On the coloured light of the binary stars and some other stars of the heavens () is a treatise written by Christian Doppler in 1842Some sources mention 1843 as year of publication because in that year the article was published in the Proceedings of the Bohemian Society of Sciences. Doppler himself referred to the publication as "Prag 1842 bei Borrosch und André", because in 1842 he had a preliminary edition printed that he distributed independently. , in which he postulated his principle that the observed frequency changes were due to the motion of source and/or the observer. This was later named the Doppler effect.
Title The subtitle "" (Attempt at a general theory including Bradley's theorem as an integral part) describes the intent of the book: to develop a theory explaining the colours of binary stars, and relate it to Bradley's stellar aberration.In 1728 Bradley discovered and explained the so called aberration of star light. This aberration was one of the first compelling pieces of evidence for the finite speed of light. Bradley's aberration is approximately proportional to v/c, the ratio of the speed of the Earth over the speed of light. The Doppler effect contains a similar proportionality to v/c. The observed aberrations and color shifts implied the speed of light was very large, ~104 v, but not infinite. % WikiSource
Content
§ 1 Doppler discusses state of the theory that light is a wave, and describes the debate as to whether it is a transverse wave in the aether or not. Proponents claim this is necessary to explain polarized light, whereas opponents object to implications for the aether. Doppler doesn't choose sides, although the issue returns in § 6.
§ 2 At this time, optics and acoustics were treated similarly. Doppler observes that colour is a manifestation of the frequency of the aether pulses, but intensity comes from the amplitude. He emphasizes that these perceptions depend on the observer, not just the source and medium. He describes his theory that a frequency shift occurs when the source or the observer moves. A ship meets waves at a faster rate when sailing against the waves than when sailing along with them. The same goes for light as for sound and water waves.
§ 3 In this section Doppler derives his equations for the frequency shift, in two cases: Equation DopplerDoppler uses other symbols for the variables than we usually do today: f = 1/n, f ' = 1/x, vo = αo, vs = αs. (Note n=n" and x=x", as in number of seconds = time). Modern equation 1. Observer approaching stationary source with speed vo 2. Source approaching stationary observer with speed vs
§ 4 Doppler gives imaginary examples of large and small frequency shifts for sound: vo = -c f = 0 frequency shift down to inaudibly low tones vs = -c f / f = 0.5 frequency shift down over 1 octave, still audible. vs = +c f / f = ∞ frequency shift up to inaudibly high tonesinaudible, except for the shock wave ignored by Doppler. vo = 40 m/s1 par.Fuss = 0.325 m (pied de roi); speed of sound 1024 par.Fuss/s = 333 m/s C to D note C shifting to D. vo = 5.4 m/s quarter note threshold for best observers with absolute hearingIn 1845 Buys Ballot used this idea of musicians with absolute hearing for the first experimental verification of the Doppler effect.
§ 5 Doppler provides similar examples of large and small frequency shifts for light from stars. Velocities are expressed in miles/s, and the light speed has a rounded value of 42000 miles/s.Meile = geografische mile = 7420 m. Doppler provides the rounded value of 42000 miles/s instead of the best accurate value of his time. The rounded value was well known and stable throughout the years, whereas the accurate value varied due to frequent new measurements. Since 1835 the accurate value was 41549 geogr. miles/s (308000 km/s), see Pierer's Universallexikon and Wüllner's Experimentalphysik Doppler assumes that 458 THz (extreme red) and 727 THz (extreme violet) are the borders of the visible spectrum,The frequencies 458 THz (extreme red) and 727 THz (extreme violet) and other colours apparently have been derived from the wavelengths mentioned by Thomas Young in his Theory of Light and Colours (1802), where Doppler would have used 309000 km/s as light speed. This explains most values in the table, except for the vs-values 19000 and 5007 that remain as calculation errors by Doppler (deviation about 25%). Colour Wavelength according to Young (nm) Frequency if c=309000km/s (THz) vs=c(1-f/f) if c=309000km/s (geogr. Miles/s) vs according to Doppler (geogr. miles/s) extreme violet 425 727 -24462 -19000 (error) yellow 577 535 -7037 -5007 (error) red 648 477 -1704 -1700 extreme red 675 458 0 0 that the spectrum emitted by stars lies exactly between these borders (except for the infrared stars of § 8), and that the colour of the light emitted by stars is white.These assumptions are wrong. Doppler ignores the emitted infrared and ultraviolet, although their presence in sun light was known since studies by Herschel (1800) and Ritter (1801). As a result Doppler overestimates the visual colour changes. He knew that stars are able to emit infrared, as he proposes so in § 8. With regard to the colours of stars, the assumption that stars emit white light is his major mistake. Nowadays we know that colour mainly depends on the star temperature. Miles/s km/s f / f vs = -19000 141000 458 / 727 shift from extreme violet to extreme red, and from other colours to invisible range beyond extreme redDoppler uses the old term homogeneous light for monochromatic light. vs = -5007 37200 458 / ? shift from yellow to extreme red vs = -1700 12600 458 / ? shift from red to extreme red vs = -33 244 458 / 458.37 threshold for visual perception of colour changesDerivation of the threshold value 458.37: Herschel stated that white light, obtained by mixing red, yellow and blue light, undergoes a visually perceptible colour change if the intensity of any of these three components changes by at least 1%. According to Doppler this implies that white star light undergoes a perceptible colour change if the frequency shift is at least 1% of the red segment of the spectrum. Using Young's definition of the red segment (wavelength 625 - 675nm, Theory of Light and Colours, see above) and c=309000km/s (see above), the red segment corresponds to the frequency range 458 - 495THz. The value in that segment at 1% distance from the border is 458.37THz. shift from a shade of red to next shade of red approaching white star gets a green shade receding white star gets an orange shade
§ 6 Doppler summarizes: The natural colour of stars is white or a weak yellow. A white star approaching with progressive speed would successively turn to green, blue, violet, and invisible (ultraviolet). A white star receding with progressive speed would turn to yellow, orange, red, and invisible (infrared).
Doppler wishes that his frequency shift theory will soon be tested by another method to determine the radial velocity of stars. He thinks, without reason, that a confirmation of his theory would imply that light is not a transverse but a longitudinal wave.Bolzano, in his review in 1843, points out that Doppler's thought that his theory would not apply for transverse waves is a mistake. Annalen der Physik 1843
§ 7 Doppler argues that his theory applies mainly to binary stars. In his opinion the fixed starsIn Doppler's article, 'fixed stars' are single stars that are not part of a binary star. The idea of their immobility is a legacy from antiquity, when the ideal fixed stars were contrasted with the planets. are immobile and white.Bolzano argues in his review in 1843 that the idea of the immobility of single stars is unnecessary, and that the observed proper motion of many stars indicates that single stars do move. Annalen der Physik 1843 In a binary star high speeds could be possible due to orbital motion,Later it turned out that the orbital speed of binary stars is not particularly large compared to the proper motion speed of stars. Speeds up to about 200 km/s are observed in eclipsing binaries. An exception is the fastest binary star, a rare type of two white dwarfs, with a period of 5 minutes, an orbit diameter of 80000 km, and an orbital speed of more than 1000 km/s. RX J0806.3+1527At present, the highest radial speed of nearby single stars is about 300 km/s. (Doppler effect#Astronomy) and binaries appear to be colourful.With a few known facts Doppler could have easily estimated that the orbital speed of the visual binaries, which appear to be colourful, is smaller than the orbital speed of the Earth. The distance from the Earth to stars is at least 4 light years (that is the distance to the nearest star). A traditional telescope at sea level has a resolving power of 1 arc second or worse, due to atmospheric turbulence. Hence, the two stars that compose a visual binary have a distance of at least 1 AU. The shortest period of a visual binary is 1.7 year. Therefore the orbital speed of visual binaries (with a circular orbit) is smaller than that of the Earth, below the threshold for visual colour changes (see § 9). That is another flaw in Doppler's explanation of the colours of visual binaries. Doppler divides the binaries into two groups: (1) binary stars of unequal brightness; and (2) binary stars of equal brightness. His interpretation is: in case (1) the brighter star is the heavier one, the weaker star revolves around it; in case (2) both stars revolve around a center of mass in the middle, or around a dark third star. In case (2) the colours are usually complementary. Doppler rules out that the rich complementary colours of binaries are contrast illusions, because an astronomer said he had observed that covering one star does not change the colour impression of the other star. Doppler claims that his theory is supported by the fact that for many binary stars the colour indication in Struve's catalogue is different from that in Herschel's older catalogue, attributing the difference to progress of the orbital motion.An additional motive for Doppler to focus on binary stars might have been that binary stars were a hot topic in astronomy. Accurate binary star catalogues had been composed by Herschel and by Struve. It had been discovered that binary stars are not static, but that they revolve in an orbit around a center, bound by gravity. The orbit parameters (speed, period, and excentricity) were determined. It had become clear that visually single, variable stars with a particular brightness development, were actually binary stars (eclipsing binaries, like Algol).
§ 8 Doppler presents two groups of variable stars that in his opinion can be explained as binary stars with the Doppler effect. These are the "other stars in the heavens" from the title. Periodic variable stars that are invisible for most of the time, and that brighten up with a red colour for a short while once per cycle. In Doppler's opinion they are binary stars. Such a star is usually invisible because it emits infrared instead of white light. In the orbit section with the maximal radial speed in the direction of Earth, the observed frequency on Earth is shifted from infrared to visible red.