TomRad Any thoughts how to solve this problem?
Was your target within 5º of the celestial pole?
When the coordinates are close to the pole, ASIAIR apparently does not use an alternate method to plate solve for the center of what is called the "tangent plane" (the so-called gnomonic mapping of the sky (Equatorial) coordinates to the x-y coordinates of a camera). The "tangent-plane" is basically the rectangle areas that your sensors sees (as long as focal length is long enough, or if the sensor is small enough).
The ASIAIR simply gives up trying to solve for the tangent plane near the pole.
The standard equation of obtaining the tangent plane for a given RA and declination angle involves division by an expression that becomes zero right at the pole. The division by zero (or numbers close to, results in a very inaccurate result, even if the numerator also is close to zero).
See here if you wish to see the details of the tangent plane mapping and gnomonic projections:
https://www.ing.iac.es//Astronomy/observing/manuals/html_manuals/varia/gss_man/old/node20.html
https://mathworld.wolfram.com/GnomonicProjection.html
I.e., you have to somehow go from the surface of a sphere (i.e., the sky) to a flat plane (i.e., the camera sensor).
The two denominators become zero when the coordinates represent one of the celestial poles. Notice that the two denominators can be expressed as the cosine of some angle C, that is shown in the Wolfram link. The C in Wolfram approaches 90º as we approach the pole, thus the cosine approaches zero.
However, if you look at the equations carefully, the numerators of those two equations also approaches zero near the pole.
And if you remember from high school Calculus, you can apply l'Hopital's rule to find the limit of the result when both numerator and denominator of an expression approaches zero (i.e., by taking derivatives of both numerator and denominator).
https://en.wikipedia.org/wiki/L%27Hôpital%27s_rule
ZWO apparently did not bother to do that, and instead, just put out an error message that you cannot do a mount sync within 5º of the pole.
ZWO simply need to use a different expression (e.g., using the l'Hopital rule) when looking down at the pole. There must be someone at ZWO who can understand the math.
Yes, the projection at the pole exists (as is obvious when you look down at a globe, or a beach ball) -- see Fig 2 here for the gnomic projection at the pole:
https://en.wikipedia.org/wiki/Gnomonic_projection
BTW, this is also the reason why you cannot calibrate autoguiding near to the pole. Auto-guiding calibration is also based on mapping movements of the guide star in Equatorial coordinates (RA, declination) to the x-y coordinate of the camera (i.e., involves the tangent plane). When you calibrate near the pole, those two denominators I mentioned is very small and yield inaccurate mapping when you try to later used those calibrations for a target nearer to the Equator.
Chen
