Institute of Geodesy
GGOS and Reference Systems
Time systems / Time scales
2015-11-30
Torsten Mayer-Gürr
Institute of Geodesy, NAWI Graz
Technische Universität Graz
Torsten Mayer-Gürr
1
Institute of Geodesy
How long is a day?
Torsten Mayer-Gürr
2
Institute of Geodesy
Time systems overview
TDB
GST

LST
EqE
(Equation of the Equinox)
ET
=
GMST
TT
f  1
32.184 s
TAI

leap seconds
36 s (7/2015)
UTC
1h
~ 19 s
MEZ
GPS
1h
UT 1
UT1/GMT

LMST
1
365.25

LMT
EqT
(Equation of time)
GAT

LAT
MESZ
Greenwich
Torsten Mayer-Gürr
local
3
Institute of Geodesy
Time systems overview
TDB
GST
=
GMST
TT
f  1
32.184 s
TAI
leap seconds
36 s (7/2015)
UTC
1h
Time
scales
based
on
~ 19 s
atomic clocks
MEZ
GPS
LST
Time scales based on
EqE
Earth rotation
(Equation of the Equinox)
(sidereal day)
Time scales based on
orbital motion
ET

1h
UT 1
UT1/GMT

LMST
1
365.25

LMT
EqT
Time scales based on
(Equation
time)
Earthofrotation
(solar day)
GAT
LAT

MESZ
Greenwich
Torsten Mayer-Gürr
local
4
Institute of Geodesy
Time systems overview
TDB
GST

LST
EqE
(Equation of the Equinox)
ET
=
GMST
TT
f  1
32.184 s
TAI

leap seconds
36 s (7/2015)
UTC
1h
~ 19 s
MEZ
GPS
1h
UT 1
UT1/GMT

LMST
1
365.25

LMT
EqT
(Equation of time)
GAT

LAT
MESZ
Greenwich
Torsten Mayer-Gürr
local
5
Institute of Geodesy
Time scales based on Earth rotation
Time scales based on Earth rotation
are not strictly uniform.
Today the times has to be understood
as angles (hour angles) 24 h  2
Solar day: interval between two consecutive
transits of the sun across the meridian
Hour angle of the sun ±12h:
LAT: Local apparent (true) time
GAT: Greenwich apparent (true) time
GST

LST
EqE
(Equation of the Equinox)
GMST
f  1
UT1/GMT

LMST
1
365.25

LMT
EqT
(Equation of time)
GAT
Greenwich
Torsten Mayer-Gürr

LAT
local
6
Institute of Geodesy
Time scales based on Earth rotation
Time scales based on Earth rotation
are not strictly uniform.
Today the times has to be understood
as angles (hour angles) 24 h  2
Solar day: interval between two consecutive
transits of the sun across the meridian
Hour angle of the sun ±12h:
LAT: Local apparent (true) time
GAT: Greenwich apparent (true) time
Mean time (MT):
refers to a fictitious sun; it moves in the plane
of the equator with constant velocity
LMT: Local mean time
GMT: Greenwich mean time
Universal Time (UT) = GMT:
UT is the Greenwich hour angle of the mean sun+12h
Torsten Mayer-Gürr
GST

LST
EqE
(Equation of the Equinox)
GMST
f  1
UT1/GMT

LMST
1
365.25

LMT
EqT
(Equation of time)
GAT
Greenwich

LAT
local
7
Institute of Geodesy
Time scales based on Earth rotation
True sun
GST
Local
meridian λ
Mean sun
EqT
f  1
GAT
LAT
UT1/GMT
LMT = GMT + λ
Greenwich

LMST
1
365.25

LMT
EqT
(Equation of time)
GAT
Greenwich
Torsten Mayer-Gürr
LST
EqE
(Equation of the Equinox)
GMST
GMT


LAT
local
8
Institute of Geodesy
Solar day and siderial day
Siderial day: interval
between two consecutive
upper transits of the
vernal equinox across
the meridian
GST
f  1
UT1/GMT
23 : 56 h
Torsten Mayer-Gürr

LMST
1
365.25

LMT
EqT
(Equation of time)
GAT
24 : 00 h
LST
EqE
(Equation of the Equinox)
GMST
Solar day: interval
between two consecutive
transits of the sun across
the meridian

Greenwich

LAT
local
9
Institute of Geodesy
GMST, GST, LMST and LST
GST
Local
meridian λ
True VE
EqE
f  1
GST
GMST
LST
UT1/GMT
LMST = GMST + λ
Greenwich

LMST
1
365.25

LMT
EqT
(Equation of time)
GAT
Greenwich
Torsten Mayer-Gürr
LST
EqE
(Equation of the Equinox)
GMST
Mean
VE


LAT
local
10
Institute of Geodesy
Universal Time (UT)
Raw universal time: UT0
• Determined at an observatory,
uncorrected for polar motion
• Pseudo-universal time scale
Principal universal time: UT1
• Corrected for polar motion
• Defines the actual orientation
of the Earth w.r.t. space
• Contains all variations in the Earth‘s rotation rate,
hence is not uniform
Smoothed universal time: UT2
• Correction to UT1 for seasonal variations applied
• Rarely used anymore (mostly of historic interest)
• Has been the international time standard before
atomic time was introduced
GST
LST
EqE
(Equation of the Equinox)
GMST
f  1
UT1/GMT

LMST
1
365.25

LMT
EqT
(Equation of time)
GAT
Greenwich
Torsten Mayer-Gürr


LAT
local
11
Institute of Geodesy
Time scales based on atomic clocks
Time unit: SI second
in the International System of Units (SI)
GST
LST
International atomic time
(TAI, Temps Atomique International)
•
•
•
TAI “replaced” UT2 in 1958:
1.1.1958 0h TAI = 1.1.1958 0h UT2
Computed as the weighted mean of
individual clocks (around 200)
TAI is strictly uniform
•
•

Definition (since 1967): The second is the
EqE
duration of 9192631770 periods of the
(Equation of the Equinox)
radiation corresponding to the transition
between the two hyperfine levels of the
LMST
GMST
ground state of the caesium
133 atom

In 1997 added: "refers1 to a caesium atom at
f  1
rest at a temperature
of 0 K."
365.25
TAI
•
•
•
•
•
leap seconds
36 s (7/2015)
UTC
UT 1
UT1/GMT

EqT
Universal Time Coordinated (UTC)
(Equation of time)
Introduced 1972
Adaption to UT1, i.e., Earth rotation
GAT
1.1.1958 0h UTC = 1.1.1958 0h TAI

If the difference between UTC and UT1 becomes larger than 0.9,
a leap second is added to UTC
Since 1.7.2015, the difference between TAI and UTC is TAI-UTC = 36s
Greenwich
Torsten Mayer-Gürr
LMT
LAT
local
12
Institute of Geodesy
UT1-TAI
Torsten Mayer-Gürr
13
Institute of Geodesy
UTC-TAI
Torsten Mayer-Gürr
14
Institute of Geodesy
UT1-UTC
Leap seconds in
UTC
Torsten Mayer-Gürr
15
Institute of Geodesy
Time scales based on atomic clocks
Time unit: SI second
in the International System of Units (SI)
GST
LST
International atomic time
(TAI, Temps Atomique International)
•
•
•
TAI “replaced” UT2 in 1958:
1.1.1958 0h TAI = 1.1.1958 0h UT2
Computed as the weighted mean of
individual clocks (around 200)
TAI is strictly uniform
•
•

Definition (since 1967): The second is the
EqE
duration of 9192631770 periods of the
(Equation of the Equinox)
radiation corresponding to the transition
between the two hyperfine levels of the
LMST
GMST
ground state of the caesium
133 atom

In 1997 added: "refers1 to a caesium atom at
f  1
rest at a temperature
of 0 K."
365.25
TAI
•
•
•
•
•
leap seconds
36 s (7/2015)
UTC
UT 1
UT1/GMT

EqT
Universal Time Coordinated (UTC)
(Equation of time)
Introduced 1972
Adaption to UT1, i.e., Earth rotation
GAT
1.1.1958 0h UTC = 1.1.1958 0h TAI

If the difference between UTC and UT1 becomes larger than 0.9,
a leap second is added to UTC
Since 1.7.2015, the difference between TAI and UTC is TAI-UTC = 36s
Greenwich
Torsten Mayer-Gürr
LMT
LAT
local
16
Institute of Geodesy
Time scales based on atomic clocks
•
•
•
•
GPS time
6.1.1980 0h GPS time = 6.1.1980 0h UTC
Not incremented by leap seconds
Derived from atomic clocks
which form part of the GPS system
TAI and GPS time show slight differences
(in the order of ns)
GST
leap seconds
36 s (7/2015)
~ 19 s
GPS
UTC
UT 1
GMST
UT1/GMT

LMST
1
365.25

LMT
EqT
(Equation of time)
GAT
Greenwich
Torsten Mayer-Gürr
LST
EqE
(Equation of the Equinox)
f  1
TAI


LAT
local
17
Institute of Geodesy
Time scales based on atomic clocks
GST

LST
EqE
(Equation of the Equinox)
GMST
f  1
TAI
leap seconds
36 s (7/2015)
UTC
1h
~ 19 s
MEZ
GPS
1h
UT 1
UT1/GMT

LMST
1
365.25

LMT
EqT
(Equation of time)
GAT

LAT
MESZ
Greenwich
Torsten Mayer-Gürr
local
18
Institute of Geodesy
UTC offsets worldwide
Wikipedia
Torsten Mayer-Gürr
19
Institute of Geodesy
UTC offsets worldwide
Wikipedia
MEZ = UTC + 1h
MESZ = UTC + 2h
Torsten Mayer-Gürr
20
Institute of Geodesy
Time systems overview
TDB
GST

LST
EqE
(Equation of the Equinox)
ET
=
GMST
TT
f  1
32.184 s
TAI

leap seconds
36 s (7/2015)
UTC
1h
~ 19 s
MEZ
GPS
1h
UT 1
UT1/GMT

LMST
1
365.25

LMT
EqT
(Equation of time)
GAT

LAT
MESZ
Greenwich
Torsten Mayer-Gürr
local
21
Institute of Geodesy
Ephemeris time
1952
Ephemeris Time (ET)
• Introduced in 1952 (ephemeris second)
• Tied to the positions and dynamics of celestial bodies
• Theoretically uniform time scale for the use with ephemeris
ET was used for the calibration of atomic clocks in the 1950s.
1967
SI second: defined with reference to the cesium atomic clock
1976
Ephemeris Time be replaced by two relativistic time scales
TDT:
Terrestrial Dynamical Time
TDB:
Barycentric Dynamical Time
1990
Superseded
TT:
GCT(TCG):
BCT(TCB):
Torsten Mayer-Gürr
Terrestrial Time
Geocentric Coordinate Time
Barycentric Coordinate Time
22
Institute of Geodesy
Calendars
Torsten Mayer-Gürr
23
Institute of Geodesy
Calendars
-
Sidereal year:
Tropical year:
-
Julian calendar:
-
revolution period of the sun along the ecliptic (~365.2563 d)
interval between two consecutive transits of the sun across
the mean vernal equinox (~365.2422 d)
civil calendars are based on the tropical year
in use until 1582
simple consideration of leap years based on the Julian year
year: 365.25 d
Gregorian calendar: presently in use
more sophisticated consideration of leap years
based on the Gregorian year
year: 365.2425 d
Torsten Mayer-Gürr
24
Institute of Geodesy
Calendars
Julian Date (JD)
• Introduced in 1582 by Joseph Justus Scaliger
• Continuous count of days used primarily by astronomers
• Number of days elapsed since 1.1.4713 B.C. 12h (Julian calendar)
• Examples:
1 January 12:00 (J2000)
= 2451545.00 JD
30 November 2015 18:00
= 2457357.25 JD
Modified Julian Date (MJD)
• introduced by the Smithsonian Astrophysical Observatory in 1957 to record Sputnik
• Abbreviated version of JD
• Number of days elapsed since 17.11.1858 0h
MJD = JD – 2400000.5
• Number of days elapsed since 1.1.4713 B.C. 12h (Julian calendar)
Examples:
1 January 12:00 (J2000)
30 November 2015 18:00
Torsten Mayer-Gürr
= 2451545.00 JD
= 51544.50 MJD
= 2457357.25 JD
= 57356.75 MJD
25