Sidereal Time Calculator (GMST / LST)
Sidereal time is the clock that measures Earth's rotation relative to the vernal equinox. One sidereal day = 23h 56m 4.0905s of solar time — roughly *3m 56s shorter* than a solar day, which means *one extra rotation per year* against the stars. Given UTC date / time / longitude, the tool returns *Greenwich Mean Sidereal Time (GMST)* and *Local Sidereal Time (LST)*. LST is exactly equal to the *right ascension currently on your local meridian* — the foundation of telescope setting circles, transit prediction and amateur astronomy.
Enter a valid UTC date, time and longitude in (−180°, 180°].
GMST — Greenwich Mean Sidereal Time
—
LST — Local Sidereal Time
—
Julian Day
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Right ascension currently on the meridian
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*Sidereal time* is the clock that measures Earth's rotation against the vernal equinox — one sidereal day = 23h 56m 4.0905s of solar time. Local Sidereal Time (LST) equals the *right ascension currently on the local meridian*: telescope mounts, star-chart matching and finding when an object transits all read directly off LST. This tool implements the *IAU 1982 mean-sidereal-time polynomial* (equivalent to NOVAS / SOFA `iauGmst82()`); GMST accuracy versus any UT in the 1900–2100 range is about ±0.1 s, well below any backyard-telescope pointing tolerance. It does *not* apply nutation corrections for *apparent* sidereal time (≈ ±1 s) — for sub-arcsecond precision use IAU 2006 / SOFA `iauGst06a`.
Formula
T = (JD_{UT, 0h} − 2451545.0) / 36525 GMST(0h UT) = 24110.54841 + 8640184.812866·T + 0.093104·T² − 6.2×10⁻⁶·T³ [seconds] GMST = GMST(0h UT) + 1.00273790935·UT_seconds (mod 86400) LST = GMST + longitude / 15h (mod 24)
- · *Sidereal vs solar*: a solar day is one rotation relative to the Sun (24 h); a sidereal day is one rotation relative to the *vernal equinox / distant stars* (23h 56m 4.0905s). The difference reflects Earth's annual revolution: in one year the planet completes ≈ 365.25 revolutions about the Sun but ≈ 366.25 rotations relative to the stars — one extra spin.
- · *Why LST is useful*: (1) telescope setting circles — point the RA axis at LST and the hour angle is zero (the object is transiting the meridian); (2) star-chart matching — knowing LST = 18 h tells you RA 18 h is overhead now; (3) imaging timing — an object reaches maximum altitude (least air-mass) exactly when LST = RA.
- · *Mean vs apparent*: this tool returns *mean sidereal time*, which uses only Earth's rotation and the J2000 mean equinox. *Apparent sidereal time* (GAST / LAST) adds the *equation of the equinoxes* (nutation in longitude), differing by ≈ ±1.1 s. That is invisible to amateur pointing (≈ 10 arcsec ≈ 0.67 s), but for sub-arcsecond work use IAU 2006 / SOFA `iauGst06a`.
- · *ΔT and UT1 − UTC*: this tool treats input as UT1 (≈ UTC). Actual UT1 − UTC is bounded by ±0.9 s and published by IERS Bulletin A; leap-second jumps can swing ΔT by ±1 s. Using UTC directly is accurate enough for almost any visual or imaging observation.
- · *Longitude convention*: this tool uses *east positive, west negative*, range (−180°, 180°]. Hong Kong = +114.16°, New York = −74.01°, London ≈ 0°, Tokyo = +139.69°, Sydney = +151.21°.
- · *Sources*: U.S. Naval Observatory *Astronomical Almanac* page B6; Seidelmann (ed.) *Explanatory Supplement to the Astronomical Almanac* 1992 §2.24; IAU 1982 Resolution C2; Meeus *Astronomical Algorithms* 2e §12; SOFA Tools for Earth Attitude (`iauGmst82`, `iauGst06a`).
Frequently asked
Why do GMST and LST differ by hours?
Because LST = GMST + observer longitude / 15 h. Earth rotates 360° in 24 hours → *15° = 1 sidereal hour*. Each 15° east advances LST by one hour relative to GMST, because the vernal equinox crosses your meridian first and Greenwich after. Examples: Hong Kong at +114.16° → LST = GMST + 7h 36m 38s; at GMST = 6 h, Hong Kong LST ≈ 13h 36m. London ≈ 0° so GMST = LST; New York at −74° → LST trails GMST by 4h 56m. In practice apps like SkySafari and Stellarium read your GPS / clock automatically; this tool is for hand checks, traditional setting circles, observatory operations or timing verification.
How do I actually use LST at a telescope?
Workflow: (1) pick a target — say the *Orion Nebula M42*, RA = 5h 35m 17s, Dec = −5° 23'; (2) compute the current LST with this tool; (3) the *hour angle HA = LST − RA*. HA = 0 means the target is transiting the meridian (highest in the sky, best seeing); HA > 0 means it has already crossed (setting in the west); HA < 0 means it has yet to rise. Example: LST = 6h 00m and M42 RA = 5h 35m → HA = 0h 25m, so M42 crossed the meridian 25 minutes ago and is still well placed. To slew, set the telescope's RA axis to LST, then dial RA 5h 35m on the setting circle — the tube swings to M42 (assuming a properly polar-aligned mount and a calibrated home position).
Why does LST at the same clock time differ a year later?
Because sidereal and solar time run at different rates. Each solar day, LST gains *3m 56.555s* against the wall clock. Over a year (365.25 solar days) the accumulated gain is ≈ 23h 59m 39s ≈ 24 h — *LST completes one full extra cycle per year*. Example: tonight at 21:00 UTC in Hong Kong, LST ≈ 12h 36m; in 365 days at the same 21:00 UTC the LST is again ≈ 12h 36m (off by a few seconds); but 182 days later at 21:00 UTC, LST ≈ 12h 36m + 12 h = 00h 36m. That is why *constellations visible at 9 pm in summer return at 3 am six months later* — the same LST shows the same sky, but the solar clock has shifted.
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