A more reliable solution would be to use track and stack software. Much of it is free but I prefer to use Astrometrica which also does your precision Astrometric and general photometric image measurement as well (including tracked and stacked images). This way you can take a lot of short exposure images then get the software to align it base don the targets know motion.
Astrometrica costs 20E I think (shareware) but it's pretty much standard fare for the Astrometry crowd (
www.astrometrica.at)
Cheers