Re: [Utah-astronomy] Polar Alignment and RA/Dec Drift
Thanks Daniel, I'm not sure if it reduces to just coordinate translation but good luck. I'd be interested to see what you come up with. Here's an interesting essay http://www.stargazing.net/yizen/fieldrotation.html Cheers David
--- Naz & David <naz_david@msn.com> wrote: <snip> David, Appendix B to Micheal Covington's _Astrophotography for the Amateur_ (1999, 2ed), entitled "Matematical analysis of polar-axis misalignment, Covington works through the problem of one-star alignment from the viewpoint of changes in the rate of declination drift change. See Section. B2.2 "Rate of declination drift at any particular time." Covington works through the problem forward from an assumed misalignment back to an estimated declination drift. Covington's math is similar to the equations that Daniel is working on. Covington does not reverse solve the problem -> known declination drift to misalignment error. Reverse solving the equation for declination drift for a star and a misaligned scope is difficult because you solving for two unknowns: 1) The distance from the false pole to the true pole. 2) The hour angle between the false pole and the meridian of the test star. There are many combinations of hour angle and distance error for any observed declination drift. That is probably why Convington does not do present a reverse solution. Essentially, you take an initial guess at the misalignment and repeat until the error is reduced. My GOTO 1-, 2- and 3-star controller seems to use this method. The scope's initial 1-star alignment guess is usually horribly off - by as much as 10 degrees. After the first star is manually sync'd, the 2nd and 3rd stars rapidly compensate for the alignment error. But, it would be nice to have a simple small-angle table showing by drift direction (a position angle) and arcsecs of drift for let's say 30 secs, the corresponding direction and degree of polar misalignment error. - Canopus56(Kurt) P.S. - Another set of equations and program code for polar misalignment is Taki's. http://www.asahi-net.or.jp/~zs3t-tk/aim/aim.htm and published at Taki, T. Feb. 1989. Program for pointing a telescope. Sky & Telescope. pp. 194-196. I looked at this some time ago, and grabbed his code implementation from Taki's website. But the map was over my head and I did not pursue it. But I thought I'd pass the reference on. Also see the discussion in Covington's informal paper regarding one-star initialization alginment of the LX Meade200. "Polar Alignment by Iterating on One Star and Polaries" 4/8/2001. << www.covingtoninnovations.com/astro/iterating.pdf accessed 11/2005 >>. __________________________________ Yahoo! Mail - PC Magazine Editors' Choice 2005 http://mail.yahoo.com
--- Canopus56 <canopus56@yahoo.com> wrote: <snip all> P.S. - In the back of Appendix B, Covington also includes some java code for his declination drift equations and for field rotation. The java rountine in the book is distributed through his website with a note that it can be freely redistributed. Here it is: // Polar.java - M. Covington 1997 /* To accompany Astrophotography for the Amateur, 1998 edition. You may freely redistribute this program. */ /* Snip input output routines */ // THE COMPUTATION ITSELF // Library functions and constants double cos(double x) { return Math.cos(x); } double sin(double x) { return Math.sin(x); } double acos(double x) { return Math.acos(x); } double asin(double x) { return Math.asin(x); } double square(double x) { return x*x; } double sqrt(double x) { return Math.sqrt(x); } double abs(double x) { return Math.abs(x); } double DR = 180/Math.PI; // degrees-to-radians factor, ~57.3 double decdrift( // Declination drift, in arc-seconds, computed from: double e, // Polar misalignment, in degrees double h, // Hr angle of star - hr angle of false pole, degrees double delta, // Declination of star, in degrees double t) // Duration of exposure, in minutes of time { double x, y, z; // local variables e = e/DR; // convert to radians h = h/DR; delta = delta/DR; t = (t/4)/DR; x = sin(delta)*cos(e); // core of computation y = cos(delta)*sin(e); z = acos(cos(h+t)*y + x) - acos(cos(h)*y + x); z = z * DR * 3600; // convert to arc-seconds if (abs(z) < 0.0001) z = 0.0; // discard if too small (imprecise) return z; } double rotation( // Field rotation, in degrees double e, // Polar misalignment, in degrees double h, // Hr angle of star - hr angle of false pole, degrees double delta, // Declination of star, in degrees double t) // Duration of exposure, in minutes of time { double w, x, y, z; // local variables e = e/DR; // convert to radians h = h/DR; delta = delta/DR; t = (t/4)/DR; w = sin(e); // core of computation x = sin(delta)*cos(e); y = cos(delta)*w; z = asin(w*sin(h+t) / sqrt(1 - square(cos(h+t)*y + x))) - asin(w*sin(h) / sqrt(1 - square(cos(h)*y + x))); z = z * DR; // convert to degrees if (abs(z) < 0.0001) z = 0.0; // discard if too small (imprecise) return z; } - Best of luck - Canopus56(Kurt) __________________________________ Yahoo! Mail - PC Magazine Editors' Choice 2005 http://mail.yahoo.com
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