeds of 35 mph or less, either a pedestrian hybrid beacon face should be installed on each side of the approach (if a median of sufficient width exists) or at least one of the pedestrian hybrid beacon faces should be installed over the roadway.

Guidance: 07 The steady yellow interval should have a minimum duration of 3 seconds and a maximum duration of 6 seconds (see Section 4D.26). The longer intervals should be reserved for use on approaches with higher speeds.

DOPC may be implemented using phase-shifting holography, which requires precise alignment of optical components for an accurate phase measurement. The incident reference beam should be orthogonal to the SLM to make a uniform reference beam with both constant amplitude and phase interfere with the scattered light to maximize the period of the fringes. If the SLM is tilted or tipped out of alignment, the reference beam and, subsequently, the back-reflected sample beam, will also become misaligned, reducing the focal quality of the DOPC system. It should be noted, however, that this statement applies only to systems where the SLM is viewed by the sCMOS camera, which have become increasingly common due to their relative ease of alignment. DOPC systems in which the sCMOS camera does not view the SLM are also used, and require that the SLM be held at the same angle as the sCMOS camera with respect to the reference and sample beams, necessitating different methods of alignment and optimization.15,28 041b061a72