This document discusses various systems of time measurement. It describes: 1. Solar time, which is based on the sun's apparent daily motion, and mean solar time, which averages small variations. 2. Sidereal time, which is based on fixed stars' daily motions rather than the sun. 3. Universal Time (UT) and its variants, which are based on mean solar time at the Greenwich meridian. 4. International Atomic Time (TAI) and Coordinated Universal Time (UTC), which are atomic clock-based time standards. 5. Time scales used in global navigation satellite systems like GPS, GLONASS, Galileo, and BeiDou.

1. Lecture 5.
Systems of time measurement

2. Time measurement (timing) is based on periodically
repeated processes. Such as change of the moon phases,
alternation of seasons, alternations of day and night,
sunrise and sunset, mechanical oscillations.
Scales of time measurement
Time is the measure of durations of events and the intervals between them.
The main requirement to the units of time measurement
is stability.
Periodic events and periodic
motion have long served as
standards for units of time.
Examples include the apparent
motion of the sun across the
sky, the phases of the moon, the
swing of a pendulum.

3. Solar time
Solar time follows the apparent revolution of the Sun around the Earth. A solar
day is the interval between two successive passages of the Sun through the
meridian. Of course, this apparent revolution only reflects the true rotation of
the Earth. Complete turnover of the Earth around its axis relative to the
direction of the Sun is called true solar day.
The duration of the true solar day varies with the seasons. This is a
consequence both of the eccentricity of the Earth's orbit and the obliquity of the
ecliptic (the tilt of Earth's rotation axis).

4. Mean solar time
Firstly, the Earth moves at different speeds in different parts of its elliptical
orbit, according to Kepler's second law, hence the sun seems to move at
different speeds among the stars. Secondly, even with a perfectly circular
Earth orbit, the Sun would move evenly
along the ecliptic but its projection onto the
celestial equator would move at varying speeds.
To obtain a more even time scale, one defines a
fictitious ``Mean Sun''. This Mean Sun takes the
same time from one vernal equinox to the next
as the true Sun, but it is supposed to move with
constant velocity along the celestial equator.
The difference between True and Mean Solar Time
is called the equation of time.

5. Because two different effects with different time scales overlap (the
eccentricity causes a period of one year, the obliquity of the ecliptic one of
half a year), the equation of time has two minima and two maxima per year:
Equation of time
~ 11.Feb ~ -14.5 min
~ 14.Mai ~ +4 min
~ 26.Jul ~ -6.4 min
~ 3.Nov ~ +16.3 min

6. Sidereal time
The sidereal time is deduced from the revolution of the Earth with respect
to the distant stars. A sidereal day can be defined in a first approximation
as the time interval between two successive passages of the same star
through the meridian.

7. Left: a distant star (the small red circle)
and the Sun are at culmination, on the
local meridian.
Centre: only the distant star is at
culmination (a mean sidereal day).
Right: a few minutes later the Sun is on
the local meridian again. A solar day is
complete.
Sidereal time vs solar time

8. Universal Time
Universal Time (UT) is time scale based on the rotation of the Earth. It is
the mean solar time on the Prime Meridian at Greenwich.
This time includes year, month, day, hour, minute and second. The first
three values measured by Gregorian calendar, others – local mean time at
Greenwich. UT is the same everywhere on Earth.
There are several versions of Universal Time:
UT0 – determined at an observatory by observing the motion of stars,
Moon and artificial Earth satellites.
UT1 – calculated in accordance with movements of the poles.
UT2 – time UT1 with seasonal corrections.

9. Terrestrial Dynamical Time (TDT)
Due to irregularity of the daily rotation of the Earth sidereal and solar days
slightly vary. For accurate astronomic calculations is used ephemeris second
calculated as 1/86400 share of the average day on Jan. 1 1900 .
The ephemeris second is unit of Terrestrial Dynamical Time (TDT), which is
used in astronomical tables of positions (ephemerides) of the Sun, Moon and
planets as seen from the Earth. Dynamic time also is used for determination
satellite ephemerides.

10. International Atomic Time (TAI)
Introduced in 1971, and based on a line in spectrum of cesium (Cs).
TAI is based on SI second which = 9,192,631,770 periods of radiation emitted
by Cs133.
TAI is a time scale is a weighted average of the time kept by over 200 atomic
clocks in about 70 national laboratories worldwide. The clocks are compared
using satellites. Due to averaging it is far more stable than any clock would
be alone.
TAI is currently the best
realization of a timescale
based on the SI-second,
with a relative accuracy
of +/- 2 ∙ 10−14

11. Coordinated Universal Time(UTC)
Coordinated Universal Time (abbreviated UTC) is the time standard by which the
world regulates clocks and time. It is a time standard based on International
Atomic Time (TAI) with leap seconds added at irregular intervals to compensate
for the Earth’s slowing rotation. Time zones around the world are expressed
using positive or negative offsets from UTC.

12. Time scales of GNSS
GPS Time (GPST)
GPS Time (GPST) is a continuous time scale (no leap seconds) defined by the GPS
Control segment on the basis of a set of atomic clocks at the Monitor Stations and
onboard the satellites. It starts at 0h UTC (midnight) of January 5th to 6th 1980.
At that epoch, the difference TAI−UTC was 19 seconds, thence GPS−UTC=n −
19s. GPS time is synchronized with the UTC at 1 microsecond level (modulo one
second), but actually is kept within 25 ns.

13. GLONASS Time (GLONASST)
GLONASS Time (GLONASST) is generated by the GLONASS Central
Synchronizer and the difference between the UTC(SU) and GLONASST should
not exceed 1 millisecond plus three hours (i.e., GLONASST=UTC+3h - τ, where
𝜏 < 1𝑚𝑖𝑙𝑖𝑠𝑒𝑐), but τ is typically better than 1 microsecond. Unlike GPS,
Galileo or BeiDou, GLONASS time scale implements leap seconds, like UTC.
Galileo System Time (GST)
Galileo System Time (GST) is a continuous time scale maintained by the Galileo
Central Segment and synchronised with TAI with a nominal offset below 50 ns.
The GST start epoch is 0h UTC on Sunday, 22 August 1999 (midnight between 21
and 22 August).
BeiDou (BDT)
BeiDou Time (BDT) is a continuous time scale starting at 0h UTC on January
1st, 2006 and is synchronised with UTC within 100 ns< (modulo one second).