Speculations in Science and Technology 18, Sept. 1995
Frank Pio Russo
P.O. Box 90 Campbelltown 5074 South Australia
Conceived Sept. 21 1992; written form evolving since Sept. 22 1992.
This edition September 18, 1994.
ABSTRACT:
The process of correcting the annual stellar aberration for the velocity of the earth's rotation using diurnal aberration is currently done inappropriately. When this is done better, one ends up with an aberration constant of 20.18 seconds of arc. This in turn gives a more accurate "real" speed for light of 304,476 km/sec plus or minus about 125 km/sec. This "real" speed can be triangulated with the experimental relative speed of light of 299,792,458 m/sec to give one the "real" speed of the earth as 53,198 km/sec plus or minus about 710km/sec.
INTRODUCTION
There are three types of stellar aberration: annual, diurnal and secular. The last one, from the motion of the solar system's centre of mass relative to the galaxy is stable in normal timescales. Stellar aberration was discovered by the great James Bradley and represents the angle at which one has to adjust his telescope to view a star : the angle being dependant on the speed at which one is traveling, in our case the earth at 29,790 m/sec 1 (this is usually done whilst the star is in zenith so that one has a reference point to work from, and this was especially true in Bradley's case because he used a plumb line to make sure his telescope was adjusted correctly). Two observations are usually done at sixmonthly intervals. It is interesting that a star at the pole of the ecliptic describes a circle during the year with the radius being the aberration constant: this is according to the German work "Meyers Konversations"  Lexicon 5th edition,1893; but of course the aberration constant is only constant by definition, whereas in practice it would vary according to the elliptical orbit of the earth hence the description is that of an ellipse. Along the ecliptic they would just describe a line backwards and forwards with an ellipse being the inbetween result. The usual way of describing the aberration has been with an analogy to what happens when one runs with an umbrella in the rain, he obviously has to angle the umbrella. Another one is that one gets wet when travelling in the rain in a covered vehicle which has no windscreen . It is worth noting that the failure of this aberration effect near the earth, has been given special significance by many such as Carl Zapffe 2 . However, this is nothing more than the mysterious "fly in the car" effect: the fly does not smash into the back windscreen, because it has the velocity of the car, as it flies around after first landing in the car. Likewise, objects very near the earth usually have the earth's velocity or a component of it.
BRADLEY'S RESULTS
Most astronomical books will tell you that Bradley used observations of the star Gamma Draconis as his source of his observations of stellar aberration 3 . This was because it "passed through the zenith in London and thus asymmetries due to refraction of light in the earth's atmosphere were eliminated." 4 As for the other star on which Bradley did a lot of work, although he calls it eta Ursae Majoris, it appears to be epsilon Ursae Majoris: perhaps Bradley got confused because they are both equivalents of the English "e"...anyway, stellar nomenclature was very young in those days...nevertheless, the solution might be simpler than that : I just got up and checked the Big Bear's tail in a map by the Swiss astronomer Hevelius of the 17th century, the declinations are somewhat different to the modern ones 5 .
For the early observations, the telescope used, was fixed to a chimney so that it had a fixed transit, and it just so happens that Gamma Draconis has a declination of 51 degrees 30 minutes which would have made it virtually above Bradley's telescope 6 . It is interesting that in those days i.e. 1700's, there were no very good clocks so one could not see any aberration as a change in right ascension. These days the diurnal aberration is used in "corrections" for aberration purely in right ascension. However, Bradley had to do the whole thing through changes in declination and the crucial aspect of the foregoing is that Bradley's results peaked at 6 a.m. and 6 p.m., at six monthly intervals, this is because he was using changes in declination which only line up fully with the orbital velocity at 6am and 6pm.
That would have been the only way of looking at the same star in zenith at six monthly intervals whilst maximizing the change in declination which one would observe. This means that the rotational component due to the rotation of the earth (at 6 a.m. and 6 p.m.) was zero and would have explained why Bradley got a mean value of 20.2" with improved equipment 7 . The accepted modern value is 20.496" but this is a calculated value rather than an experimental one, despite the fact that the scientific world believes that the 2 are one and the same. Most persons were quite happy with the experimental aberration constant of 20.47" and physics books were quite favourably disposed to it: anyway according to Smart's Textbook of Spherical Astronomy, this was derived through calculations as well.
Continuing on with Bradley's work... later on when Bradley discovered that by observing Polaris, he could make the observations at any time of night and get close to the full result because of the 90 degrees angle, I believe that then he introduced the effect due to the rotation of the earth! At the time, he actually said "neglecting the small Difference on the Account of the Earth's diurnal Revolution on its axis" 8 . And this is why he later got a value up to 20.5 seconds of arc 9 . According to Theo Theocharis, 10 the textbooks begin to mention diurnal aberration in "the 1890s. The earliest reference known to this researcher was made in an 1891 publication". Of course this is not strictly true because Bradley and Bessel referred to it, but nevertheless if it was not appreciated as being significant until the 1890s: no wonder, they did not all correct the annual aberration for it. It has been brought to my attention that Bessel as early as 1815 gave a correction for Bradley's value of +0".4530 =0".07063 11 which would have made the aberration constant a purported 20".65 . However, according to the lexicon mentioned near the start of my paper, (ie Meyers), Nyrens measured it as 20".492 . The Encyclopedia Britannica of 1825 sheds further light on this subject by saying "Though he [Bradley] afterwards discovered that the maxima in most of these stars, do not happen exactly when they pass at those hours": this can only be referring to the maxima brought about by the diurnal aberration's lining up with the annual aberration at midnight, thus increasing the aberration constant by about 0.29 arc seconds on the equinoctial equator at midnight.
It is possible to infer that this is why the aberration constant was stuck on 20.47", namely that was about the maximum for a Londoner's observation at his latitude. Anyway, such an inference could only be made retrospectively for in Bradley's day, the error margin of his measurements must have been quite considerable, for as Dr. R.R. Burman (Uni. of Western Australia) pointed out, Bradley's declination measurements had an error no greater than 2 arc seconds 12 . However, having now actually consulted the original papers of Bradley, (my thanks to Dr. Burman for kindly supplying them), I can now see the true greatness of the man! For a start, he claimed that his measurements could be "securely depended upon to half a second".13 Some of his figures are extremely accurate even by today's standards: for the aberration (without the rotation of the earth incorporated in), I calculate a value of 20.18" and Bradley got 20.2"!
With good reason, I have therefore checked Dr. Burman's reference and it appears that it is referring to the early equipment belonging to Molyneux and not Bradley's. Hence, if you take the 20.2" and add 0.17" for the latitude's rotation component, and then add a 0.1 possible error: one gets the modern aberration constant of 20.47". The values obtained by Greenwich are 20.445" for the years 191927 14 and 20.489" for the years 191136 15 . When this data is added to the 20.2" obtained by Bradley and the 20.4" put forth by the 1875 Encyclopedia Britannica, (once again under the entry for aberration), one comes up with the conclusion that the constant of aberration has been gradually going up so as to keep up with the speeds of the earth and light, without any consideration for the diurnal factor. (Of course there were many other measurements but the trend is as I have outlined it.)
Hence, these values have only limited meaning if they have an error interspersed through them. Hence I leave the definitive quantification of the real velocities of light and of the earth, to the time when the technical excellence becomes standardized in all the observatories.
COMPLICATIONS
If one has a good look at aberration, then one is able to separate the true value from the complications of the elliptical orbit. This can be done by using equinoctial days or near equinoctial days for the observations, for then one does not even need to work out the actual earth's velocity. For the correction factor in
V' = V.(2/r  1) ^{1/2}
(1)
becomes very close to one (the r is the radius of the earth's orbit available for every day of the year from almanacs).
By using equinoctial days, one would also avoid the complication of seasonal variation due to the solstice. The other complication is due to polar motion (Chandler's wobble), but this presents no problem as a meanaccumulated experimental aberration constant over many years would eliminate any minor oscillations due to "polar motion", especially seeing that everything can be itemized these days.
The biggest complication by far, is the method of correcting observations for diurnal aberration for it disarms most persons, by giving the impression that the corrections are done correctly. It appears to be a simple method of itemizing the different aberrations. What they do is measure the aberration constant in such a way so that the maximum value is at midnight on the equator, then they subtract a correction for the rotation of the earth: starting with a large corrective subtraction for the rotation of the earth tapering down to the pole 16 . However, the cardinal error is that the diurnal corrections are done in right ascension, hence they do not affect the aberration constant at all! All that they change is the actual time at which the various transits occur, rather than changing the actual aberration longitude angle.
The correct procedure would be to measure the aberration constant on the equinoctial equator at midnight and then account for the rotational velocity: it makes little difference what value one adopts, whether 20.47 or 20.18 provided one specifies whether it is equatorial or polar. Further evidence that the flaw with the system which I am describing is real, can be further seen by returning to the 1875 Encyclopedia Britannica. Under the same heading on page 48 it says: "As we proceed from the pole, the apparent orbits the stars describe become more and more elliptical, till in the plane of the ecliptic the apparent motion is in a straight line. The length of this line ...amounts in angular measure to about 40.8". This is clearly backing up my contention that the diurnal component is included because, at 6am or 6pm an ecliptic star would show no orbital aberration as its position would be almost the same as the one pointed to, by the earth's velocity.
THE ACTUAL VELOCITIES
At the equinoxes because of the inclination of the earth, the vector of rotation in line with the earth's orbit would only be 426.6 m/sec, (this is using the division of the earth's circumference by the sidereal rotation period 17 giving a rotational velocity of 465.10 m/sec). Therefore the true velocity of light can be derived using the compound velocity of the earth (at midnight).
ie Aberration cons.=[(29,790 + 426.6)m/sec /c]radians=20.47"
(2)
Solving for c using trigonometry gives the true velocity of light as 304,475,873.2 m/sec. This represents a figure higher than the current value by 4,683.4 km/sec. Of course it merely represents a mean value for one must be conscious of the inherent errors of the figures used in deriving it. The rotational velocity of the earth is very accurate and as such adds little error. On the other hand, the orbital speed of the earth is accurate to plus or minus 5 metres and this together with the very imprecise experimental aberration constant, give the real velocity of light an inherent error of plus or minus 125 km/sec. This represents only about 2.7% of the increase seen.
If this is the real speed of light, (I hesitate to use the word "absolute" velocity, as that might offend and alienate my readers), then the 299,792,458 m/sec must be the relative speed. What is more, is that one can calculate an actual velocity for the earth, by triangulating the two velocities of light and employing the aid of Pythagoras. By actual velocity of the earth, I mean the endresultant velocity from the many "merrygo rounds"... i.e. the earth is going around the sun at about 30 km/sec ... but the sun is already going at about 250 km/sec around the galaxy ... but the galaxy is already going at about 700 km/sec around the cluster ... but the cluster is already going at about 900 km/sec around the supercluster and so on!
Using the two speeds of light one gets a calculated real velocity for the earth of 53,198 km/sec plus or minus about 710 km/sec.
CONCLUSION
First of all, I must point out that there are more steps on the cosmic "rollercoaster"...I never said that the supercluster was the centre of the universe.
The derived speed of light cannot compete in accuracy to the 9 digit accuracy of the conventional value: however it is not my intention for the two to compete, for I want the two to coexist. One as the "real" speed and the other as the relative speed. A very good facet of my paper was raised by Dr R. R. Burman. Namely that "aberration might yield a significant value of the oneway speed of light, as distinct from the average outandback that we normally measure. The aberration would need to be measured for a single star or for a few stars in nearly the same direction. Romer's original evaluation of c was of the oneway speed (Jupiter to Earth)." 18 Of course in order to get the most out of the exercise one would have to test many directions till one strikes upon the axis of the absolute motion where one would find the greatest effect.
This aberration question must be considered by my peers ... I shudder to think that all the textbooks may be wrong ... perhaps we need to harmonize the MichelsonMorley experiment without time dilation and length contraction ... well! There is a way!
REFERENCES
1. Reidy D & Wallace K. 1991. THE SOLAR SYSTEM A Practical Guide. p.2 Allen & Unwin Australia Pty Ltd.
2. Zapffe Carl A.; "Bradley Aberration and Einstein spacetime"; Indian Jounal of Theoretical Physics; Vol. 40 No. 9;1992pp145148.
3. Abbott David (Ed.). Biographical Dictionary of Scientists: Astronomers. Bradley James. p.28. P Edrick Books , New York.
4. Freier George D. 1965. University Physics: Richard M Sutton (Ed.). p.426. AppletonCenturyCrofts , New York.
5. RobinsonRowan M. 1990. Universe. pp3435. Longman Group UK Limited.
6. Lloyd Motz and Carrol Nathanson. 1988. The Constellation: An enthusiast's guide to the night sky. p.60. Doubleday,New York.
7. Bradley James. 17278. Philosophical Transactions. Vol. 35 pp 653654. Royal Society , London.
8. Bradley James. 17278. Philosophical Transactions. Vol. 35 p.649. Royal Society, London.
9. Abbott David (Ed.). 1984. Biographical Dictionary of Scientists: Astronomers. Bradley James. p.28. P. Edrick Books, New York.
10. Theocharis T. 1990. "Diurnal terrestrial aberration of light". Speculations in Science and Technology.Vol.15.No1 p.72.
11. Bessel F.W., 1875, Abhandlungen von Friedrich Wilhelm Bessel ed.R. Engelmann, Verlag von Wilhelm Engelmann, Band 1 p 261,285,286 291,313,316, Liepzig.
12. Pannekoek A. 1961. A History of Astronomy. p.209. Interscience New York.
13. Bradley James. 17278. Philosophical Transactions. Vol. 35 p.643. Royal Society, London.
14. Smart W.M. 1977. Textbook on Spherical Astronomy. 6th edition; Revised by R.M. Green. p.190. Cambridge.
15. Enc. Britannica. 1986. Micropedia: parallax. Vol. 9 p.141.
16. Explanatory Supplement to the Astronomical Ephemeris. (UK) 1961. 2D pp4950. H.M.S.O.
17. Enc. Britannica 1986. Macropaedia. Solar System. Vol. 27 p.530.
18. Personal correspondence.
540 The Incredible Bradley: Why his Aberration Work was so Accurate even Bettering most Modern Renditions ! (Enabling the Extrication of the Diurnal Factor.) Written by: Frank Pio Russo  March 19, 2016; Posted : March 21, 2016.
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