This program predicts the angle to the north or south of true east at which the sun will rise at a given latitude and day of the year. This program has been written assuming that the earth is a sphere and the observer's horizon is a plane tangent to the earth. The tilt of the earth's axis towards the sun does not vary uniformly during a year, and in order to verify if the program produces an accurate result, one must know the tilt on the day when, and the latitude of the location where the observation is made. The following websites give the declination, and the latitude of important places respectively:
I myself have not made concrete measurements to verify the accuracy of the program's result due to lack of outdoor space, but the observation I made required an estimation, and the program's result was within the range of estimated values. The following is the description of the method I used.
The shadow cast by the tip of a pole traces a hyperbola anywhere between the arctic and antarctic circles. The asymptotes of the hyperbola (please see the figure at the bottom of page) will point in the direction of sunrise and sunset. The angle between the asymptote and true east can then be measured. True north-south direction would be the line joining the pole's base and the point on the shadow's path closest to the base.
Please contact me if you verify the results of my program. Thanks for reading this page.