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    Re: The Navigation Lamp Post
    From: Brad Morris
    Date: 2013 Feb 15, 22:06 -0500
    Hi Norm
    Forgive me for not using the terms in precisely the correct manner.
    We are instructed that the light rays from the distant star strike us everywhere on the earth at the same angle (or nearly so).  It was my intention to show that this is not the case, since the rays are not parallel to each other, just nearly so.  The angle is so vanishingly small that two observers may treat the rays as parallel, but this is not true.  There is a minor correction for radius of the circle of equal altitude based upon the altitude of the observed object.  That correction is far less than 1 arc second.  This can be as small as zero when the object is at the zenith and as great as 1/10000 arcsecond when the altitude of the object is zero.  In other words, too small to worry about when we measure to 6 arc seconds with our sextants.  The stars would have to be much much closer to us to shift by
    In the parallax observation, I was attempting to illustrate how in the 1800's, the distance to stars was attempted by measuring the shift of foreground objects against the background objects.  So Alpha Centauri, the angle to the star shifts by 0.88 arcseconds over a 6 month period.  This is why the measurement was unsuccessful and we were forced to calculate the distances to stars by other means. 
    With todays orbital telescopes, the pointing precision is far greater than instruments of the 1800's, consequently, I believe we could measure the parallax to Alpha Centauri (Rigil Kentaurus)

    On Fri, Feb 15, 2013 at 8:15 PM, Norm Goldblatt <ngold@pacbell.net> wrote:

    I think the statement that rays are parallel is different from parallelism in the context of parallax. In the former, we are interested in the angle between two rays from the source, which strike either side of whatever aperture we're using to observe the object- our eye pupil, the diameter of our binocs or sextant telescope. This is vanishingly small, as we say in mathematics! However, as you say, if the base angle is not the eye pupil but the 2x92 million miles of the Earth's position 6 months apart, it is NOT vanishingly small anymore, but when we design the imaging optics in a telescope we are unconcerned with this angle. This parallax angle defines the angular difference of the bearing of a star, or, said another way, it's relative position with respect with objects much farther away.

    The idea of non-parallelism is used to define a unit of stellar distance, the parsec. An object which, when viewed 6 months apart, appears to have changed it's bearing by 1 second, is at a distance, by definition, of exactly 1 parsec (an incredible distance 3.2 Light years, trillions of miles.

    It's a silly unit of measure, if you ask me, because the nearer an object to us, the BIGGER the parallax, yet it comes up measuring a smaller number for the distance measured in parsecs. Actually, the change in angle, in parsecs due to parallex is the inverse of the distance in parsecs.


    Above, a link to a nice description of distance by parallax and the limitations.

    By the way, this idea of parallel rays from a distant object is the hardest thing for Optics students to grasp, at first. I think it's because one can not see the apex of the fan of rays (off scale, as we say).

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