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If you look up in the sky, you see stars and planets. BY CONVENTION, we humans have decided to create a coordinate system based on the latitude and longitude system on the Earth's surface. Celestial latitude is called Declination and is measured in degrees starting at the celestial Equator and increasing to +90 degrees at the North Celestial Pole near Polaris, and decreasing to -90 degrees towards the South Celestial Pole. Celestial longitude is called Right Ascension, but instead of being measured in degrees increasing to the west from Greenwich, England, it increases to the West from the so-called First Point in Aries.
Local Sidereal Time is the exact Right Ascension of an object which has just arrived at your local meridian. If you were to draw a line on the sky that went from the North Celestial Pole ( near Polaris), passed exactly over head ( through your Zenith) and then connected with the South Celestial Pole, this line would be your local Meridian. No two observers on the Earth, even separated by as little as a few hundred feet, have exactly the same meridian. The Local Sidereal Time is just the Right Ascension of the object that just transited your local meridian. Because the Earth moves in its orbit, the 'LST' on two consecutive nights is slightly different by about 24/365 = 1/15 of an hour or about 4 minutes.