Sidereal Day (sidereal day) - Unit Information & Conversion
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What is a Sidereal Day?
A sidereal day is the time it takes for Earth to complete exactly one rotation (360 degrees) on its axis relative to the distant fixed stars, measuring approximately 23 hours, 56 minutes, and 4.091 seconds (86,164.091 seconds). This is about 3 minutes 56 seconds shorter than the familiar 24-hour solar day, which measures Earth's rotation relative to the Sun. The difference arises because Earth orbits the Sun while rotating: after one complete rotation relative to the stars, Earth has moved roughly 1 degree along its orbital path, requiring an additional ~4 minutes of rotation to bring the Sun back to the same position in the sky. Sidereal time is the astronomer's clock—observatories worldwide use sidereal clocks to track when specific stars, galaxies, and celestial objects will cross the meridian (the imaginary north-south line through the zenith), enabling precise telescope pointing. The term "sidereal" comes from the Latin "sidus" (star), emphasizing that this measurement references the stellar background rather than the Sun. Ancient astronomers discovered sidereal time by observing that stars rise approximately 4 minutes earlier each night relative to solar time, completing a full cycle over the course of a year as Earth orbits the Sun.
History of the Sidereal Day
The concept of sidereal time dates to ancient Babylonian and Greek astronomy (circa 2000-300 BCE), when astronomers noticed that stellar positions shifted slightly earlier each night relative to the Sun's cycle, implying Earth's rotation period differed depending on the reference point. Greek astronomer Hipparchus (circa 150 BCE) used sidereal observations to measure the precession of the equinoxes—the slow 26,000-year wobble of Earth's rotational axis. The distinction between sidereal and solar days became mathematically formalized during the Scientific Revolution: Nicolaus Copernicus (1543) and Johannes Kepler (1609-1619) explained that Earth's orbital motion around the Sun created the discrepancy between the two day lengths. By the 17th century, as telescopic astronomy advanced, accurate sidereal clocks became essential for predicting stellar transits. The Royal Observatory at Greenwich (founded 1675) and Paris Observatory (founded 1667) standardized sidereal timekeeping for astronomical observations. The mean sidereal day was precisely defined as 86,164.0905 seconds by the International Astronomical Union (IAU) in the 20th century, based on Earth's rotation relative to the vernal equinox (the point where the Sun crosses the celestial equator in spring). Modern definitions use the International Celestial Reference Frame (ICRF), anchored to distant quasars billions of light-years away, providing an effectively fixed reference. Today, sidereal time remains critical for professional observatories, satellite tracking systems, and space navigation, though civil society uses solar time (UTC) for daily activities. The difference between sidereal and solar days elegantly demonstrates Earth's dual motion: rotation on its axis and revolution around the Sun.
Quick Answer
1 sidereal day = 23 hours, 56 minutes, 4.091 seconds = 86,164.091 seconds
Definition: The time for Earth to rotate 360° relative to distant stars (not the Sun)
Difference from solar day: ~3 minutes 56 seconds shorter than a 24-hour day
Why the difference? Earth orbits the Sun while rotating, so it must rotate ~361° to bring the Sun back to the same position
Quick Comparison Table
| Time Period | Duration (seconds) | Duration (h:m:s) |
|---|---|---|
| Sidereal day | 86,164.091 s | 23:56:04.091 |
| Solar day (mean) | 86,400 s | 24:00:00 |
| Difference | ~236 s | ~3:56 |
| Sidereal year | 365.256363 sidereal days | 366.256363 solar days |
| Solar year (tropical) | 365.242199 solar days | 366.242199 sidereal days |
Key insight: There is one extra sidereal day per year compared to solar days because of Earth's orbit!
Definition
What Is a Sidereal Day?
A sidereal day is the time required for Earth to complete one full rotation (360 degrees) on its axis relative to the fixed background stars.
Precise value: 1 sidereal day = 86,164.0905 seconds (mean sidereal day) = 23 hours, 56 minutes, 4.0905 seconds
Sidereal vs. Solar Day
Sidereal day (stellar reference):
- Earth's rotation relative to distant stars
- Duration: 23h 56m 4.091s
- Used by astronomers for telescope pointing
Solar day (Sun reference):
- Earth's rotation relative to the Sun
- Duration: 24h 00m 00s (mean solar day)
- Used for civil timekeeping (clocks, calendars)
The difference: ~3 minutes 56 seconds
Why Are They Different?
The sidereal-solar day difference arises from Earth's orbital motion around the Sun:
- Start position: Earth completes one full 360° rotation relative to stars (1 sidereal day)
- Orbital motion: During that rotation, Earth has moved ~1° along its orbit around the Sun
- Extra rotation needed: Earth must rotate an additional ~1° (~4 minutes) to bring the Sun back to the same position in the sky
- Result: Solar day = sidereal day + ~4 minutes
Analogy: Imagine walking around a merry-go-round while it spins. If you walk one full circle relative to the surrounding park (sidereal), you'll need to walk a bit farther to return to the same position relative to the merry-go-round center (solar).
One Extra Day Per Year
A surprising consequence: There is one more sidereal day than solar day in a year!
- Solar year: 365.242199 solar days
- Sidereal year: 365.256363 sidereal days
- Extra sidereal days: 366.256363 - 365.242199 ≈ 1 extra day
Why? Earth makes 366.25 full rotations relative to the stars during one orbit, but we only experience 365.25 sunrises because we're moving around the Sun.
History
Ancient Observations (2000-300 BCE)
Babylonian astronomy (circa 2000-1500 BCE):
- Babylonian astronomers tracked stellar positions for astrological and calendrical purposes
- Noticed stars rose earlier each night relative to the Sun's position
- Created star catalogs showing this gradual eastward drift
Greek astronomy (circa 600-300 BCE):
- Thales of Miletus (624-546 BCE): Used stellar observations for navigation
- Meton of Athens (432 BCE): Discovered the 19-year Metonic cycle, reconciling lunar months with solar years
- Recognized that stellar year differed from seasonal year
Hipparchus and Precession (150 BCE)
Hipparchus of Nicaea (circa 190-120 BCE), one of history's greatest astronomers:
Discovery: By comparing ancient Babylonian star catalogs with his own observations, Hipparchus discovered precession of the equinoxes—the slow westward drift of the vernal equinox against the stellar background
Sidereal measurements: To detect this subtle effect (1 degree per 72 years), Hipparchus needed precise sidereal positions, implicitly understanding the sidereal day concept
Legacy: His work established the difference between:
- Sidereal year: One orbit relative to stars (365.256363 days)
- Tropical year: One cycle of seasons (365.242199 days)
The ~20-minute difference between these years arises from precession.
Ptolemy's Almagest (150 CE)
Claudius Ptolemy compiled Greek astronomical knowledge in the Almagest, including:
- Star catalogs with sidereal positions
- Mathematical models for predicting stellar rising times
- Understanding that stars complete one full circuit of the sky slightly faster than the Sun
Though Ptolemy's geocentric model was wrong, his sidereal observations were accurate and useful for centuries.
Islamic Golden Age (800-1400 CE)
Islamic astronomers refined sidereal timekeeping:
Al-Battani (850-929 CE):
- Measured the tropical year to high precision
- Created improved star catalogs using sidereal positions
Ulugh Beg (1394-1449 CE):
- Built the Samarkand Observatory with advanced instruments
- Produced star catalogs accurate to ~1 arcminute using sidereal measurements
Copernican Revolution (1543)
Nicolaus Copernicus (De revolutionibus orbium coelestium, 1543):
Heliocentric model: Placing the Sun (not Earth) at the center explained the sidereal-solar day difference:
- Earth rotates on its axis (sidereal day)
- Earth orbits the Sun (creating solar day difference)
- The 4-minute discrepancy results from Earth's ~1° daily orbital motion
This was strong evidence for heliocentrism, though it took decades for acceptance.
Kepler's Laws (1609-1619)
Johannes Kepler formulated laws of planetary motion using sidereal periods:
Third Law: The square of a planet's orbital period is proportional to the cube of its orbit's semi-major axis
Application: Calculating planetary positions required precise sidereal reference frames, not solar time
Rise of Telescopic Astronomy (1600s-1700s)
Galileo Galilei (1609):
- Telescopic observations required tracking celestial objects as they moved across the sky
- Sidereal time became essential for predicting when objects would be visible
Royal Observatory, Greenwich (1675):
- Founded by King Charles II with John Flamsteed as first Astronomer Royal
- Developed accurate sidereal clocks to time stellar transits
- Greenwich Mean Sidereal Time (GMST) became the astronomical standard
Paris Observatory (1667):
- French astronomers developed precision pendulum clocks for sidereal timekeeping
- Cassini family produced detailed planetary observations using sidereal coordinates
Precision Timekeeping (1800s)
19th century: Mechanical sidereal clocks achieved second-level accuracy:
Sidereal clock design: Modified to tick 366.2422/365.2422 times faster than solar clocks (accounting for the extra sidereal day per year)
Observatory operations: Major observatories (Greenwich, Paris, Harvard, Lick, Yerkes) used sidereal clocks as primary timekeeping for scheduling observations
Photography: Long-exposure astrophotography required tracking objects at the sidereal rate to prevent star trailing
IAU Standardization (1900s)
International Astronomical Union (IAU) formalized definitions:
Mean sidereal day: 86,164.0905 seconds (exactly, by definition)
Greenwich Mean Sidereal Time (GMST): Standard sidereal time referenced to Greenwich meridian
Vernal equinox reference: Traditional sidereal time measures Earth's rotation relative to the vernal equinox (intersection of celestial equator and ecliptic)
Modern Era: ICRF (1997-Present)
International Celestial Reference Frame (ICRF):
Problem: The vernal equinox shifts due to precession, making it an imperfect reference
Solution: ICRF uses ~300 distant quasars (billions of light-years away) as fixed reference points
Accuracy: Defines celestial positions to milliarcsecond precision
Atomic time: Sidereal time is now calculated from International Atomic Time (TAI) and Earth orientation parameters measured by Very Long Baseline Interferometry (VLBI)
Modern sidereal clocks: Digital, GPS-synchronized, automatically updated for Earth rotation variations
Real-World Examples
Timescale Comparisons
1 hour of sidereal time = 59 minutes 50.17 seconds of solar time 1 hour of solar time = 1 hour 0 minutes 9.86 seconds of sidereal time
Example:
- A star rises at 20:00 sidereal time tonight
- Tomorrow it will rise at 20:00 sidereal time again (same stellar position)
- But that's ~3 minutes 56 seconds earlier in solar time each day
Star Rise Times Through the Year
Orion example (visible in northern winter):
- December 1: Orion rises at 18:00 solar time (6 PM)
- December 31: Orion rises at ~16:00 solar time (4 PM) — 2 hours earlier!
- January 30: Orion rises at ~14:00 solar time (2 PM)
Each month, Orion rises ~2 hours earlier because of the accumulated 4-minute daily shift (30 days × 4 min ≈ 120 minutes).
After one year, Orion returns to rising at 18:00 solar time—completing the cycle.
Observatory Scheduling
Astronomer's planning (using sidereal time):
Target: The Andromeda Galaxy (M31) transits the meridian at 01:30 sidereal time
When to observe?
- October 15: 01:30 sidereal = ~midnight solar time (perfect!)
- November 15: 01:30 sidereal = ~22:00 solar time (10 PM)
- December 15: 01:30 sidereal = ~20:00 solar time (8 PM)
- January 15: 01:30 sidereal = ~18:00 solar time (too early, twilight)
The sidereal time tells astronomers exactly when an object will be optimally placed, regardless of the season.
Satellite Tracking
GPS satellites orbit at specific sidereal rates:
- GPS orbital period: ~11 hours 58 minutes (half a sidereal day)
- Result: GPS satellites return to the same position in the sky every sidereal day (23h 56m 4s)
- Ground track: Repeat every sidereal day, not solar day
This synchronization with sidereal time ensures consistent satellite visibility patterns.
Earth's Rotation Rate
Rotation speed (equator):
- Earth's circumference: 40,075 km
- Sidereal day: 86,164.091 s
- Equatorial rotation speed: 40,075 km / 86,164.091 s = 465.1 m/s (1,674 km/h or 1,040 mph)
This is Earth's "true" rotation speed relative to the universe.
Common Uses
1. Telescope Pointing and Tracking
Professional observatories use sidereal time to point telescopes:
Right Ascension (RA): Celestial equivalent of longitude, measured in hours of sidereal time (0h to 24h)
Local Sidereal Time (LST): The current RA crossing the meridian
Pointing formula: If LST = 18h 30m, objects with RA ≈ 18h 30m are currently at their highest point (zenith)
Tracking rate: Telescope motors rotate at the sidereal rate (1 rotation per 23h 56m 4s) to follow stars across the sky as Earth rotates
Example:
- Vega: RA = 18h 37m
- When LST = 18:37, Vega crosses the meridian (highest in sky)
- Observer can plan observations when object will be optimally placed
2. Astrophotography
Long-exposure astrophotography requires tracking at the sidereal rate:
Problem: Earth's rotation makes stars trail across the image during long exposures
Solution: Equatorial mounts with sidereal drive motors:
- Rotate at exactly 1 revolution per sidereal day
- Keep stars fixed in the camera's field of view
- Enables exposures of minutes to hours without star trailing
Adjustment: Solar rate ≠ sidereal rate; photographers must use sidereal tracking for stars, solar tracking for Sun/Moon
3. Satellite Orbit Planning
Satellite engineers use sidereal time for orbit design:
Sun-synchronous orbits: Satellites that always cross the equator at the same local solar time
- Orbital period is chosen to precess at the solar rate, not sidereal rate
Geosynchronous orbits: Satellites that hover over one point on Earth
- Orbital period = 1 sidereal day (23h 56m 4s)
- NOT 24 hours! Common misconception.
Molniya orbits: High-eccentricity orbits with period = 0.5 sidereal days for optimal high-latitude coverage
4. Very Long Baseline Interferometry (VLBI)
Radio astronomers use VLBI to achieve ultra-high resolution:
Technique: Combine signals from radio telescopes across continents
Timing requirement: Sidereal time must be synchronized to nanosecond precision across all telescopes
Result: VLBI can resolve features 1,000 times smaller than Hubble Space Telescope (angular resolution ~0.0001 arcseconds)
Application: Measures Earth's rotation variations by observing quasars at precise sidereal times
5. Navigation and Geodesy
Sidereal time is used for precise Earth orientation measurements:
Earth Orientation Parameters (EOPs):
- Polar motion (wobble of Earth's axis)
- UT1 (Earth rotation angle, related to Greenwich sidereal time)
- Length of day variations
GPS accuracy: GPS navigation requires knowing Earth's orientation to ~1 meter precision, necessitating sidereal time corrections
Tidal forces: Moon and Sun create tidal bulges that affect Earth's rotation, causing sidereal day variations at the millisecond level
6. Space Navigation
Spacecraft use sidereal reference frames:
Star trackers: Autonomous spacecraft orientation using star patterns
- Compare observed stellar positions with catalog
- Catalog uses sidereal coordinates (RA/Dec)
Interplanetary navigation: Voyager, New Horizons, and other deep-space probes navigate using sidereal reference frames (ICRF)
Mars rovers: Use Martian sidereal time ("sols") for mission planning
- 1 Mars sol = 24h 39m 35s (Mars rotates slower than Earth)
7. Amateur Astronomy
Amateur astronomers use sidereal time for planning:
Planispheres: Rotating star charts that show which constellations are visible at any given sidereal time and date
Computerized telescopes: GoTo mounts require accurate sidereal time for automatic star finding
Observation logs: Record sidereal time of observations for repeatability
Conversion Guide
Converting Between Sidereal and Solar Time
Sidereal Day to Solar Day
Formula: Solar days = Sidereal days × 0.99726958
Example:
- 10 sidereal days = 10 × 0.99726958 = 9.973 solar days
Why? There's one fewer solar day than sidereal day per year, so sidereal days are slightly "shorter" when counted against solar days.
Solar Day to Sidereal Day
Formula: Sidereal days = Solar days × 1.00273791
Example:
- 10 solar days = 10 × 1.00273791 = 10.027 sidereal days
Sidereal Seconds to Solar Seconds
1 sidereal second = 0.99726958 solar seconds
1 solar second = 1.00273791 sidereal seconds
Local Sidereal Time Calculation
Formula: LST = GMST + Longitude / 15°
Where:
- LST: Local Sidereal Time
- GMST: Greenwich Mean Sidereal Time
- Longitude: Observer's longitude (positive east, negative west)
- Divide longitude by 15 to convert degrees to hours
Example:
- Location: Los Angeles (118.25°W = -118.25°)
- GMST: 12:00
- LST = 12:00 + (-118.25/15) = 12:00 - 7:53 = 04:07
Rate Conversion
Sidereal rate to solar rate:
1 rotation per sidereal day = 1.00273791 rotations per solar day
Example (telescope mount):
- Sidereal tracking motor: 15.041 arcseconds per second
- Solar tracking motor: 15.000 arcseconds per second
- Difference: 0.041 arcsec/s (critical for long exposures!)
Common Conversion Mistakes
1. Confusing Sidereal Time with Solar Time for Geosynchronous Satellites
The Mistake: Thinking geosynchronous satellites orbit every 24 hours (solar day)
Why It Happens: "Geo-synchronous" sounds like "synchronized with Earth's day"
The Truth: Geosynchronous satellites orbit every 23 hours 56 minutes 4 seconds (1 sidereal day), not 24 hours!
Why? To stay above the same point on Earth, satellites must complete one orbit in the time Earth rotates 360° relative to the stars (sidereal day).
Impact: Using 24 hours gives wrong orbital calculations; satellite would slowly drift westward
Correct understanding: "Synchronous with Earth's rotation" = sidereal day
2. Mixing Up Which Day Is Longer
The Mistake: Thinking the sidereal day is longer than the solar day
Why It Happens: Confusion about the extra day per year
The Truth: Sidereal day is ~4 minutes SHORTER than solar day
- Sidereal: 23h 56m 4s
- Solar: 24h 00m 0s
Correct understanding: Sidereal days are shorter individually, but there's one MORE of them per year
3. Incorrect Annual Sidereal Day Count
The Mistake: Thinking there are 365.25 sidereal days per year (same as solar days)
Why It Happens: Assuming all "days" are the same
The Truth:
- Solar year: 365.242199 solar days
- Sidereal year: 366.256363 sidereal days
- One extra sidereal day!
Why? Earth makes 366.25 complete rotations relative to stars during one orbit, but we only experience 365.25 sunrises
4. Forgetting to Account for Longitude When Calculating LST
The Mistake: Using Greenwich Mean Sidereal Time (GMST) for local observations without longitude correction
Why It Happens: Overlooking that sidereal time, like solar time, depends on longitude
The Truth: LST = GMST ± (longitude offset)
Example error:
- Observer in New York (74°W)
- GMST = 12:00
- Wrong: LST = 12:00
- Correct: LST = 12:00 - (74°/15°) = 12:00 - 4h 56m = 07:04
Impact: Telescope will point ~5 hours wrong!
5. Using Wrong Tracking Rate for Astrophotography
The Mistake: Using solar tracking rate (15.000 arcsec/s) instead of sidereal rate (15.041 arcsec/s) for star photography
Why It Happens: Most telescope mounts default to solar tracking for Sun/Moon
The Truth: Stars require sidereal tracking (15.041 arcsec/s)
Impact on 10-minute exposure:
- Error accumulation: 0.041 arcsec/s × 600s = ~25 arcseconds
- Result: Noticeable star trailing (stars appear elongated)
Correct approach: Switch mount to sidereal mode for deep-sky astrophotography
6. Incorrectly Converting Sidereal Hours to Solar Hours
The Mistake: Thinking 1 sidereal hour = 1 solar hour
The Truth: 1 sidereal hour = 59 minutes 50.17 seconds of solar time
Example:
- Event duration: 2 sidereal hours
- Wrong conversion: 2 hours solar time
- Correct conversion: 2 × 59.836 min = 119.67 min = 1 hour 59 minutes 40 seconds solar time
Impact: Observation timing errors accumulate over hours
Sidereal Day Conversion Formulas
To Second:
To Minute:
To Hour:
To Day:
To Week:
To Month:
To Year:
To Millisecond:
To Microsecond:
To Nanosecond:
To Decade:
To Century:
To Millennium:
To Fortnight:
To Planck Time:
To Shake:
To Sidereal Year:
Frequently Asked Questions
Answer: 23 hours, 56 minutes, 4.091 seconds (or 86,164.091 seconds) This is the time for Earth to rotate exactly 360 degrees relative to distant stars. Precise value: 1 mean sidereal day = 86,164.0905 seconds Comparison to solar day:
- Solar day: 86,400 seconds (24 hours)
- Sidereal day: 86,164.091 seconds
- Difference: ~236 seconds shorter (~3 min 56 sec) Important: This is the mean sidereal day. Earth's actual rotation rate varies slightly (milliseconds) due to tidal forces, atmospheric winds, earthquakes, and core-mantle coupling.
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Sidereal Day Quick Info
Related Time Units
Popular Conversions
- Sidereal Day to SecondConvert →1 sidereal day = 86164.091 s
- Sidereal Day to MinuteConvert →1 sidereal day = 1436.068183 min
- Sidereal Day to HourConvert →1 sidereal day = 23.93447 h
- Sidereal Day to DayConvert →1 sidereal day = 0.99727 d
- Sidereal Day to WeekConvert →1 sidereal day = 0.142467 wk
- Sidereal Day to MonthConvert →1 sidereal day = 0.032765 mo