Maximal exposure from tripod without star trails

For a while I was trying to find out what is origin of famous 600 rule without success. Here is what I learned so far. That would be rule applicable to picture taken from tripod, without tracking. That rule says that maximal exposure time for star with declination of 0 degrees is equal 600 divided with focal length in seconds. Here we are talking about 35mm film, so for DSLR camera we need to multiply focal length with crop factor, 1.5 for Nikon and 1.6 for Canon. Declination 0 degrees is celestial equator. Further, rule talks about 0.1mm at 254mm, reading distance, so I assume that image is printed on A4 paper. Since 35mm film went to history that 0.1 mm somehow is mapped to 8 pixels for DSLR camera. Is 8 pixels acceptable or not is another issue. There is even formula:

Maximal exposure = sidereal day * acceptable trail * pixel size /(focal length*2*π*cos(declination))

The sidereal day is 23 h 56 m 4.09 s, acceptable trail is 8 pixels, pixel size for Canon EOS 600D/Ti3 is 0.00429 mm, focal length is 80 mm (50 mm * 1.6), cos(0) is 1. All values must be expressed in the same units. When we convert sidereal day into seconds we have 86164.09 s. After substituting values into equation we got result 5.883066121 s. Some sensor data is available on http://www.sensorgen.info/, crop factor for Nikon and Sony is 1.5, what is acceptable trail for you I do not know, feel free to use it instead of suggested 8 pixels. To find out what is declination of some star, install Stellarium, ignore negative declination on southern hemisphere and use absolute value.
Trigonometric functions are available in any calculator on any OS, just switch into scientific mode. How that cosine influences result? For Orion we can neglect it, but if we want to take picture of Southern Cross about 60 degrees declination our maximal exposure doubles. For declination of 90 degrees we have singular point where exposure grows to infinity, if there is a star at celestial pole we can take whole night exposure - it is not moving. Closer to celestial pole you are, longer exposures are acceptable.