The star field on our homepage isn’t a stock animation or a random particle scatter — every point is a real star, plotted from its actual right ascension and declination, run through the same altitude-azimuth transform a telescope’s tracking software uses.
That transform takes three real inputs — the star’s fixed sky coordinates, an observer’s latitude, and the current Local Sidereal Time — and produces where that star actually sits above the horizon, right now, from that spot on Earth. Advance the simulated time and every star moves exactly the way the real sky does: rising in the east, arcing across, setting in the west, all without a single frame being hand-animated.
We sped the clock up for the homepage — a real night takes hours to visibly turn, and most visitors don’t have hours to spare — but the underlying math is the same equation printed in any spherical astronomy textbook.