Robert, Thank you. A fine contribution. I would be very interested in the Doppler shift distribution that you propose, especially as MS already describes redshift as a "statistical" phenomenon. Also, if you decide to write something up on these negative parallaxes for your own site, then I would like to link to it if that's okay? (May I suggest a change of colours, though, just to make it more obvious when you are commenting and when you are quoting?) Neville. Robert Bennett <robert.bennett@xxxxxxx> wrote: Neville, I struggled to understand how parallax could be negative, in terms of its angular definition. So I did some surfing. Even astronomers themselves don?t trust negative parallax (or HIP) : ?T Tauri is 462 ± 9 light-years from Earth. This result is far more precise than any previous parallax for the star. For example, the distance the Hipparcos satellite determined for T Tauri had an uncertainty of more than 100 light-years. And the star's negative parallax in the 1995 edition of The General Catalogue of Trigonometric Stellar Parallaxes is useless. http://www.kencroswell.com/TTauri.html ??.Parallaxes less than about 0.01 arcsecond in older catalogs, or 0.001 arcsecond in the Hipparcos Catalog, are usually poor, and should be used with caution. If the parallax is zero, missing, or negative, the parallax for that star is very bad, and you shouldn't even bother trying to calculate its 3D motions at all. http://astronexus.com/node/40 A value of 10000000 indicates missing or dubious (e.g., negative) parallax data in Hipparcos. http://astronexus.com/node/34 Still, no answer to why or how a parallax could be <0. Then?.. Derek Jones [a relative?] Evolution of Eddington?s ideas One evening Dyson was sitting next to Eddington at dinner and described to him the histogram of observed stellar parallaxes. Because of observational errors, the histogram had a tail of physically absurd negative values. Eddington thought for a moment and then wrote out a method for solving the problem on the back of the menu. He later published the method (Eddington 1913); this short paper covers only two pages, consonant with its origin. Dyson (1925, 1926) went on to apply the method to the Greenwich Parallax Observations and effectively removed all the stars of negative parallax. Later, Jeffreys (1938) demonstrated that the method was fallacious on several grounds. In layman?s terms one should never attempt to differentiate an observed histogram as differentiation is effectively a noise magnifier. In the same paper he suggested that it would be better to apply Fisher?s (1936)Method of Maximum Likelihood without himself pursuing this approach. Eddington (1940) returned to the problem and confirmed the validity of his earlier work with the proviso that contrary to what is generally assumed, the frequency curve of the improved parallaxes is not usually a better approximation to the true frequency curve than the frequency curve of the uncorrected parallaxes. None of the above alter the conclusions of my paper (Jones 2001) which shows that in spite of the accuracy of the Hipparcos trigonometric parallaxes, the luminosity of the RR Lyraes is much better measured from their statistical parallax. Dr D H P Jones FRAS, Institute of Astronomy, Madingley Road, Cambridge CB3 0HA. Eddington, likelihood and stellar parallaxes In his reference to Clube and Jones, Derek Jones (A & G42 5.8) credits these authors with pioneering the use of maximum likelihood in the determination of statistical parallax. I am puzzled by this. In various publications, A S Eddington used likelihood distributions in the determination of stellar parallaxes. He pointed out in particular that the maximum likelihood cannot be identified with the parallax, since the parallax maximizing the likelihood of the observations may well be negative. He also pointed out that the a priori probability of the parallax must not be factored twice into the combination of two or more parallax estimates. For example, separate most-probable estimates must be just averaged. Prof. Emeritus P B Fellgett, FRS, Little Brighter, St Kew Highway, Bodmin, Cornwall PL30 3DU. http://www.blackwellpublishing.com/products/journals/aag/aag_December01/aag42609.htm So negative parallax isn?t a reversal of near and far star labeling, nor an indicator of distance. Along with positive parallax it?s the result of a statistical average of many observations that ?occasionally? produces a negative result?. Why, then, do Neville and son find as many + as - parallaxes??! This peek into the astronomer?s workshop seems like a visit to a gypsy reading tea leaves ?.. or looking through Schiaparelli?s telescope to see Martian canali It?s said, ?Never be present when laws are being passed or sausage is being made.? Add to those two, when MS stellar motions are being computed. Has the proper motion of each star been subtracted from the stellar observations? Has the much larger stellar aberration of 20,500 mas/yr , common to all stars, been corrected for latitude and subtracted from the stellar observations? Has the annual Milky Way N-S motion of 920,000 mas per day for each star been subtracted from the stellar observations? I agree that the catalogs of parallaxes appear to be no more than a normal distribution of errors around the mean ?fixed? position. And this calls into question the reliability/integrity of the other stellar motions: proper and aberration and recession/red shift. Are these experimental errors or errors of understanding/interpretation? Hard to tell unless you know what ALL the MS assumptions are, and when and how they apply them. I?ll be looking at the blue vs. red shifts in the catalogs for a similar random pattern around zero recession. Anyone care to join the hunt? If the parallaxes are just random errors, then the MS basis for determining near space distances falls apart. Who knows how far to Proxima Centauri?? The HIP and Tycho catalogs only survey the brightest (and nearest) stars in the Milky Way, not the galaxy background that MS considers fixed. The 46% ?fixed? stars in the catalog analysis had no detectable motion with reference to the galactic background. If the catalog stars were actually moving with respect to the deep space galaxies, this would not contradict the MS/BB model. The greater the distance, the less observed motion. In the GS model, orbits increase revolution speed with distance, unlike Newtonian orbits. So the slowest orbits in the stellatum are the closest, the fastest are the furthest, as the GS T vs R graph will show. If the slowest and fastest objects can be measured, the thickness of the stellatum can be found. Conclusion This negative parallax concept is a just-opened can of worms that will need a lot of time and work to resolve? Geocentrism evidence 5 - Negative Parallax This page is now back up on the website www.geocentricperspective.com and has been modified to reflect my current understanding and to incorporate the comments that some of you made. Your consideration and opinions would be greatly appreciated, particularly if you have any suggestions as to how the stars would achieve the necessary motion within the stellatum. Neville. . --------------------------------- New Yahoo! Mail is the ultimate force in competitive emailing. Find out more at the Yahoo! Mail Championships. Plus: play games and win prizes.