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Dennis D. McCarthy U. S. Naval Observatory Evolution of Timescales from Astronomy to Physical Metrology
TIMEKEEPING BASICS • Repeatable Phenomenon • Length between repetitions • Beginning of the repetition • Names for the successive repetitions • Timescales driven by timekeeping technology
THE SKY PROVIDES DAY MONTH WEEK YEAR
DAY • Basic Unit of Time • Begins at sunrise? or sunset? or midnight?
HOUR • Egyptians: 10 daylight seasonal hours + 1 for morning twilight and 1 for evening twilight – also 12 nighttime hours. • “Equinoctial hours” began by Hipparchus (Hellenist astronomer 130 BCE) • Claudius Ptolemeus (Alexandria - 137) began use of minutes (first divisions)
Time from the Sun Shadows provide a handy clock Or the Sun’s direction in the sky
Apparent Solar Time Could be local or at some special place like Greenwich
Apparent Solar Time • Local • Greenwich
When you can’t see the sky :Early Devices that Don’t Use the Sky (Almost)
Length of the apparent solar day varies during the year because Earth’s orbit is inclined and is really an ellipse. • Ptolemy (90-168 CE) knew this • Mean Solar Time • Local • Greenwich • Apparent Solar Time • Local • Greenwich
Easier and more accurate IF you know the direction of the Sun with respect to the stars Solar Time Sidereal Time
Mechanical Clocks Verge & Foliot- 13/14th Century Pendulum - 1639 Equinoctial hours gradually replace temporal hours
Improvements Huygen’s Horologium Anchor Escapement Tabular arguments of the British Nautical Almanac changed to mean solar time in 1834
State-of-the-Art Pendulums Riefler Clock - 1904 Shortt Clock - 1929
Three Forms • UT1 is measure of Earth’s rotation angle defined • By observed sidereal time using conventional expression • GMST= f1(UT1) • by Earth Rotation Angle • q = f2(UT1) • UTO is UT1 plus effects of polar motion • UT2 is UT1 corrected by conventional expression for annual variation in Earth’s rotational speed Universal Time • Mean Solar Time • Local • Greenwich • Apparent Solar Time • Local • Greenwich
Astronomical Timekeeping Observations Predict Transit Times Star Catalogs Determine Clock Corrections
Earth Rotation • Well documented deceleration • Tidal • Change in figure
annual quasi-biennial oscillation atmospheric modes southern oscillation solid Earth and ocean tides semi -annual 40-50 -day oscillations Power monthly fortnightly decade fluctuations (from core?) atmospheric tides 0.1 year-1 0.2 year-1 1 year-1 0.1 month-1 Frequency Variations in Length of Day
Time that brings the observed positions of solar system objects into accord with ephemerides based on Newtonian theory of gravitation • Uniform measure of time determined by the orbital motions of the celestial bodies • Defined by revolution of the Earth about the Sun represented by Newcomb’s Tables of the Sun • Geometric mean longitude of the Sun for the epoch January 0, 1900, 12 h UT where T is ET elapsed since 1900 in Julian centuries of 36 525 days In practice ET measured by observations of the Moon with respect to the stars Ephemeris Time Universal Time • Since the tropical year of 1900 contains • [(360 60 60)/129 602 768.13] 36 525 86 400 s = 31 556 925.9747 s • the ET second is 1/31 556 925.9747 of the tropical year 1900 • Adopted by CIPM as definition of the second in 1956 and ratified by the 11th CGPM in 1960 • ET replaced UT1 as independent variable of astronomical ephemerides in 1960 • Mean Solar Time • Local • Greenwich • Apparent Solar Time • Local • Greenwich
Atomic Time • First Caesium-133 atomic clock established at National Physical Laboratory in UK in 1955 • Frequency of transition measured in terms of the second of ET • 9 192 631 770 20 Hz • Definition of the Système international d'unités (SI) second adopted in 1967 • Atomic time = ET second Second = duration of 9 192 631 770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom
Universal Time • Mean Solar Time • Local • Greenwich Ephemeris Time • Apparent Solar Time • Local • Greenwich • Atomic Time • A.1, etc.
Definition of Seconds • Rotational Second • 1 / 86,400 of mean solar day • Ephemeris Second • First used in 1956 • 1/31,556,925.9747 of the (tropical) year 1900 • Length of year based on 19th century astronomical observations • Atomic second • SI second: 9,192,631,770 periods of the radiation corresponding to the transition between 2 hyperfine levels of the ground state of the caesium 133 atom (adopted 1964) • Realizes the Ephemeris Second • Frequency based on lunar observations from 1954.25 to 1958.25 The SI second preserves the rotational second of the mid-19th century
Coordinate time scale in geocentric reference system • Scale unit is SI second realized on the rotating geoid • Continuous atomic time scale • Originally determined by Bureau International de l’Heure (BIH) • Now maintained by Bureau International des Poids et Mesures (BIPM) • Became AT (or TA) in 1969, TAI in 1971 • TAI = UT2 on January 1, 1958 0 h Universal Time • International Atomic Time • EchelleAtomiqueLibre + corrections • Mean Solar Time • Local • Greenwich Ephemeris Time • Atomic Time • A.1, etc. • Apparent Solar Time • Local • Greenwich
Name adopted in 1967 • From 1961 to 1972 UTC contained both frequency offsets and steps (less than 1 s) to maintain agreement with UT2 within about 0.1 s • In 1970 formalized by International Telecommunication Union (ITU) so that it corresponds exactly in rate with TAI but differs by integral number of seconds, adjusted by insertion or deletion of seconds to ensure agreement within 0.9 s of UT1. Leap Seconds may be introduced as the last second of any UTC month. December and June preferred, March and September second choice. Universal Time Coordinated Universal Time • Mean Solar Time • Local • Greenwich • International Atomic Time • EchelleAtomiqueLibre + corrections Ephemeris Time • Apparent Solar Time • Local • Greenwich • Atomic Time • A.1, etc.
Formation of UTC(k) BIPM INSTITUTION k EAL Free Running Continuous Time Scale Local Clocks Combination Procedure Primary Frequency Standards Local Time Scale Combination Steering Procedure IERS Leap Seconds TAI UTC UTC(k) UTC-UTC(k)Circular T UTC(k) – UTC(j) Local clocks – UTC(k)
Relativistic Concepts • Ephemeris Time (ET) based on the Newtonian theory of gravitation • No distinction between proper time and coordinate time • Proper Time • Actual reading of a clock • Depends on clock’s position and state of motion with respect to its environment • Coordinate Time • Independent variable in equations of motion of material bodies and equations for propagation of electromagnetic waves • Mathematical coordinate in four-dimensional spacetime of the chosen coordinate system • For a given event, coordinate time has the same value everywhere
In 1976 IAU defined dynamical time scales consistent with general relativity to distinguish between time scales with origins at the geocenter and the barycenter.of the solar system • Named Terrestrial Dynamical Time (TDT) and Barycentric Dynamical Time (TDB) in 1979 • At the instant 1977 January 01 d 00h 00m 00s TAI, the value of the new time scale for apparent geocentric ephemerides is 1977 January 1d 00h 00m 32.184 exactly. • The unit is a day of 86400 SI seconds at mean sea level. • The timescales for equations of motion referred to the barycenter of the solar system is such that there will be only periodic variations between these timescales and those of the apparent geocentric ephemerides. • TDT maintains continuity with ET • By choosing an appropriate scaling factor TDB determined from TDT by a conventional mathematical expression • Dynamical Time • Terrestrial • Dynamical Coordinated Universal Time Universal Time • International Atomic Time • EchelleAtomiqueLibre + corrections • Mean Solar Time • Local • Greenwich Ephemeris Time • Atomic Time • A.1, etc. • Apparent Solar Time • Local • Greenwich
In 1991 IAU renamed TDT as Terrestrial Time (TT) • Unit is the SI second on the geoid and is defined by atomic clocks on the surface of the Earth • Origin of January 1, 1977 0 h • TT = TAI + 32.184 s • Maintains continuity with Ephemeris Time (ET) • Theoretical equivalence of time measured by quantum mechanical atomic interaction and time measured by gravitational planetary interaction • To be used as the time reference for apparent geocentric ephemerides. • Any difference between TAI and TT is a consequence of the physical defects of atomic time standards, and has probably remained within the approximate limits of ± 10µs. It may increase slowly in the future as time standards improve. In most cases, and particularly for the publication of ephemerides, this deviation is negligible. • Dynamical Time • Terrestrial • Dynamical Terrestrial Time Coordinated Universal Time Universal Time • International Atomic Time • EchelleAtomiqueLibre + corrections • Mean Solar Time • Local • Greenwich Ephemeris Time • Atomic Time • A.1, etc. • Apparent Solar Time • Local • Greenwich
Geocentric Coordinate Time (TCG) • Coordinate Time • Time with respect to center of Earth Defining value of LG, chosen to provide continuity with the definition of TT so that its measurement unit agrees with the SI second on the geoid is 6.969290134×10-10
Barycentric Coordinate Time (TCB) • Coordinate Time where LC = 1.480 826 867 41 10−8 ( 1.28 ms/d), P represents periodic terms with largest having amplitude 1.7 ms, and last term has amplitude 2.1 s • TCB and TDB differ in rate where P0 represents periodic terms of order 10-4 seconds. Present estimate of LB is 1.55051976772×10-8 (±2×10-17). However, since no precise definition of TDB exists, there is no definitive value of LB, and such an expression should be used with caution
Teph • Time argument used in the JPL solar system ephemerides since the mid-1960’s • True relativistic coordinate time, rigorously equivalent to TCB • TCB differs from Teph only by a rate and an offset • differs from TT by periodic terms with an amplitude < 2 ms of time
Geocentric Coordinate Time(TCG) • Coordinate Time with respect to center of Earth • Defining value of LG, provides continuity with the definition of TT so that its measurement unit agrees with the SI second on the geoid ET TDT TDB TT Terrestrial Dynamical Time (TDT) Barycentric Dynamical Time (TDB) Teph • Defined in1976 • SI second • Origin at the geocenter • Named in 1979 • Continuous with ET • On 1 January 1984 replaced Ephemeris Time in national ephemerides • Defined in1976 • Origin at the solar system barycenter • Named in 1979 • Periodic difference between TDB and TDT • Theory dependent Teph Terrestrial Time (TT) • Coordinate time • related to TCB by offset and scale factor • Ephemerides based on Teph adjusted so rate of Teph has no overall difference from rate of TT • So no difference from the rate of TDB • Space coordinates obtained from ephemerides are consistent with TDB. • renamed TDT in 1991 • Unit is SI second on the geoid • Defined by atomic clocks on the surface of the Earth • On January 1, 1977 0 h TT = TAI + 32.184 s • Any difference between TAI and TT result of physical defects of atomic time standards • Maintains continuity with Ephemeris Time (ET) • Time reference for apparent geocentric ephemerides. • Theoretical equivalence of time measured by quantum mechanics and time measured by gravitational planetary interaction Barycentric Coordinate Time (TCB)
A User’s View of Time Scales UTC TAI-UTC (from Table) UT1–UTC (from IERS) TAI UT1 32.184 s standard formula Software available at www.iausofa.org TT GMST SI seconds Earth rotation standard linear relation eq. of equinoxes TCG GAST formulas formula longitude TCB TDB* LAST * Different rate than TCB: based on SI seconds on the geoid
Evolution of Time Scales TT TCG TCB Teph TAI TDT TDB UTC Ephemeris Time UT0 UT1 UT2 Greenwich Greenwich Greenwich Greenwich Local Local Local Local Apparent Mean Apparent Mean Solar Time Sidereal Time Earth Rotation
The Next Evolutionary Step? UTC without leap seconds?
23:59:60 Issues Why? Concerns Navigation 1 second = 1/4 mile at the equator Legacy computer software Assumption that UT1=UTC near enough? Legal definitions Mean solar time? • Frequency of leap seconds will increase • Increasing public annoyance • Software issues • Unpredictable: can’t be programmed in advance • Dealing with days of 86,401 seconds • Time-stamping 23h 59m 60s • Communications problems • coordination of events during a leap second • Growth of time scales • Expensive to implement
What’s Next? Single atom clock Pulsars
Future • Leap seconds? • Navigational satellite time scales • Time scales for space exploration • Time scales to meet future requirements for precision • Galactic Coordinate Time?
Evolution of Timekeeping Sun’s Shadow Water Clocks Stars Verge & Follett Solar Time Sidereal Time Pendulums Mechanical Time Atomic Time Relativistic Time Quartz Moon Atomic Clocks Pulsars