What sidereal time measures
The clock on the wall follows the Sun: a solar day is the interval between two successive passages of the Sun across your meridian, and it averages exactly 24 hours. Sidereal time follows the stars instead. It is defined as the hour angle of the vernal equinox — how far, in hours, the vernal equinox has turned west of your local meridian. When sidereal time reads 0h, the vernal equinox is crossing the meridian.
Because right ascension is counted from the same vernal equinox, sidereal time has a very practical meaning: local sidereal time (LST) equals the right ascension of the stars that are crossing your meridian at that moment. If your sidereal clock reads 18h 38m, Vega (right ascension about 18h 38m) is at its highest point in the sky. A glance at a sidereal clock therefore tells an observer which part of the sky is best placed for observation.
Why a sidereal day is shorter than a solar day
Earth turns once on its axis relative to the distant stars in about 23 h 56 m 4 s of ordinary time. During that turn it also moves about 1/365 of the way around its orbit, so the Sun appears to shift roughly 1° eastward among the stars. Earth has to rotate that extra degree — about 3 minutes 56 seconds — before the Sun comes back to the meridian. That is why the mean solar day lasts 24 h while the sidereal day lasts 23 h 56 m 4 s.
The difference is visible every night: a given star rises, culminates and sets about 3 m 56 s earlier each day, or roughly two hours earlier each month. Over a year it adds up to exactly one extra rotation, so a year contains about 366.24 sidereal days but only 365.24 solar days. This is why Orion dominates January evenings but is lost in the daytime sky in July.
| Quantity | Value |
|---|---|
| Mean solar day | 24 h 00 m 00 s |
| Sidereal day | 23 h 56 m 04.09 s |
| Difference per day | 3 m 55.91 s |
| Solar days in a tropical year | ≈ 365.2422 |
| Sidereal days in a tropical year | ≈ 366.2422 |
| Sidereal time gained per solar day | ≈ 3 m 56.56 s |
Computing Greenwich sidereal time
Jean Meeus gives a compact formula for the mean sidereal time at Greenwich, θ₀, at any instant. It uses the Julian Day JD of that instant (in Universal Time) and T, the number of Julian centuries elapsed since the standard epoch J2000.0:
T = (JD − 2451545.0) / 36525θ₀ = 280.46061837° + 360.98564736629° × (JD − 2451545.0) + 0.000387933° × T² − T³ / 38 710 000Reduce the result to the range 0°–360° and divide by 15 to express it in hours. The large coefficient of 360.9856° per day is simply Earth's rotation measured against the equinox: slightly more than one full turn per solar day. The T² and T³ terms are tiny corrections that come from the slow motion of the equinox itself (precession).
This value is the mean sidereal time. Adding the nutation in longitude multiplied by the cosine of the obliquity — the so-called equation of the equinoxes, never more than about one second — gives the apparent sidereal time, used for the most precise telescope pointing.
From Greenwich to your location
Sidereal time depends on longitude exactly as solar time does. Local sidereal time is Greenwich sidereal time plus the observer's longitude, counted positive towards the east and converted to time at the rate of 15° per hour:
LST = θ₀ + λ(east) / 15 (hours)H = LST − α (hour angle)The hour angle H of any object follows immediately from its right ascension α. H = 0 means the object is on the meridian; a positive hour angle means it has already crossed the meridian and is moving toward the west; a negative one means it is still rising in the east. Hour angle and declination are exactly what an equatorial telescope mount uses to point at a target.
Worked example: when does Vega cross the meridian over Paris?
- Date and time: 1 October 2026 at 0h UT. The Julian Day is JD = 2461314.5.
- Applying the formula above gives a Greenwich mean sidereal time of θ₀ ≈ 0h 38m 58s.
- Paris lies at longitude 2.35° E, which is 2.35 / 15 = 0h 09m 24s. Local sidereal time at 0h UT is therefore about 0h 48m 23s.
- Vega's right ascension for 2026 is about 18h 37m 51s (its J2000.0 value of 18h 36m 56s, advanced by precession).
- Vega transits when LST reaches 18h 37m 51s, that is after 17h 49m 28s of sidereal time. Converting to solar time (dividing by 1.0027379) gives 17h 46m 33s.
- Vega therefore culminates over Paris at about 17:47 UT, or 19:47 local summer time, almost overhead at about 80° above the southern horizon.
The same method tells you when any star, planet or deep-sky object is best placed: it is highest, and its light crosses the least atmosphere, when local sidereal time equals its right ascension.
Sidereal time on AstroAlgos
The sky disk and the 3D night-sky view compute local sidereal time for every frame they draw: it is the angle that rotates the star catalogue into your local horizon. When you press Play and watch the stars wheel around the celestial pole, you are watching sidereal time run about 4 minutes per day ahead of the clock shown in the control bar.
Explore it on AstroAlgos
Frequently asked questions
Is sidereal time the same everywhere on Earth?
No. Like solar time it depends on longitude: local sidereal time is Greenwich sidereal time plus the observer's east longitude expressed in hours. Two observers on the same meridian share the same sidereal time whatever their latitude.
What is the difference between a sidereal day and a stellar day?
The sidereal day is measured relative to the moving vernal equinox and lasts 23 h 56 m 4.091 s. The stellar day is measured relative to the fixed stars and is about 8 milliseconds longer because of precession. For observing purposes the difference is negligible.
Why do astronomers use sidereal time?
Because it tells you directly which part of the sky is on the meridian. An object is highest in the sky when local sidereal time equals its right ascension, so telescope mounts, observatory schedules and star atlases all rely on it.