Local Siderial Time is the 'star time'. It is the hour angle of the vernal equinox. Or in more useful terms, the right ascension of the stars on your local celestial meridian.
Julian Day is a linear count of days starting on January 1, 4713 BC and is commonly used for astronomical calculations. The Julian Day starts at Noon Universal Time (UT) hence at 0h UT the Julian day is some whole number + 0.5.
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Updated with corrections for errors- 7 Nov, 2000
Siderial Time > 24 hr corrected - Nov 20,2002