# Time scales

This calculator represents time in different time scales.

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#### Anton

Created: 2021-05-13 17:25:54, Last updated: 2021-05-13 17:25:54

Physicists at the Goethe University in Frankfurt recently found that a photon takes 247 zeptoseconds (10 –21 seconds) to travel through a hydrogen molecule1. Modern science can measure such a short process with high accuracy.
The SI unit of time is the second. Today, the second is defined very precisely by the cesium atom periodic oscillations. Atomic clocks are the most accurate time and frequency standards known at the moment.
In the past, people did not have such precise instruments and deep knowledge. For timekeeping, people used periodical processes accessible in nature, for example, the change of day and night or the period of the Earth's revolution around the Sun. The accuracy of these time scales even now is sufficient enough for solving a large number of problems. Our calculator translates the time value from one timescale to another.
The article below the calculator describes the history of calculating time and time scales.

#### Time scales

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Solar and UT0 time scales require the observer latitude and longitude. Uncheck to enter the coordinates by hand.
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Digits after the decimal point: 3
Latitude

Longitude

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Sidereal time, degrees

## Time units

It once seemed that there is nothing more stable for time measuring than the regular change of day and night. Every morning the Sun rises in the east and sets in the west in the evening. This periodical phenomenon was used to determine the time during the day using a sundial. The shadow cast by a long vertical object changed its length and direction, reflecting the passing of the day.
Ancients divided the scale of the sundial into 12 equal parts, hours. Why exactly 12? Nobody knows for sure. It was too long ago. However, the number 12 is notable in that it is divisible without remainder in many different ways. For example, dividing by 2, we get the first and second half of the day, 6 hours each. Dividing by 3, we get morning, afternoon, and evening - each interval of 4 hours. It also can be divided without remainder by 4, as well as by 6. The number 12 is much better for division than number 10 because 10 has only two divisors: 2 and 5.
The hour had to be divided into lesser units to orientate in time even more accurately. These units were minutes and seconds. Why there are 60 of them is known quite reliably. Sexagesimal number system is one of the oldest on earth, and it was also very popular with ancient astronomers, who were the first to measure the exact time intervals.
People have used this system for more than one millennium. But, by the time a second became too coarse to measure even shorter periods, the sexagesimal system had long gone out of fashion and was replaced by the decimal one. Therefore, milliseconds, microseconds and other smaller fractions of time are now decimal.

## Local Apparent Time (LAT)

The working principle of a sundial is based on the direction of the shadow cast by a vertical object - gnomon. At noon, the shadow disappears or lays strictly from north to south. The rest of the time, the angle of the shadow gradually changes.
The oldest sundial found in the Valley of the Kings, Egypt, dates back to the 13th century. BC. Even more ancient structures - the obelisks of Ancient Egypt (3rd millennium BC) are also considered the first gnomons that marked definite periods of the day.2
Local apparent time LAT is equal to the geocentric hour angle of the center of the visible disk of the Sun t, measured relative to the meridian of the place of observation, plus 12 hours 3.
$LAT=t_{\odot}+12^{h}$

## Local Mean Time (LMT)

The sundial does not work in bad weather, when the sun is not visible, or at night. This is not to say that it greatly bothered most people millennia ago. They didn't have to get to university by 9:30 or to work by 8:15 am. Vigorous activity simply began no earlier than dawn and ended somewhere before sunset.
Exact time intervals, regardless of the weather, had to be measured by an extremely narrow circle of people, for example, astronomers. One of the most ancient devices for time counting was a water clock based on the principle of a uniform flow or inflow of liquid. Judging by the most ancient find (klepsydra from Karnak, the era of Pharaoh Amenhotep III 1379–1342 BC), the water clock began to be used as long as the solar clock. Clepsydra was a bowl with a narrow hole at the base, from which water gradually flowed out. Comparing the water level with the marks on the inner surface, it was possible to judge the elapsed time.
The first mechanical watches appeared in the 13th century AD. The clock measured time regardless of the presence of the sun in the sky. However, the clock was adjusted for a long time according to the sun. The first watches were not very precise. Even so, it was possible to realize that noon, measured by a mechanical clock, on most days of the year does not coincide with noon, according to the sundial.
The deviation of the time of noon counted by a uniformly running clock from noon by sundial is not constant. It changes throughout the year and at a maximum can reach 16 minutes. The phenomenon was already known to Hipparchus (2nd century BC). To distinguish the not even time shown by the sundial from the uniform one, we had to give them separate names. The first is local apparent time, LAT, and the second - local mean time , LMT. The local mean time , for a long time, could not be measured with anything (until the advent of mechanical watches). The local mean time could only be calculated by mathematical methods knowing as equation of time, EoT(t). The local mean time, the value of the equation of time, and the local apparent time are related by the relation:
$LMT=LAT-EoT(t)$
The British Scientific Association in 1862 stated that "All men of science are agreed to use the second of mean solar time as the unit of time." So the first definition of the second was 1/86400 of the mean solar day. Further, this definition was included in the CGS and ISS systems of measurement units and existed until the middle of the 20th century.

## Standard Time (ST), Introduction

Each degree of longitude corresponds to 4 minutes of sundial time. If you go by 15 degrees to the west in one hour, the sundial will show the same time. Thus, the sundial shows the solar time for a specific longitude on Earth.
After the invention of mechanical clocks, all clocks in every city showed the local solar time. Thus, the difference in time in neighboring cities corresponded to the distance between them in longitude. When travel between cities was infrequent and unhurried, and the clock was not as accurate, it was not a hassle.
But with the development of fast transport links, the problem has become noticeable. English railway companies were the first to realize the situation in the 40s of the 19th century. It was easier to accept a uniform time throughout the country than to explain to each passenger that his clock needs to be adjusted immediately upon arrival in another city. Soon, all clocks and watches in the region began to show the same London time, which corresponded to the mean solar time at the longitude of the Greenwich Observatory. The standard time of Greenwich Observatory meridian is called Greenwich Mean Time (GMT).

## Universal Time (UT)

Some other countries initially proposed their local meridians for counting standard time. But fortunately, representatives of the scientific world from different countries were able to agree and chose the Greenwich meridian as a reference point for time counting everywhere.
The World Meridian Conference held in Washington to unify the prime meridian in 1884 chose the Greenwich Observatory's meridian as a single prime meridian. The conference recommended using time at the prime meridian as a single point of reference wherever it would be convenient. In the early 20th century, the International Astronomical Union proposed using the name Universal Time (UT) instead of Greenwich Mean Time to denote the mean solar time at the prime meridian with the beginning of the day at midnight.

## Ephemeris Time (ET)

Universal Time is based on the rotation of the Earth. However, accurate astronomical observations have proved that the Earth's rotation is uneven due to changes in the angular speed of rotation and the movement of the pole (change in the position of the axis of rotation). As a new, more accurate time scale, it was proposed to use a time scale based on the periodic motion of bodies in the solar system. This scale is called ephemeris time (ET). Accordingly, the new definition of the second in 1952 was as follows: 1/31 556 925.9747 of the tropical year for January 0, 1900 at 12 o'clock ephemeris time.
Ephemeris time can be expressed in terms of universal time as follows:
$ET = UT+{\varDelta}T$
Astronomical almanacs regularly publish ΔT data.

## International Atomic Time (TAI)

With the invention of the atomic clock, people received the most stable way of measuring time. Since 1967, scientists have moved from ephemeris time to time counted by atomic clocks. They tried to make a second of atomic time exactly the same length as in the ephemeris scale, but expressed its definition in other terms: "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom". On January 1, 1958, atomic time exactly corresponded to universal time. At the same moment, the shift in ephemeris time (ET) was 32.184 s to universal time.
Accordingly, TAI is expressed by ET as:
$TAI = ET+32,184s$

## Coordinated Universal Time (UTC)

The traditional way of measuring time by the Earth's rotation is familiar to people. But the solar time is varying, due to the unevenness of the Earth's revolving. Atomic time is stable, but after years it differs notably from solar time. To get a stable time tied to the change of day and night on Earth, science men decided to create a scale, the unit of which will be a stable atomic second, but occasionally 61 seconds will be added (or 60 seconds removed) so that the difference between this time and the universal did not exceed 0.9 seconds. The time is called Coordinated Universal Time, UTC.
The International Earth Rotation Service (IERS) publishes the difference between UTC and Coordinated Time, ΔUT, and a list and dates for the introduction of leap seconds on a daily basis.
There are several versions of universal time. The IERS publishes the difference ΔUT1 between UT1 and UTC. UT1 is currently the main version of universal time, which value is determined by very long baseline radio interferometry (VLBI).
Accordingly:
$UTC=UT1-{\varDelta}UT1$
Other versions of universal time are almost out of use: UT0 and UT2.
UT0 was the baseline UT based on observations at a specific observatory. UT0 does not consider the effect of the pole shift, which means that different observation stations will receive various values. Since the 1980s, the UT0 value has ceased to be tracked by all observatories. Our calculator derives the UT0 value from the equation:
UT1= UT0−(xp sin λ + yp cos λ ) tan ϕ
где xp, yp - coordinates of the instant pole, ϕ, λ - coordinates of the observation point3
UT2 is universal time without taking into account the seasonal fluctuations in the Earth's rotation. Calculated by the formula:
UT2 = UT1+0,0220 sin2πθ − 0,0120 cos 2πθ − 0,0060 sin 4πθ + 0,0070 cos 4πθ,
где θ = 2000,0+ (JD − 2451544, 533)/365, 2422, JD - Julian date of observation3

## Standard Time (ST)

After the world meridian conference, most countries began to use the time at the prime meridian (universal time) as a reference time to determine their own standard time. At present, standard time is defined as an offset from Coordinated Universal Time (UTC). Typically, a country standard time differs from UTC by an integer number of hours. But there are exceptions, for example, Standard Time in Nepal differs from UTC by 5:45. In theory, the time zone changes every 15 degrees to the west or east. But in practice, the boundaries of time zones are determined by the borders of countries or administrative units in big countries. Countries wide sprawling from west to east, such as Russia or the United States, have several time zones so that the standard time in remote parts of the country does not differ so much from the local solar time. This calculator uses historical time zone data from the time zone database, which, in addition to standard time, also contains data of applying the daylight time.

1. Sven Grundmann,Daniel Trabert, Kilian Fehre, Nico Strenger, Andreas Pier, Leon Kaiser,Max Kircher, Miriam Weller, Sebastian Eckart,Ph. H. Schmidt,Florian Trinter, Till Jahnke, Markus S. Schöffler, Reinhard Dörner. Zeptosecond birth time delay in molecular photoionization Science October, 16th, 2020, vol. 370, issue 6514, pp. 339-341

2. Pipunyrov V. N. The history of clocks from ancient times to the present day. M.: Nauka, 1982.

3. V. A. Zharov, Spherical astronomy, Fryasino, 2006, par. 4.1

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