# Presentation: 154702

## Coordinated Universal Time (UTC) and the Future of the Leap Second

- Robert A. Nelson
- Satellite Engineering Research Corporation
- Dennis D. McCarthy
- US Naval Observatory
- Civil GPS Service Interface Committee
- September 13, 2005

## Historical Measures of Time

- Universal Time
- Time based on the angular rotation of the Earth on its axis
- Ephemeris Time
- Time based on the revolution of the Earth around the Sun
- Atomic Time
- Time based on the hyperfine transition of the cesium 133 atom

## Universal Time (UT)

- Time measured by the rotation of the Earth on its axis with respect to the Sun
- UT = mean solar time reckoned from midnight on the Greenwich meridian
- Traditional definition of the second used in astronomy
- 	**Mean solar second = 1/86 400 mean solar day**

## Mean time vs. apparent time

- Difference between mean time and apparent time is called the “equation of time”
-   Mean noon precedes apparent noon by 14.5 minutes on February 12
-   Apparent noon precedes mean noon by 16.5 minutes on November 3
- Mean solar time (clock time)
-   Mornings (sunrise to mean noon) are half hour shorter than afternoons in February
-   Afternoons (mean noon to sunset) are half hour shorter than mornings in November

- After B.M. Oliver, “The Shape of the Analemma,” *Sky and Telescope*, July, 1972, 20 - 22

- inclination effect

- combined effect

- eccentricity effect

## Variations in the Earth’s rotation

- UT is not uniform
- Variations in the Earth’s rotation (Length of Day)
- Steady deceleration (well established by early 20th century)
- Periodic variations (detected in 1930s)
- Random decade fluctuations (measured in 1950s)
- Conservation of angular momentum
- As the Earth’s rotation decreases, the Moon moves farther away

## Eclipse of 136 BC observed from Babylon

- *T* = 0

- *T* = 11 700 s = 3.25 h

*Reference:*  F.R. Stephenson, *Historical Eclipses and Earth’s Rotation *(Cambridge, 1997), p. 66

## Forms of Universal Time (UT)

- UT1
-   True measure of the Earth’s rotation angle in inertial reference system
-   Defined in terms of Greenwich Mean Sidereal Time (GMST)

- UT2 (no longer used)
-   UT1 corrected for the seasonal variation ( 30 ms)

## Ephemeris Time (ET)

- Uniform measure of time determined by the orbital motions of the celestial bodies
- ET is defined as the time that brings the observed positions into accord with the theoretical positions as determined using the Newtonian theory of gravitation
- 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

## Definition of Ephemeris Second

- Definition of the SI second adopted by the CIPM in 1956 and ratified by the 11th CGPM in 1960
-    **Ephemeris second = the fraction 1/31 556 925.9747 of the tropical year 1900**
- Newcomb assumed that UT1 is uniform in calculating his formula for the mean longitude of the Sun.  However, the Earth’s rotation has been slowing due to tidal friction at the rate of approximately 1.4 ms/d/cy over the past 1000 years
- Observations analyzed by Newcomb ranged in date from 1750 to 1892 with a mean epoch of approximately 1820
-            **Ephemeris second  =  mean solar second of approximately 1820**

## Atomic definition of the second

- Definition of the SI second adopted by the 13th CGPM in 1967
-    **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**
- Second of atomic time = second of Ephemeris Time (ET)

## International Atomic Time (TAI)

-   TAI is a coordinate time scale defined in a geocentric reference frame with the
-    SI second as realized on the rotating geoid as the scale unit
-   Uniform time measured by frequency of cesium-133 hyperfine transition
-   Unit interval = SI second
-   Continuous atomic time scale determined by Bureau International de l’Heure (BIH)
-    since 1958, now maintained by Bureau International des Poids et Mesures (BIPM)
- TAI  =  UT2 on January 1, 1958  0 h
-   Named TAI in 1971

## Terrestrial Time (TT)

-   Terrestrial Time (TT) is defined by atomic clocks on the surface of the Earth
-   TT has same rate as TAI with unit interval of the SI second
-   Maintains continuity with Ephemeris Time (ET)
-   TT has origin of January 1, 1977 0 h
-   Practical realization of TT
- 			 TT  =  TAI + 32.184 s
-   Constant offset is the difference between ET and UT1 at the epoch of TAI
-   Theoretical equivalence of time measured by quantum mechanical atomic
-     interaction and time measured by gravitational planetary interaction
- 			          TT  =  ET

## Length of Day Since 1600

**Length of Day Since 1600**

- After F.R. Stephenson and L.V. Morrison, *Phil. Trans. R. Soc. London* **A313**, 47 – 70 (1984)

- decade fluctuations

- trend over past 1000 years

## T since 1600

- After F.R. Stephenson and L.V. Morrison, *Phil. Trans. R. Soc. London* **A351**, 165 – 202 (1995)

- TT

- ET

**1977.0**

## Coordinated Universal Time (UTC)

-   Coordination of worldwide atomic time and frequency radio transmissions
-    by BIH began in 1961
-   Reference frequency of 9 192 631 830 Hz for cesium based on second of ET
-   Details of UTC system were formalized by International Radio Consultative
-    Committee (CCIR) of International Telecommunication Union (ITU) in 1962
-   Name Coordinated Universal Time (UTC) adopted by IAU in 1967
-   From 1961 to 1972 UTC contained both frequency offsets and fractional
-    (less than 1 s) steps to maintain agreement with UT2 within about 0.1 s
-   In 1972 present UTC system was adopted, with 1 s (leap second) steps
-    but no frequency offsets to maintain agreement with UT1 within 0.9 s
-   Definition of UTC is a compromise to provide both the SI second and an
-    approximation to UT1 for celestial navigation in same radio emission

## Duration of time scale units

- Second of TT or TAI = SI second = Second of ET
**	****Thus the SI second represents the second of UT1 in the early**
**	****19th century (mean solar second of approximately 1820)**
- LOD has been increasing at rate of about 1.4 ms/d/cy
- Present LOD is about 86 400.025 SI seconds (modified by short term fluctuations)
**	****Difference of 2.5 ms from SI day of exactly 86 400 SI seconds**
**	****accumulates to about 1 second in a year**
- For broadcast UTC time signals, accumulated excess in LOD initially compensated
- by frequency offsets and fractional steps, now compensated by leap second steps

**Duration of time scale units**

## UTC frequency offsets

- Courtesy of E.F. Arias, B. Guinot, and T.J. Quinn, *ITU-R SRG Colloquium on the UTC Time Scale*
- (Torino, Italy, May 28 – 29, 2003)

- (Relative frequency offset in units of 10-10)

## Evolution of UTC time steps

- Courtesy of E.F. Arias, B. Guinot, and T.J. Quinn, *ITU-R SRG Colloquium on the UTC Time Scale*
- (Torino, Italy, May 28 – 29, 2003)

## UTC since 1961

- 22 leap seconds have been added since 1972
- Presently TAI – UTC = 32 s

- slope = (2.1  0.05) ms per day

- Difference after 50 years = 1 minute
- Difference after 100 years = 2.5 minutes
- Difference after 1000 years = 1 hour

- Courtesy of E.F. Arias, B. Guinot, and T.J. Quinn, *ITU-R SRG Colloquium on the UTC Time Scale  *(Torino, Italy, May 28 – 29, 2003)

- UT1  uniform time without leap seconds

- Elimination of leap seconds would have no practical effect on customary social conventions

## Data for UT1

- When it was introduced in 1972, UTC was still the most readily available worldwide system for independent determination of position
- The development of GPS and the wide availability of satellite navigation systems has diminished the need for a broadcast approximation to UT1
- UT1 does not represent time as commonly defined today;  instead it is an angle used to determine the Earth’s orientation in space.
- The International Earth rotation and Reference system Service (IERS) produces weekly bulletins in printed and electronic formats with daily updates that provide the current value of  UT1 – UTC along with predictions.  These data provide to astronomers knowledge of UT1 many orders of magnitude more accurately than what is obtainable on the gross assumption that UT1 is the same as UTC.
- Currently the error in substituting UTC for UT1 can be as much as 900 milliseconds. Improvements in telescope pointing software made possible by using IERS data could be implemented as part of routine upgrade maintenance. The IERS maintains web sites with this information and is planning on making the data even more accessible in the future.

## Legal definition of civil time

- Since 1988 international timekeeping has been governed by the International Bureau of Weights and Measures (BIPM) under the authority of the General Conference on Weights and Measures (CGPM).
- Both the CGPM and the ITU recognize UTC as the basis of civil time and as the scientific equivalent of Greenwich Mean Time (GMT) or mean solar time. The CGPM and ITU are treaty organizations to which most industrialized nations belong, including the US and the UK.
- British political opposition to eliminating leap seconds from UTC because GMT is established in its domestic laws is unfounded.  Ironically, the Greenwich Observatory no longer exists and the British Broadcasting Company derives its time signal from the realization of UTC that is obtained from the GPS, which is maintained by the US Naval Observatory.

## GPS System Time (GPS Time)

- No leap seconds
- Origin is midnight of January 5/6, 1980 UTC
- Steered to within 1 s of UTC(USNO), except no leap seconds are inserted
- Relationships with TAI and UTC (within statistical error)
-   GPS Time = TAI – 19 s = constant
-   GPS Time = UTC + 13 s presently

## Issues

- Problems with current system
- communications
- time stamping
- proliferation of non-standard time scales
- Impact of keeping or changing present system
- Many people envision major problems in the future
- Integral steps in civil time
- Need for multiple leap seconds per year in the future
- Others depend on the difference UTC - UT1 being less than one second; they will need to upgrade their systems if leap seconds are eliminated
- Astronomical observatories
- Geolocation systems
- Important policy issues
- Philosophy of whether or not to eliminate leap seconds from UTC
- Problem is really the expense of making changes in current software being used by observatories, satellite systems, geolocation systems
- If leap seconds were eliminated, what would be appropriate deadline
- What is the role of GNSS time scales in international timekeeping

## International discussions

- UTC is international standard for civil time
- Time distributed by GNSS has become a *de facto* means to obtain UTC globally
- Leap seconds in UTC encourage the use of alternative time scales that are continuous
- Discussions are under way to possibly modify UTC by eliminating leap seconds
- ITU-R SRG Colloquium on the UTC Time Scale (Torino, Italy, May 28 – 29, 2003)
- CCTF (April 2004)
- ITU WP 7A (currently)

## Conclusions

- Continued use of current definition of UTC with leap second steps presents potential difficulties in complex timekeeping systems
- Leap second planned for end of 2005 (the first since 1998) will be an important case study
- The GPS will continue to disseminate UTC, regardless of whether it is redefined.  It will continue to be an international standard for time.