Second to Sidereal Day Converter
Convert seconds to sidereal days with our free online time converter.
Quick Answer
1 Second = 0.0000116 sidereal days
Formula: Second × conversion factor = Sidereal Day
Use the calculator below for instant, accurate conversions.
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All conversion formulas on UnitsConverter.io have been verified against NIST (National Institute of Standards and Technology) guidelines and international SI standards. Our calculations are accurate to 10 decimal places for standard conversions and use arbitrary precision arithmetic for astronomical units.
Second to Sidereal Day Calculator
How to Use the Second to Sidereal Day Calculator:
- Enter the value you want to convert in the 'From' field (Second).
- The converted value in Sidereal Day will appear automatically in the 'To' field.
- Use the dropdown menus to select different units within the Time category.
- Click the swap button (⇌) to reverse the conversion direction.
How to Convert Second to Sidereal Day: Step-by-Step Guide
Converting Second to Sidereal Day involves multiplying the value by a specific conversion factor, as shown in the formula below.
Formula:
1 Second = 1.1606e-5 sidereal daysExample Calculation:
Convert 60 seconds: 60 × 1.1606e-5 = 0.000696346 sidereal days
Disclaimer: For Reference Only
These conversion results are provided for informational purposes only. While we strive for accuracy, we make no guarantees regarding the precision of these results, especially for conversions involving extremely large or small numbers which may be subject to the inherent limitations of standard computer floating-point arithmetic.
Not for professional use. Results should be verified before use in any critical application. View our Terms of Service for more information.
Need to convert to other time units?
View all Time conversions →What is a Second and a Sidereal Day?
What Is a Second?
The second (symbol: s) is the SI base unit of time, defined with extraordinary precision using atomic physics rather than astronomical observations.
Official SI definition (since 1967): The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at absolute zero temperature and at rest.
In simpler terms:
- Caesium-133 atoms oscillate at a precise frequency when energized
- One second equals exactly 9,192,631,770 of these oscillations
- This provides a natural, unchanging standard independent of Earth's rotation
Why this matters: This atomic definition provides accuracy to better than 1 second in 100 million years for modern atomic clocks, enabling:
- GPS navigation (accuracy requires nanosecond precision)
- Global telecommunications synchronization
- Scientific experiments requiring extreme precision
- Financial transaction timestamps
- Internet infrastructure coordination
Second vs. Other Time Units
Subdivisions of the second:
- 1 decisecond (ds) = 0.1 s = 10⁻¹ s (rarely used)
- 1 centisecond (cs) = 0.01 s = 10⁻² s (stopwatch hundredths)
- 1 millisecond (ms) = 0.001 s = 10⁻³ s (computer operations)
- 1 microsecond (μs) = 0.000001 s = 10⁻⁶ s (electronics, photography)
- 1 nanosecond (ns) = 0.000000001 s = 10⁻⁹ s (computer processors, GPS)
- 1 picosecond (ps) = 10⁻¹² s (laser physics, molecular vibrations)
- 1 femtosecond (fs) = 10⁻¹⁵ s (ultrafast lasers, chemical reactions)
Multiples of the second:
- 60 seconds = 1 minute
- 3,600 seconds = 1 hour
- 86,400 seconds = 1 day
- 604,800 seconds = 1 week
- 31,536,000 seconds = 1 year (365 days)
- 31,557,600 seconds = 1 Julian year (365.25 days)
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.
Note: The Second is part of the imperial/US customary system, primarily used in the US, UK, and Canada for everyday measurements. The Sidereal Day belongs to the imperial/US customary system.
History of the Second and Sidereal Day
Ancient Origins: Babylonian Mathematics (3000 BCE)
The division of time into units of 60 has roots in ancient Babylonian sexagesimal (base-60) mathematics:
Why base-60?
- Highly divisible: 60 has divisors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Finger counting: Babylonians counted 12 finger segments (phalanges) on one hand using the thumb, repeated 5 times for the other hand (12 × 5 = 60)
- Astronomical convenience: 360 days approximated the year (6 × 60), aligning with the 360-degree circle
Time divisions established:
- 1 day = 24 hours (2 × 12)
- 1 hour = 60 minutes
- 1 minute = 60 seconds
This system spread through ancient Egypt, Greece, and Rome, persisting for over 4,000 years.
Medieval Development: Mechanical Clocks (1200s-1600s)
The word "second" derives from Medieval Latin "pars minuta secunda" meaning "second minute part" (the second division of the hour):
- First division: Hour divided into 60 "pars minuta prima" (first minute parts) = minutes
- Second division: Minute divided into 60 "pars minuta secunda" (second minute parts) = seconds
Early mechanical clocks (1200s-1300s):
- Displayed only hours, no minute or second hands
- Too imprecise to measure seconds accurately
- Driven by falling weights and escapement mechanisms
Pendulum revolution (1656):
- Christiaan Huygens invented the pendulum clock
- First clocks accurate enough to measure seconds reliably
- Pendulum period provided regular "tick" for second counting
- Accuracy improved from 15 minutes/day to 15 seconds/day
Marine chronometers (1700s):
- John Harrison developed precise clocks for navigation (1730s-1760s)
- Accurate timekeeping enabled longitude determination at sea
- Precision to within 1 second per day
Astronomical Definition: Mean Solar Second (1832-1967)
In 1832, the second was formally defined as 1/86,400 of a mean solar day:
- Mean solar day: Average length of a solar day over a year (accounts for Earth's elliptical orbit)
- 86,400 seconds: 24 hours × 60 minutes × 60 seconds
Problems with astronomical definition:
- Earth's rotation is irregular: Tidal friction gradually slows rotation (~2 milliseconds per century)
- Seasonal variations: Earth's orbit affects day length by milliseconds
- Unpredictable fluctuations: Earthquakes, atmospheric changes affect rotation
- Increasing demand for precision: Radio, telecommunications, science required better accuracy
By the 1950s, astronomical observations showed the "second" was not constant—the length varied by parts per million depending on the era.
Atomic Revolution: Caesium Standard (1955-1967)
1955 - First caesium atomic clock:
- Louis Essen and Jack Parry at UK's National Physical Laboratory built the first caesium atomic clock
- Demonstrated caesium-133 atoms oscillate at precisely 9,192,631,770 Hz
- Accuracy: 1 second in 300 years (far exceeding astronomical clocks)
1967 - Official redefinition: The 13th General Conference on Weights and Measures (CGPM) redefined the second:
"The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom."
Why caesium-133?
- Atomic property: Transition frequency is a fundamental constant of nature
- Highly stable: Unaffected by temperature, pressure, or electromagnetic fields
- Reproducible: Any caesium-133 atom behaves identically
- Practical: Relatively easy to construct atomic clocks using caesium
Impact:
- Timekeeping became independent of Earth's rotation
- Precision improved from parts per million to parts per trillion
- Enabled GPS, internet synchronization, telecommunications, and modern science
Modern Atomic Clocks (1990s-Present)
Caesium fountain clocks (1990s):
- Atoms launched upward in "fountain" configuration
- Gravity slows atoms, allowing longer measurement time
- Accuracy: 1 second in 100 million years
Optical lattice clocks (2000s-2020s):
- Use strontium or ytterbium atoms instead of caesium
- Operate at optical frequencies (100,000× higher than caesium)
- Accuracy: 1 second in 15 billion years (age of the universe!)
- May redefine the second in future decades
Applications requiring atomic precision:
- GPS satellites: Nanosecond errors cause position errors of ~1 foot
- High-frequency trading: Microsecond timestamps for financial transactions
- Telecommunications: Synchronizing cell towers and internet infrastructure
- Science: Detecting gravitational waves, testing relativity, fundamental physics
Leap Seconds: Reconciling Atomic and Astronomical Time
The problem:
- Atomic time (TAI): Runs at constant rate based on caesium clocks
- Earth rotation (UT1): Slows gradually due to tidal friction
- Difference: ~2 milliseconds per day (accumulates ~1 second every 18 months)
Solution: Leap seconds (since 1972):
- Coordinated Universal Time (UTC) = atomic time adjusted to stay within 0.9 seconds of Earth rotation
- Leap second: Extra second added (or removed) on June 30 or December 31
- 27 leap seconds added between 1972-2016 (none since 2016)
Controversy:
- Leap seconds cause problems for computer systems, GPS, networks
- Debate ongoing about abolishing leap seconds in favor of pure atomic time
- Possible change may occur in the 2030s
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
Common Uses and Applications: seconds vs sidereal days
Explore the typical applications for both Second (imperial/US) and Sidereal Day (imperial/US) to understand their common contexts.
Common Uses for seconds
The second is the universal foundation for all time measurement in modern civilization:
1. Timekeeping and Clocks
Everyday timekeeping:
- Wristwatches and clocks display hours, minutes, seconds
- Smartphones synchronize to atomic time via network
- Wall clocks, alarm clocks, digital displays
- Public time displays (train stations, airports, town squares)
Precision timekeeping:
- Atomic clocks: Caesium, rubidium, hydrogen maser clocks
- GPS satellites: Carry atomic clocks for navigation
- Scientific facilities: National metrology institutes maintain primary time standards
- Network Time Protocol (NTP): Synchronizes computer clocks to microsecond accuracy
2. Scientific Research and Experiments
Physics experiments:
- Measuring particle lifetimes (nanoseconds to picoseconds)
- Timing light pulses in lasers (femtoseconds)
- Gravitational wave detection (millisecond timing precision)
- Quantum mechanics experiments (Planck time: 10⁻⁴⁴ seconds)
Chemistry:
- Reaction kinetics and rates
- Spectroscopy (measuring light absorption/emission frequencies)
- Femtochemistry (bond breaking/forming at femtosecond scale)
Biology:
- Neural signal timing (milliseconds)
- Cellular processes (seconds to hours)
- Ecological cycles (days, seasons, years measured in seconds)
3. Computing and Digital Systems
Processor operations:
- CPU clock speeds measured in GHz (billions of cycles/second)
- Instruction execution times (nanoseconds)
- Cache latency, memory access times
Software and programming:
- Timestamps (Unix time: seconds since January 1, 1970)
- Timeouts and delays
- Animation frame rates (60 frames/second = 0.0167 s/frame)
- Video frame rates (24, 30, 60 FPS)
Database and logging:
- Transaction timestamps (millisecond or microsecond precision)
- System logs with second-level granularity
- Performance monitoring (operations/second)
4. Telecommunications and Networking
Network synchronization:
- Cell towers synchronized to GPS time (nanosecond precision)
- Internet infrastructure timing
- 5G networks require nanosecond coordination
- Precision Time Protocol (PTP) for industrial networks
Data transmission:
- Bit rates measured in bits/second (Mbps, Gbps)
- Latency measured in milliseconds
- Packet timing and queuing
5. Navigation and GPS
Global Positioning System:
- Atomic clocks on satellites (accuracy ~10 nanoseconds)
- Signal travel time calculations
- Position accuracy requires nanosecond precision
- GNSS systems (GPS, GLONASS, Galileo, BeiDou)
Aviation:
- Aircraft navigation timing
- Air traffic control coordination
- Flight duration measurements
6. Financial and Trading
High-frequency trading:
- Microsecond timestamps on transactions
- Trading algorithms execute in microseconds
- Market data feeds timestamped to nanoseconds
- Regulatory requirements for precise time-stamping
Banking:
- Transaction timestamps
- Interest calculations (per second for some instruments)
- Automated trading systems
7. Sports and Athletics
Competition timing:
- Track and field (0.01 second precision)
- Swimming (0.01 second precision)
- Skiing, bobsled (0.01 second precision)
- Motor racing (0.001 second precision)
Training and performance:
- Stopwatches for interval training
- Heart rate monitors (beats/second)
- Pace calculations (minutes per kilometer/mile)
- Reaction time testing
8. Manufacturing and Industrial
Process control:
- Machine cycle times (seconds)
- Assembly line timing
- Quality control measurements
- Synchronization of robots and automation
Industrial timing:
- Conveyor belt speeds
- Injection molding cycle times (2-60 seconds typical)
- 3D printing layer times
- Chemical process durations
When to Use sidereal days
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
Additional Unit Information
About Second (s)
What is the base unit of time in the SI system?
The second (s) is the base unit of time in the International System of Units (SI). It's one of the seven SI base units, alongside meter (length), kilogram (mass), ampere (current), kelvin (temperature), mole (amount of substance), and candela (luminous intensity).
All other time units (minute, hour, day, year) are derived from the second.
Why is the second defined using atoms?
The atomic definition provides a much more stable and precise standard than relying on Earth's rotation, which fluctuates.
Problems with astronomical definition:
- Earth's rotation slows by ~2 milliseconds per century (tidal friction)
- Seasonal variations affect day length
- Unpredictable fluctuations from earthquakes, atmospheric changes
- Accuracy limited to ~1 part per million
Advantages of atomic definition:
- Fundamental constant: Caesium-133 transition frequency is a property of nature
- Reproducible: Any caesium-133 atom behaves identically
- Stable: Unaffected by external conditions (temperature, pressure)
- Precise: Modern atomic clocks accurate to 1 second in 100 million years
Result: GPS, telecommunications, science, and technology require nanosecond precision impossible with astronomical timekeeping.
How many seconds are in a minute?
There are exactly 60 seconds in 1 minute.
This derives from ancient Babylonian base-60 (sexagesimal) mathematics, which established 60 as the standard division for time over 4,000 years ago.
Conversions:
- 1 minute = 60 seconds
- 2 minutes = 120 seconds
- 5 minutes = 300 seconds
- 10 minutes = 600 seconds
How many seconds are in an hour?
There are exactly 3,600 seconds in 1 hour.
Calculation:
- 1 hour = 60 minutes
- 1 minute = 60 seconds
- 1 hour = 60 × 60 = 3,600 seconds
Conversions:
- 1 hour = 3,600 seconds
- 2 hours = 7,200 seconds
- 12 hours = 43,200 seconds
- 24 hours (1 day) = 86,400 seconds
How many seconds are in a day?
There are 86,400 seconds in 1 day (24 hours).
Calculation:
- 1 day = 24 hours
- 1 hour = 3,600 seconds
- 1 day = 24 × 3,600 = 86,400 seconds
Breakdown:
- 24 hours × 60 minutes/hour × 60 seconds/minute = 86,400 seconds
Note: This assumes a standard 24-hour day. Due to Earth's rotation irregularities, actual solar days vary by milliseconds. Leap seconds are occasionally added to keep atomic time synchronized with Earth rotation.
How many seconds are in a year?
A standard 365-day year contains 31,536,000 seconds.
Calculation:
- 365 days × 24 hours/day × 60 minutes/hour × 60 seconds/minute
- = 365 × 86,400
- = 31,536,000 seconds
Variations:
- Leap year (366 days): 31,622,400 seconds
- Julian year (365.25 days, average): 31,557,600 seconds
- Tropical year (365.2422 days, Earth orbit): 31,556,925 seconds
Fun fact: The song "Seasons of Love" from Rent states "525,600 minutes" in a year, which equals 31,536,000 seconds (365 days).
What is a millisecond?
A millisecond (ms) is one-thousandth of a second: 0.001 seconds or 10⁻³ seconds.
Conversions:
- 1 second = 1,000 milliseconds
- 1 millisecond = 0.001 seconds
- 1 minute = 60,000 milliseconds
Common uses:
- Computer response times (1-100 ms)
- Network ping times (1-300 ms typical)
- Human reaction time (~200 ms)
- Video frame duration (60 FPS = 16.67 ms/frame)
- Stopwatch hundredths (0.01 s = 10 ms)
What is a nanosecond?
A nanosecond (ns) is one-billionth of a second: 0.000000001 seconds or 10⁻⁹ seconds.
Conversions:
- 1 second = 1,000,000,000 nanoseconds (1 billion)
- 1 millisecond = 1,000,000 nanoseconds (1 million)
- 1 microsecond = 1,000 nanoseconds
Reference points:
- Light travels 30 cm (1 foot) in 1 nanosecond
- Computer processor operations: ~0.2-1 nanosecond
- GPS timing precision: ~10 nanoseconds
- RAM memory access: ~50-100 nanoseconds
Grace Hopper's demonstration: Computer pioneer Grace Hopper famously distributed 30cm lengths of wire to represent "one nanosecond" (distance light travels in 1 ns) to illustrate the importance of speed in computing.
Why are there 60 seconds in a minute instead of 100?
The 60-second minute derives from ancient Babylonian base-60 (sexagesimal) mathematics developed around 3000 BCE, over 1,000 years before the decimal system.
Reasons for base-60:
1. High divisibility: 60 has 12 divisors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Easy to divide into halves, thirds, quarters, fifths, sixths
- 100 (decimal) has only 9 divisors: 1, 2, 4, 5, 10, 20, 25, 50, 100
2. Finger counting method:
- Count 12 finger segments (phalanges) on one hand using thumb
- Track count on other hand: 12 × 5 fingers = 60
3. Astronomical convenience:
- ~360 days per year ≈ 6 × 60
- Circle divided into 360 degrees (6 × 60)
- Babylonian astronomy used these divisions
4. Historical persistence: The system spread through Egyptian, Greek, and Roman civilizations and became too entrenched to change. When mechanical clocks developed in medieval Europe, they adopted the existing Babylonian time divisions.
Attempts to decimalize time:
- French Revolutionary Calendar (1793-1805): 10-hour day, 100-minute hour, 100-second minute
- Failed: Too difficult to change clocks, conversion from traditional system
- Result: We still use Babylonian base-60 for time, but base-10 (decimal) for most other measurements
How accurate are atomic clocks?
Modern atomic clocks are extraordinarily accurate:
Caesium atomic clocks (standard):
- Accuracy: 1 second in 100 million years
- Precision: Parts per trillion (10⁻¹²)
- Used in GPS satellites, national time standards
Caesium fountain clocks (advanced):
- Accuracy: 1 second in 300 million years
- Precision: Better than 10⁻¹⁵
- Used by metrology institutes (NIST, PTB, NPL)
Optical lattice clocks (state-of-the-art):
- Accuracy: 1 second in 15-30 billion years
- Precision: 10⁻¹⁸ to 10⁻¹⁹
- Use strontium, ytterbium, or aluminum ions
- So precise they detect gravitational time dilation across centimeters of height
Comparison:
- Quartz watch: 1 second in 1-10 days (10⁻⁵ accuracy)
- Mechanical watch: 1-10 seconds per day (10⁻⁴ to 10⁻⁵)
- Sundial: Minutes per day (10⁻³)
- Atomic clock: 1 second in 100 million years (10⁻¹⁶)
Why this matters: GPS requires 10-nanosecond precision; a 1-microsecond error causes 300-meter position errors.
What are leap seconds and why do we need them?
Leap seconds are occasional one-second adjustments added to Coordinated Universal Time (UTC) to keep it synchronized with Earth's rotation.
The problem:
- Atomic time (TAI): Runs at constant rate based on caesium clocks, unchanging
- Earth rotation (UT1): Slows gradually due to tidal friction (~2 milliseconds per day longer)
- Discrepancy: Accumulates ~1 second every 18-24 months
Solution:
- Add (or theoretically remove) 1 second on June 30 or December 31
- Keeps UTC within 0.9 seconds of Earth rotation time (UT1)
- 27 leap seconds added between 1972 and 2016
- No leap seconds since 2016 (Earth rotation has been slightly faster recently)
How it works: Instead of 23:59:59 → 00:00:00, the sequence is: 23:59:59 → 23:59:60 → 00:00:00 (leap second inserted)
Controversy:
- Problems: Computer systems, GPS, networks struggle with leap seconds (software bugs, crashes)
- Proposed solution: Abolish leap seconds, let UTC and UT1 drift apart
- Debate: Ongoing since 2000s; decision may be made in 2026-2030s
Current status: Leap seconds remain in use, but their future is uncertain.
About Sidereal Day (sidereal day)
How long is a sidereal day in standard time?
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.
Why is a sidereal day shorter than a solar day?
Answer: Because Earth orbits the Sun while rotating—requiring extra rotation to bring the Sun back to the same sky position
Step-by-step explanation:
-
Starting point: The Sun is directly overhead (noon)
-
One sidereal day later (23h 56m 4s): Earth has rotated exactly 360° relative to stars
- But Earth has also moved ~1° along its orbit around the Sun
- The Sun now appears slightly east of overhead
-
Extra rotation needed: Earth must rotate an additional ~1° (taking ~4 minutes) to bring the Sun back overhead
-
Result: Solar day (noon to noon) = sidereal day + ~4 minutes = 24 hours
Orbital motion causes the difference: Earth moves ~1°/day along its 365-day orbit (360°/365 ≈ 0.986°/day). This ~1° requires ~4 minutes of extra rotation (24 hours / 360° ≈ 4 min/degree).
Consequence: Stars rise ~4 minutes earlier each night relative to solar time, shifting ~2 hours per month, completing a full cycle annually.
Is sidereal time the same everywhere on Earth?
Answer: No—Local Sidereal Time (LST) depends on longitude, just like solar time zones
Key concepts:
Local Sidereal Time (LST): The Right Ascension (RA) currently crossing your local meridian
- Different at every longitude
- Changes by 4 minutes for every 1° of longitude
Greenwich Mean Sidereal Time (GMST): Sidereal time at 0° longitude (Greenwich meridian)
- Global reference point, like GMT/UTC for solar time
Conversion: LST = GMST ± longitude offset
- Positive (add) for east longitudes
- Negative (subtract) for west longitudes
Example:
- GMST = 12:00
- New York (74°W): LST = 12:00 - (74°/15) = 07:04
- Tokyo (139.75°E): LST = 12:00 + (139.75°/15) = 21:19
Duration is universal: A sidereal day (23h 56m 4s) is the same length everywhere—only the current sidereal time differs by location.
Do geosynchronous satellites orbit every 24 hours or 23h 56m?
Answer: 23h 56m 4s (one sidereal day)—NOT 24 hours!
This is one of the most common misconceptions about satellites.
The physics: For a satellite to remain above the same point on Earth's surface, it must orbit at Earth's rotational rate relative to the stars, not relative to the Sun.
Why sidereal?
- Earth rotates 360° in one sidereal day (23h 56m 4s)
- Satellite must complete 360° orbit in the same time
- This keeps satellite and ground point aligned relative to the stellar background
If orbit were 24 hours: The satellite would complete one orbit in one solar day, but Earth would have rotated 360° + ~1° (relative to stars) during that time. The satellite would drift ~1° westward per day, completing a full circuit westward in one year!
Geostationary orbit specifics:
- Altitude: 35,786 km above equator
- Period: 23h 56m 4.091s (1 sidereal day)
- Velocity: 3.075 km/s
Common examples: Communications satellites, weather satellites (GOES, Meteosat)
How many sidereal days are in a year?
Answer: Approximately 366.25 sidereal days—one MORE than the number of solar days!
Precise values:
- Tropical year (season to season): 365.242199 mean solar days
- Sidereal year (star to star): 365.256363 mean solar days
- Sidereal days in tropical year: 366.242199 sidereal days
One extra day: There is exactly one more complete rotation relative to stars than we experience sunrises.
Why?
- Earth makes 366.25 complete 360° rotations relative to stars per year
- But we experience only 365.25 sunrises because we orbit the Sun
- One rotation is "used up" by Earth's orbit around the Sun
Thought experiment: Stand on a rotating platform while walking around a lamp. If you walk one complete circle around the lamp (1 orbit), you'll have spun around 2 complete times relative to the room walls (2 rotations): 1 from walking the circle + 1 from the platform spinning.
Can I use a regular clock to tell sidereal time?
Answer: Not directly—sidereal clocks run about 4 minutes faster per day than solar clocks
Clock rate difference:
- Solar clock: Completes 24 hours in 1 solar day (86,400 seconds)
- Sidereal clock: Completes 24 sidereal hours in 1 sidereal day (86,164.091 seconds)
- Rate ratio: 1.00273791 (sidereal clock ticks ~0.27% faster)
Practical result: After one solar day:
- Solar clock reads: 24:00
- Sidereal clock reads: 24:03:56 (3 min 56 sec ahead)
Modern solutions:
- Sidereal clock apps: Smartphone apps calculate LST from GPS location and atomic time
- Planetarium software: Stellarium, SkySafari show current LST
- Observatory systems: Automated telescopes use GPS-synchronized sidereal clocks
Historical: Mechanical sidereal clocks used gear ratios of 366.2422/365.2422 to run at the correct rate
You can calculate: LST from solar time using formulas, but it's complex (requires Julian Date, orbital mechanics)
Why do astronomers use sidereal time instead of solar time?
Answer: Because celestial objects return to the same position every sidereal day, not solar day
Astronomical reason:
Stars and galaxies are so distant they appear "fixed" in the sky:
- A star at RA = 18h 30m crosses the meridian at LST = 18:30 every sidereal day
- Predictable, repeatable observations
If using solar time: Stars would cross the meridian ~4 minutes earlier each night, requiring daily recalculation of observation windows
Practical advantages:
1. Simple telescope pointing:
- Object's RA directly tells you when it's overhead (LST = RA)
- No date-dependent calculations needed
2. Repeatable observations:
- "Observe target at LST = 22:00" means the same sky position regardless of date
3. Right Ascension coordinate system:
- Celestial longitude measured in hours/minutes of sidereal time (0h to 24h)
- Aligns naturally with Earth's rotation
4. Tracking rate:
- Telescopes track at sidereal rate (1 revolution per 23h 56m 4s)
- Keeps stars fixed in the field of view
Historical: Before computers, sidereal time made astronomical calculations much simpler
What is the difference between a sidereal day and a sidereal year?
Answer: A sidereal day measures Earth's rotation; a sidereal year measures Earth's orbit
Sidereal Day:
- Definition: Time for Earth to rotate 360° on its axis relative to stars
- Duration: 23h 56m 4.091s (86,164.091 seconds)
- Reference: Distant "fixed" stars
- Use: Telescope tracking, astronomy observations
Sidereal Year:
- Definition: Time for Earth to orbit 360° around the Sun relative to stars
- Duration: 365.256363 days (365d 6h 9m 9s)
- Reference: Position relative to distant stars (not seasons)
- Use: Orbital mechanics, planetary astronomy
Key distinction:
- Day = rotation (Earth spinning)
- Year = revolution (Earth orbiting)
Tropical vs. Sidereal Year:
- Tropical year: 365.242199 days (season to season, used for calendars)
- Sidereal year: 365.256363 days (star to star)
- Difference: ~20 minutes, caused by precession of Earth's axis
The 20-minute precession effect: Earth's axis wobbles with a 26,000-year period, causing the vernal equinox to shift ~50 arcseconds/year westward against the stellar background. This makes the tropical year (equinox to equinox) slightly shorter than the sidereal year (star to star).
Does the Moon have a sidereal day?
Answer: Yes—the Moon's sidereal day is 27.322 Earth days, but it's tidally locked to Earth
Moon's sidereal rotation: Time for Moon to rotate 360° relative to stars = 27.322 days
Tidal locking: The Moon's rotation period equals its orbital period around Earth (both 27.322 days)
Consequence: The same face of the Moon always points toward Earth
- We only see ~59% of Moon's surface from Earth (libration allows slight wobbling)
- The "far side" never faces Earth
Moon's "solar day" (lunar day):
- Time from sunrise to sunrise on Moon's surface: 29.531 Earth days
- Different from Moon's sidereal day (27.322 days) for the same reason Earth's solar day differs from sidereal day
- Moon orbits Earth while rotating, requiring extra rotation to bring the Sun back to the same position
Lunar missions: Apollo missions and rovers used "lunar days" for mission planning—each day-night cycle lasts ~29.5 Earth days (2 weeks daylight, 2 weeks night)
How is sidereal time measured today?
Answer: Using atomic clocks, GPS, and Very Long Baseline Interferometry (VLBI) observations of distant quasars
Modern measurement system:
1. International Atomic Time (TAI):
- Network of ~450 atomic clocks worldwide
- Defines the second with nanosecond precision
- Provides base timescale
2. UT1 (Universal Time):
- Earth's rotation angle (actual rotation measured continuously)
- Monitored by VLBI observations of quasars
3. VLBI technique:
- Radio telescopes across continents simultaneously observe distant quasars
- Time differences reveal Earth's exact orientation
- Accuracy: ~0.1 milliseconds (0.005 arcseconds rotation)
4. ICRF (International Celestial Reference Frame):
- Defines "fixed" stellar background using ~300 quasars billions of light-years away
- Replaces older vernal equinox reference (which shifts due to precession)
5. GPS satellites:
- Amateur astronomers and observatories use GPS for accurate time and location
- Software calculates LST from UTC, GPS coordinates, and Earth orientation parameters
Calculation chain:
- Atomic clocks provide UTC
- Earth orientation parameters (EOP) give UT1
- Sidereal time formulas convert UT1 → GMST
- Longitude correction gives LST
Accuracy: Modern systems know Earth's orientation to ~1 centimeter (as a position on Earth's surface), requiring sidereal time precision of ~0.001 seconds
Why so complex? Earth's rotation is not uniform:
- Tidal forces (Moon/Sun) slow rotation by ~2.3 ms/century
- Atmospheric winds cause daily variations (milliseconds)
- Earthquakes can shift rotation by microseconds
- Core-mantle coupling affects long-term drift
Continuous monitoring ensures astronomical observations remain accurate.
Will sidereal time ever be replaced by something else?
Answer: Unlikely—it's fundamental to astronomy, tied directly to Earth's rotation and stellar positions
Why sidereal time persists:
1. Physical basis: Directly tied to Earth's rotation relative to the universe
- Not an arbitrary human convention like time zones
- Essential for understanding celestial mechanics
2. Coordinate system: Right Ascension (celestial longitude) is measured in sidereal hours
- All star catalogs, telescope systems, and astronomical databases use RA/Dec
- Replacing it would require re-cataloging billions of objects
3. Telescope tracking: All telescope mounts track at the sidereal rate
- Mechanically and electronically built into equipment
- Solar tracking is used only for Sun/Moon
4. International standards: IAU, observatories, space agencies globally use sidereal time
- Standardized formulas and software
5. No alternative needed: Sidereal time does its job perfectly for astronomy
Evolution, not replacement:
- Old reference: Vernal equinox (shifts due to precession)
- New reference: ICRF quasars (effectively fixed)
- Future: Increasingly precise atomic timescales and Earth rotation monitoring
Non-astronomical contexts: Civil society will continue using solar time (UTC) for daily life—there's no need for most people to know sidereal time
Conclusion: Sidereal time is here to stay as long as humans do astronomy from Earth. Even space-based observatories use sidereal coordinate systems for consistency with ground observations.
Conversion Table: Second to Sidereal Day
| Second (s) | Sidereal Day (sidereal day) |
|---|---|
| 0.5 | 0 |
| 1 | 0 |
| 1.5 | 0 |
| 2 | 0 |
| 5 | 0 |
| 10 | 0 |
| 25 | 0 |
| 50 | 0.001 |
| 100 | 0.001 |
| 250 | 0.003 |
| 500 | 0.006 |
| 1,000 | 0.012 |
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Last verified: December 3, 2025