Astronomers translate all historic dates into a common Julian calendar date. Using this calendar, any two dates (since January 1, 4713 BCE) may be precisely compared to find the interval, and thereby compute elapsed time.

Try this using the times of the three reported observations of Ceres used by Gauss in his calculations:

t1=8 hours 39 minutes 4.6 seconds p.m. on January 2, 1801

t2=7 hours 20 minutes 21.7 seconds p.m. on January 22, 1801

t3=6 hours 11 minutes 58.2 seconds on February 11, 1801

Go here for a Julian date converter.