﻿ About the accuracy, within which the independence of the speed of light from the movement of the source can be stated.
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## About the accuracy within which the independence of the speed of light from the movement of the source can be stated.

By W. de Sitter

Translated from Physik. Zeitschr. 14, 1267, (1913)
German | Scanned | English Trans

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Installed 03 Jun 2004.Latest update 27 Nov 2011.
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In Proc. Amst. Acad. February 1913 (volume 15, p. 1297) and this journal 14, 429, 1913 I showed that the existence of spectroscopic binary stars, whose movements follow Kepler's laws, in which the choice is between the light theories of Ritz (emission theory) and Lorentz (constant speed of light), decides in favor of the latter.
If one leaves the point of view that only between these two theories is to be selected, then the question evolves into another. The law for the speed of light in the direction of the source then becomes e.g.

v = c + ku.

If only k = 0 (Lorentz) or k = 1 (Ritz) are permissible, then the choice is unambiguous. Even if one permits intermediate values of k , then the question an upper limit is to be intended for k. One can never experimentally maintain a constant of any [certain] size, but only a constant within certain limits.
As Mr. P. Guthnick (Astr. Nachr. 195, p. 265) and Mr. E. Freundlich (this journal 14, 835) emphasize, in the motion an apparent eccentricity very correctly will arise, [whose] proportionally is k . u0 . Δ also, where u0 is the maximum for u.
With regard to finding an upper limit for k we take e.g. a well-known star like β Aurigae. The observational data are:

π = 0".014, e = 0.005, u0 = 110 km/sec, T = 3'.96.
We set as upper limits, which are still permissible by the inaccuracy of the observations: thus one finds:

π = 0".05,   so Δ > .65 Light-years
e < 0.015,

thus one finds:
k < 0.002 .

Perhaps other stars will give still smaller values. Naturally the smallest values [are] supplied by the stars with the smallest parallaxes. Unfortunately the parallaxes for most stars are still unknown. There is however a large number of spectroscopic binary stars with large speeds and small or infinitesimal eccentricity, and it cannot be doubted the fact that the majority of these stars have small parallaxes and therefore will give still many smaller values for k than β Aurigae. Only this star was selected, because its parallax is well known and therefore is relatively large.
Mr. Freundlich emphasizes that the statistics of the spectroscopic binary stars exhibits a certain preference of the lines of apsides for a direction toward the sun. That would speak for the hypothesis of a measurable value of k. There is however another statistical fact, which is by far more authentic, according to my opinion, which speaks against it. That is already emphasized by Mr. Guthnick. The spectroscopic binary stars with short period, thus large u, have small or infinitesimal eccentricities, while those with long periods and the visual binary stars have generally larger eccentricities. If k had a rather high value, this would have to be the other way around.
The small value of the upper limit for k, found above, seems to make however all further views of this kind redundant.
Leiden, October 1913.

Thanks to Tom Yee, ADAM27, Jerry "Cephalobus" and Frank Zenker for corrections.

For some 1908 information about the calculated orbits of spectroscopic binary stars which exhibit a directional grouping for their lines of apsides, see: J. Miller Barr (1908) [Added 02 May 2010.]

See an English Translation of Freundlich's article. [doc file] - [Added 11 July 2011.] Thanks to Mr. Tom Miles for the pdf copy of Freundlich's article. Freundlich cites Barr. [Added 13 Jan 2011.]