evolution of timescales from astronomy to physical metrology

Evolution of Timescales from Astronomy to Physical Metrology

Dennis D. McCarthyU. S. Naval Observatory

http://tf.nist.gov/cesium/parcs.htm

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

YEAR

WEEK

MONTH

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)


Mean Solar TimeLocal Greenwich

• 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 minus Apparent Solar Time - minutes

-20 -15 -10 -5 0 5 10 15 20

Da

y o

f th

e Y

ea

r

0

30

60

90

120

150

180

210

240

270

300

330

360

Sidereal Time Solar Time

Easier and more accurate IF you know the direction of the Sun with respect to the stars

Mechanical ClocksVerge & Foliot- 13/14th Century Pendulum - 1639

Equinoctial hours gradually replace temporal hours

ImprovementsHuygen’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

Quartz Crystal Clock



Universal Time

• 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

Astronomical Timekeeping

Observations

Star Catalogs

Predict Transit Times

Determine Clock Corrections

Year

-500 0 500 1000 1500 2000

T -

Sec

on

ds

0

2000

4000

6000

8000

10000

12000

14000

16000

18000 T

Year1700 1800 1900 2000

T -

sec

onds

-20

0

20

40

60

80

Earth Rotation

• Well documented deceleration– Tidal– Change in figure

Variations in Length of Day

Frequency

Pow

er

annual

semi -annual

southern oscillation

quasi-biennial oscillation

40-50 -day oscillations

monthly

fortnightly

atmospheric tides

decade fluctuations(from core?)

atmospheric modes

solid Earth and ocean tides

0.1 year-1 0.2 year-1 1 year-1 0.1 month-1



Ephemeris Time

Universal Time

2279 41 48. 04 129 602 768. 13 1. 089L T T

• 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

• 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

In practice ET measured by observations of the Moon with respect to the stars

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

ET9 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



Ephemeris Time

Universal Time

Atomic TimeA.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



Ephemeris Time

Universal Time

Atomic TimeA.1, etc.

International Atomic TimeEchelle Atomique Libre + corrections

• 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

TimekeepingPrecision



Ephemeris Time

Universal Time

Atomic TimeA.1,

etc.


Coordinated Universal Time

• 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.

Formation of UTC(k)

Local clocks – UTC(k)Local clocks – UTC(k)

UTC(k) – UTC(j)UTC(k) – UTC(j)

Local ClocksLocal Clocks

Local Time ScaleLocal Time Scale

Combination Procedure

UTC(k)UTC(k)

Steering Procedure

BIPM

UTC-UTC(k)Circular T

UTC-UTC(k)Circular T

UTCUTC

INSTITUTION kEAL

Free Running Continuous Time

Scale

EALFree Running

Continuous Time Scale

Primary Frequency StandardsCombination

IERSLeap

Seconds

TAITAI

International Time Links

Year2006 2007 2008 2009 2010 2011

UT

C-U

TC

(k)

- n

an

ose

con

ds

-60

-40

-20

0

20

40

60

UTC-UTC(USNO) Naval Observatory UTC-UTC(NIST) NISTUTC-UTC(NICT) JapanUTC-UTC(TL) Taiwan UTC-UTC(NTSC) ChinaUTC-UTC(SP) Sweeden

UTC – UTC(k)

Coordinated Universal Time (UTC)

YEAR

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Tim

e S

cale

Dif

fere

nce

s (s

eco

nd

s)

0

10

20

30

TAI-UT1 TAI-UTC

UTC Redefined

1961 Jan. 1 - 1961 Aug. 1 1.422818s + (MJD-37300) x 0.001296s

Aug. 1 - 1962 Jan. 1 1.372818s + (MJD-37300) x 0.001296s

1962 Jan. 1 - 1963 Nov. 1 1.845858s + (MJD-37665) x 0.0011232s

1963 Nov. 1 - 1964 Jan. 1 1.945858s + (MJD-37665) x 0.0011232s

1964 Jan. 1 - April 1 3.240130s + (MJD-38761) x 0.001296s

April 1 - Sept. 1 3.340130s + (MJD-38761) x 0.001296s

Sept. 1 - 1965 Jan. 1 3.440130s + (MJD-38761) x 0.001296s

1965 Jan. 1 - Mar. 1 3.540130s + (MJD-38761) x 0.001296s

Mar. 1 - Jul. 1 3.640130s + (MJD-38761) x 0.001296s

Jul. 1 - Sept. 1 3.740130s + (MJD-38761) x 0.001296s

Sept. 1 - 1966 Jan. 1 3.840130s + (MJD-38761) x 0.001296s

1966 Jan. 1 - 1968 Feb. 1 4.313170s + (MJD-39126) x 0.002592s

1968 Feb. 1 - 1972 Jan. 1 4.213170s + (MJD-39126) x 0.002592s

1972 Jan. 1 - Jul. 1 10s

Jul. 1 - 1973 Jan. 1 11s

1973 Jan. 1 - 1974 Jan. 1 12s

1974 Jan. 1 - 1975 Jan. 1 13s

1975 Jan. 1 - 1976 Jan. 1 14s

1976 Jan. 1 - 1977 Jan. 1 15s

1977 Jan. 1 - 1978 Jan. 1 16s

1978 Jan. 1 - 1979 Jan. 1 17s

1979 Jan. 1 - 1980 Jan. 1 18s

1980 Jan. 1 - 1981 Jul. 1 19s

1981 Jul. 1 - 1982 Jul. 1 20s

1982 Jul. 1 - 1983 Jul. 1 21s

1983 Jul. 1 - 1985 Jul. 1 22s

1985 Jul. 1 - 1988 Jan. 1 23s

1988 Jan. 1 - 1990 Jan. 1 24s

1990 Jan. 1 - 1991 Jan. 1 25s

1991 Jan. 1 - 1992 Jul. 1 26s

1992 Jul. 1 - 1993 Jul 1 27s

1993 Jul. 1 - 1994 Jul. 1 28s

1994 Jul. 1 - 1996 Jan. 1 29s

1996 Jan. 1 - 1997 Jul. 1 30s

1997 Jul. 1 - 1999 Jan 1 31s

1999 Jan. 1 - 2006 Jan 1 32s

2006 Jan 1 - 2009 Jan 1 33s

2009 Jan 1 34s

TAI-UTCFrom To

TAI -UTC

Relativistic Concepts

• 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

• Ephemeris Time (ET) based on the Newtonian theory of gravitation

• No distinction between proper time and coordinate time



Ephemeris Time

Universal Time

Dynamical Time Terrestrial

Dynamical

Atomic TimeA.1,

etc.



• 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



Ephemeris Time

Universal Time

Dynamical Time Terrestrial

Dynamical

Atomic TimeA.1,

etc.


Terrestrial Time

• 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.


TT-TAI-32.184s

Year

1975 1980 1985 1990 1995 2000 2005 2010

TT

-TA

I-32

.184

s (n

s)

0

10

20

30

40

50

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

864005.2443144JDLTTTCG G

Barycentric Coordinate Time (TCB)

22 2 2

1 1 1 1TCB TT ( ) ( ) ( )

2E ext E E G E E C G E EU v dt L D L D P L Dc c c

r v r r v r r

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

• Coordinate Time

0B P864002433144.5JDLTDBTCB

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

• TCB and TDB differ in rate

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

TDTTDB

ET

Terrestrial Dynamical Time (TDT)

• Defined in1976 • SI second• Origin at the geocenter • Named in 1979• Continuous with ET• On 1 January 1984

replaced Ephemeris Time in national ephemerides

orbititsinEarthofanomalymeang

s10orderoftermsdaily

s10orderoftermsplanetaryandlunar

g0.0167singsin 0.001658sTDTTDB

6

5-

Barycentric Dynamical Time (TDB)

• Defined in1976 • Origin at the solar

system barycenter• Named in 1979• Periodic difference

between TDB and TDT• Theory dependent

Terrestrial Time (TT)• 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

TTTeph

• 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.

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

Teph

GTCG TT L J D 2443144.5 86400s

00TCBB TDB86400TJDLTCBTDB

Barycentric Coordinate Time (TCB)

4ee

t

t eext

2e2 cOxxvdtxU2

vcTCGTCB0

A User’s View of Time Scales

TAI UT1

TT GMST

GAST

LAST

UT1–UTC (from IERS)TAI-UTC (from Table)

32.184 s standard formula

eq. of equinoxes

longitude

TCG

standard linear relation

TCB

formula

TDB*

formulas

Earth

rotatio

n SI

seco

nd

s

* Different rate than TCB: based on SI seconds on the geoid

UTC

Software available at

www.iausofa.org

Earth Rotation

Solar Time Sidereal Time

Apparent Mean

Local

Greenwich

Local

Greenwich

UTC

Ephemeris Time

TDBTDT

TCG TCB Teph

TAI

TT

UT1 UT2UT0

Evolution of Time Scales

Apparent Mean

Local

Greenwich

Local

Greenwich

The Next Evolutionary Step?

UTC without leap seconds?

YEAR

2050 2100 2150 2200 2250 2300 2350 2400 2450 2500

Le

ap

Se

co

nd

s p

er

Ye

ar

-1

0

1

2

3

4

5

6

-1

0

1

2

3

4

5

6

IssuesWhy?• 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

Concerns• Navigation

– 1 second = 1/4 mile at the equator

• Legacy computer software– Assumption that UT1=UTC

near enough?• Legal definitions

– Mean solar time?

23:59:60

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?

http://tf.nist.gov/cesium/parcs.htm

Evolution of Timekeeping

Sun’s

Shad

ow

Verg

e & Fo

llett

Star

s

Moon

Pend

ulum

s

Atomic Clock

s

Wat

er C

lock

s

Quartz

Pulsars

Solar

TimeSidereal

Time

Mechanical

Time

Relativistic Time

AtomicTime

evolution of timescales from astronomy to physical metrology

Documents