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    Re: Star - Star Distances
    From: Robin Stuart
    Date: 2010 Apr 27, 11:06 -0700

    With regard to the effect of aberration on the angular separation of star pairs: looking more closely at the reference to "Stars and Sextants" http://www.archive.org/details/starssextants00spri provided by Frank in http://fer3.com/arc/m2.aspx?y=201003&i=112199 I see that there it notes that the method described by the authors includes:

    3) Restricting the selection of pairs of stars to the time of year when their respective distances are practically unaffected by aberration.
    For every pair of stars there are two instants in the year when aberration has no effect on the distance between them. Near these dates the effect is small, and in proportion to the nearness and for a week on either side the effect is negligible. We have found these dates, and have classified the star pairs accordingly in the Ephemeris.

    but provide no more details as to how these dates might be found. Is the condition required for this widely known?

    My own investigation shows that, one can write down a general condition, for any pair of stars, that must be satisfied by the direction of the observer’s velocity in order for aberration not to change their angular distance. The curve traced out by the possible directions is not a great circle but in the limit that the observer's velocity tends to zero (as compared to the speed of light) it can be shown that it approaches a great circle with a pole at the midpoint been the two stars. This great circle obviously intersects the ecliptic at two points. When the direction of the observer's (Earth's) motion is at one of these intersection points the aberration has no effect on the angular distance of the stars. The direction of motion lags the position of the Sun by roughly 90 degrees as it moves along the ecliptic. This then allows the required dates to be found.

    Of course I acknowledge that in an age where ease of computation is no longer a key concern the practical need for this is limited. It is, however, an engaging exercise that can be (and was) derived by taking the limit of relativistic equations – something that could not be been done in 1904 (Einstein's annus mirabilis minus 1!) when the quoted edition of "Stars and Sextants" was published!

    Robin Stuart

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