Simulation
Withe a simulation it is possible to study the various effects of the refraction, dispersion and the alignment of the hour axis. The description should make the beginning easier because the usage of the program and the interpretation of the results needs some knowledge.
Today the properties of a real telescope designs are investigated by means of ray tracing. These programs give answers to the question: what happens to a point like source in the focal plane of a real world telescope under an ideal sky.
Here I do the complement and answer the question: what happens to a point like sources in the focal plane of an ideal diffraction limited telescope under real sky conditions.
Bringing these two aspects together we get a comprehensive picture of the star image in the focal plane.
Both animated GIFs below show how the trails of 25 stars which are located on a regular grid with an edge length of 1 degree depend on the exposure time. The simulated photograph is guided in the center at the wavelength of 550 nm (yellow pixel). The blue and the red trail corresponds to the wavelength of 450 and 650 nm (three color mode). The declination of the field center was -10 degree and at the beginning the local hour angel was 3h. The exposure time was 6 hours in steps of 30 minutes. The scale bar at the lower left has a length of 2.5 arcsecond and belongs to the star trails which are magnified by a factor of 120 in order making them visible. The star trails are larger than the resolution of the objective (20 cm diameter). Even if the exposure time is cut down to of 30 minutes the effects of the refraction and dispersion are easily seen in the first animated photograph. The field rotation and the field compression are visible as well. The figure corresponds to the analytically calculated star trails after H.H. Turner.
Same as above but cumulated star trails.
Comments, questions, corrections: markus.wildi@one-arcsec.org