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I am new to this domain and trying to understanding the fundamentals of local sidereal time. Through an online available calculator https://www.iiap.res.in/personnel/reks/software/javascript/calclst.php ,I am noting down the local sidereal time for my longitude of interest. I have repeated the exercise for same time for five consecutive days. What I observe is that the local sidereal time is advancing by 0.06/07 hours per day for the same time.Like 21.88 Hours for current date and time , 21.94 Hours for the same time next day ,22.01 Hours for next to next day and the pattern continues. Kindly let me know how this increment is happening?

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If you extrapolate, you'll find that those ~4 minutes per day add up to 24 hours per year. The difference is due to the Earth revolving around the Sun at a rate of almost 1 degree per day. For every 365$\frac{1}{4}$ solar days, there are 366$\frac{1}{4}$ sidereal days.

Civil time is based on mean solar time, in which the Sun crosses the celestial meridian every 24h 0m on average. In sidereal time, 24h 0m is the time between successive meridian transits by any given star, equivalent to 23h 56m 4s of solar time.

Sidereal time also corresponds to the right ascension of stars crossing the meridian at that time. If a star in Orion has right ascension 5h 30m, then Orion is on the meridian at 05:30 sidereal time, which occurs 2 hours earlier in the solar day per month.

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