----- Original Message ----
> From: Antoni Clavell <[EMAIL PROTECTED]>
>
> Hi Sander, A-B must be + or - 180º, i. e. 296.5º - 116.5º must be 180º.
> (Rounding can lead to an error of 1º)
It isn't necessarily rounding error, but might be the definition of PA. PA is
usually used over small distances, like describing the direction of separation
between double stars, or the long axis of an elliptical or spiral galaxy. And
in that case PA is like compass azimuth degrees, applied to celestial
directions. But for larger distances, the geometry of a sphere is not quite as
simple. More generally, PA is the angle of the "great circle" path between
star A and star B, (where angle is as I just described it for small distances)
but the "angle" of that circle will depend on where along the path you measure
it at. I'm not sure if there's a formal astronomical definition for this, but
if you're talking about the PA of star B as seen from star A, then it would
seem to make sense to define PA as the angle of the great circle where it
passes through star A. This will not be the same as the PA of A as seen from
B. Consider a star on the celestial
equator (and to give a more concrete example, lets assume it's on the
meridian- hour angle 0). Now consider a great circle going through that star
at a 45 degree angle (say, in the NE-SW direction. Then the PA of any star B
that's on this great circle in the NE direction from star A is 45, as seen from
star A. But what is the direction of star A as seen from star B? If the
separation is small, the PA will be very close to 225 (180+45, or SW). But if
you go far enough along that great circle to its point of greatest dec (this
would be at hour angle 18, and at +45 dec), then when the circle goes through
that point, at that point the circle is tangent to a circle of constant dec.
So the PA of star A as seen from that point is 270.
IOW, the compass heading of a plane flying a great circle route between two
distant cities is not constant.
-John
