What is the relationship between the width of a star trail(on a photo of 15 min exposure time) and the star's intensity?
I cannot give you an exact relationship between the width of star trails and the stellar intensity as that requires one to know the point spread function of your telescope and camera optics. However, one can say that a star with brighter intensity will produce a wider star trail. This is because of the following reason:
If you take an image of a point source (for example, a star), the resulting image will not be a point, but instead some function involving a main lobe and side lobes. This is called the point spread function of the instrument. Thus, the image that you get will be the superposition of several point spread functions shifted to the location of the stars and multiplied by the intensity of the stars. Usually, in photographic images of stars, the side lobes do not show up, but you do see the width of the main lobe. As the image consists of point spread functions multiplied by the stellar intensity, brighter stars will give a wider lobe, which gives rise to wider star trails in long exposures of stellar fields (without tracking).
This page was last updated June 28, 2015.