Astronomy education tool
Watch a 24-hour solar clock beside Greenwich sidereal time, the star-based day that lasts 23 hours, 56 minutes, and 4.090 seconds.
Solar clock vs star clock
Compare ordinary local solar time with Greenwich sidereal time, the clock astronomers use to know which right ascension is crossing the meridian.
Your local civil clock
Right ascension on Greenwich meridian
Accumulated since local midnight
Earth must rotate a little farther after one star-relative spin so the Sun appears on the meridian again. That extra angle is why the solar day is longer.
Formula note: Greenwich mean sidereal time uses the simplified Meeus expression also referenced by the U.S. Naval Observatory for approximate sidereal time.
A solar day is the familiar 24 hours from one noon to the next. A sidereal day is one full rotation of Earth measured against the distant stars: 86164.090 seconds, or 23h 56m 4.090s. The gap is almost four minutes because Earth is not only spinning; it is also moving along its orbit around the Sun.
After Earth makes one star-relative rotation, the same stars are back on the meridian, but the Sun appears slightly displaced because Earth has advanced in its orbit. Earth must rotate about one extra degree for the Sun to reach the same apparent position. That small extra turn adds about 236 seconds, so stars rise roughly four minutes earlier each night by an ordinary clock.
Astronomers use sidereal time because sky coordinates are tied to right ascension and declination, not to noon on a civil clock. If the local sidereal time is 10h, objects near right ascension 10h are crossing the local meridian. GPS and other satellite systems need both ideas: solar/civil time for users and Earth-rotation/star-frame math for transforming satellite positions into coordinates on the rotating Earth.
The two day lengths compared here are fixed constants: a mean solar day of 86,400,000 milliseconds and a mean sidereal day of 86,164,090 milliseconds. Subtracting them leaves 235,910 milliseconds, or 3 minutes 55.91 seconds, the nightly head start the stars gain on the Sun.
The sidereal clock follows the standard Greenwich Mean Sidereal Time expression from Meeus. The current instant is converted to a Julian date by dividing Unix milliseconds by 86,400,000 and adding 2,440,587.5, then counted as days from the J2000 epoch at Julian date 2,451,545.0. GMST in degrees is 280.46061837 plus 360.98564736629 for each of those days, plus two very small century-scale correction terms. That daily coefficient tells the whole story in one number: Earth turns 360.9856 degrees per solar day, and the extra 0.9856 degrees beyond a full circle is what the Sun's apparent drift along the ecliptic demands.
Suppose a star crosses your meridian at 22:00 tonight. Tomorrow it crosses near 21:56. After 30 nights the accumulated shift is 235.91 seconds multiplied by 30, roughly 7,077 seconds, so the same star now culminates close to 20:02. That two-hours-per-month drift is why each season presents a different sky at any fixed evening hour, and why observers plan targets by right ascension rather than by the civil clock.
The nightly four minutes compound into exactly one full turn per orbit. A year of about 365.25 solar days contains about 366.25 sidereal rotations, and the ratio between those two counts is the constant behind this page. The bonus rotation is the orbit itself: travel once around the Sun and the geometry hands you one additional spin relative to the stars, no matter where you start counting.
Add your longitude east of Greenwich converted at 15 degrees per hour, or subtract if you are west. An observer at 30 degrees east reads a local sidereal time two hours ahead of the Greenwich figure shown here.
Objects with right ascension near 10 hours are crossing your meridian, their highest and best-placed point. Reading a sidereal clock is reading which slice of the celestial sphere is optimally positioned right now.
It is a mean value. Earth's rotation wanders at the millisecond level because of tides, the atmosphere, and the fluid core, so precise geodesy uses measured rotation data. For a wall display and for planning observations, the mean formula is more than accurate enough.
Human schedules follow daylight. A sidereal clock gains about 3 minutes 56 seconds on the Sun every day, so sidereal noon would sweep through the entire solar day over the course of one year.
No, 24 hours is the mean. The true interval between successive solar noons varies through the year because Earth's orbit is elliptical and its axis is tilted. The accumulated difference, called the equation of time, can push apparent noon around a quarter of an hour away from clock noon.
Sources: Jean Meeus, Astronomical Algorithms; U.S. Naval Observatory approximate sidereal time; USNO sidereal time data service.