1 Introduction
Time and space are the basic forms of material existence. Time is one of the basic physical quantities, which reflects the sequence and continuity of material movement. People cannot do without time in production, scientific research and daily life.
2. Some basic concepts about the time system
Time is an important physical quantity, which puts forward high requirements on time in GPS measurement. For example, when using the ranging signal transmitted by the GPS satellite to measure the distance between the satellite and the receiver, if the ranging error is required to be less than or equal to 1 cm 1 \mathrm{~cm}1 cm , then the error of the measured signal propagation time must be less than or equal to3 × 1 0 − 11 s = 0.03 ns 3 \times 10^{-11} \mathrm{~s}=0.03 \mathrm{~ns}3×10−11 s=0.03 ns 。
2.1 Time
Time has two meanings: time interval and moment. The time interval refers to the time process experienced by the movement of things between two (instantaneous) states, which describes the continuous state of the movement of things in time; while the moment refers to the time when a certain phenomenon occurs. The so-called moment is actually a special time interval (between an agreed starting moment), and the time interval refers to the difference between the beginning and end moments of an event. Instantaneous measurement is also known as absolute time measurement, while time interval measurement is known as relative time measurement.
The time system stipulates the standard of time measurement, including the reference base (starting point) of the moment and the scale reference of time interval measurement. The time system is theoretically described by definitions and corresponding regulations, and the time system integration is realized within the same spherical range or within a certain area through timekeeping, time service, and time step rate measurement and comparison techniques and maintain a unified time system. But in actual use, sometimes these two different concepts are not strictly distinguished.
2.2 Time base
Time measurement requires a common standard scale, called time reference or time frequency reference. Generally speaking, any periodic motion that can be observed can be used as a time reference as long as it meets the following conditions:
(1) It can perform continuous periodic motion, and the motion cycle is very stable;
(2) The motion cycle has a good Reproducibility, that is, this periodic movement in different periods and places can be reproduced through observation and experiment.
There are many kinds of motions with the above characteristics in the natural world, such as the early burning incense and hourglass, the later pendulum and the vibrating of quartz crystal, and the modern electromagnetic wave oscillation signal and pulsar pulse signal emitted by atomic transition. So far, there are mainly the following types of more precise time standards in practical application:
(1) The earth's rotation period. It is the time base used to build the world, and its stability is about 1 0 − 8 10^{-8}10−8 . _
(2) The revolution period of the planets around the sun and the revolution period of the moon around the earth. It is the time base used to build the almanac, and its stability is about1 0 − 10 10^{-10}10−10 . _
(3) The oscillation frequency (period) of the electromagnetic wave signal emitted (or absorbed) by the electrons of the atomic clock when they transition from one energy level to another. It is the time reference used when building atoms, and its stability is about1 0 − 14 10^{-14}10−14 . _ The current best cesium atomic fountain clock has a stability of1 0 − 16 10^{-16}10− 16 levels.
(4) The rotation period of the pulsar, the stability of the rotation period of the best millisecond pulsar may reach1 0 − 19 10^{-19}10− 19 or better. At present, scientists from all over the world are still working hard to establish pulsar time with higher precision (than atomic time).
2.3 Time keeping system (clock)
Time-keeping systems (clocks) are used to establish and/or maintain a time-frequency reference, determining the time at any one instant. The time-keeping system can also evaluate the stability and accuracy of different clocks in the system through time-frequency measurement and comparison technology, and give different weights to each clock accordingly, so that multiple clocks can be used to jointly establish and maintain the time system frame.
2.4 Timing and time comparison
The time service system can transmit the time information and frequency information maintained by the time system to users through equipment such as telephones, televisions, computer network systems, dedicated long-wave and short-wave radio signals, transport clocks, and satellites. Different users can also achieve high-precision time comparison through the above-mentioned facilities and methods. Time service is actually a kind of time comparison, which is a time comparison between the user and the standard time.
Different time comparison methods have different accuracy, and their convenience and cost are also different. Users can choose the appropriate method according to their needs.
At present, many units and institutions in the world are establishing and maintaining various time systems, and transmitting relevant time and frequency information to users through various methods. These tasks are collectively referred to as time services. The domestic time service in our country is provided by the National Time Service Center (NTSC).
2.5 The main technical indicators of the clock
A clock is an important tool for keeping time. The clock can be used to continuously provide the user with the time ti t_i corresponding to any momentti. Since there are errors in any clock, it is necessary to compare it with the standard time regularly or irregularly to obtain the clock difference at the comparison time, and estimate ti at any time after mathematical processing (such as simple linear interpolation) . t_itiCorrect the clock difference to obtain a more accurate time. The main technical indicators for evaluating clock performance are frequency accuracy, frequency drift and frequency stability.
3. Sidereal time and solar time
Earth's rotation is a continuous periodic motion. In the early days, due to the limitation of observation accuracy and timing tools, people thought that this rotation was uniform, so it was chosen as the time reference. Both sidereal time and solar time use the earth's rotation as the time reference, and the main difference lies in the reference points selected for measuring the rotation.
3.1. Sidereal time
Sidereal time is based on the vernal equinox as a reference point. Due to the rotation of the earth, the time interval between two consecutive vernal equinoxes passing through the local meridian is one sidereal day. Divide evenly on the sidereal day basis to obtain "hours", "minutes" and "seconds" in the sidereal time system. Sidereal time is numerically equal to the hour angle of the vernal equinox relative to the local meridian. Since sidereal time begins when the vernal equinox passes through the local upper meridian, it is a local time.
Due to the influence of precession and nutation, the direction of the earth's rotation axis in space is constantly changing, so the vernal equinoxes can be divided into true vernal equinoxes and flat vernal equinoxes. The corresponding sidereal time is also divided into true sidereal time and flat sidereal time. Among them, Greenwich Mean Sidereal Time (GAST) and Greenwich Mean Sidereal Time (GMST) often appear in GPS. GAST is the angle between the true vernal equinox and the zero point of longitude (the intersection of the Greenwich origin meridian and the equator). The variation of GAST depends mainly on the rotation of the earth, but is also related to the movement of the true vernal equinox itself due to precession and nutation; GMST is the angle between the vernal equinox and the zero point of longitude, GAST − GMST = Δ ψ cos ( ε 0 + Δ ε ) \mathrm{GAST}-\mathrm{GMST}=\Delta \psi \cos \left(\varepsilon_0+ \Delta \varepsilon\right)GAST−GMST=D pscos( e0+Δ e )式中,Δ ψ \Delta \psiΔ ψ is the nutation of the Huang Jing;Δ ε \Delta \varepsilonΔε is the angle nutation, which will be introduced in detail later.
3.2. True solar time
The true solar time is based on the center of the sun as a reference point, and the time interval when the center of the sun passes through the meridian of a certain place twice is called a true solar day. Based on it, the "hour", "minute" and "second" in the true solar time system can be obtained after being evenly divided. Therefore, true solar time is a time system established based on the rotation of the earth and the ether as a reference point from the center. True solar time is numerically equal to the hour angle of the center of the sun relative to the local meridian, plus 12 hours. However, since the orbit of the earth around the sun is an ellipse, according to Kepler's three laws of planetary motion, its angular velocity is different. At the perihelion, the angular velocity is the largest; at the aphelion, the angular velocity is the smallest. Since the earth's revolution is located on the ecliptic plane, and the hour angle is measured on the equator plane, the length of true solar time is different. That is to say, true solar time does not have the basic conditions to be a time system .
3.3. Mean solar time
In daily life, people have used the sun to determine the time, arrange work and rest. In order to make up for the unevenness of the true solar time. People imagined to use a fake sun to replace the real sun. This fake sun is also doing the same annual motion as the real sun, but there are two differences: first, its annual motion trajectory is located on the equator plane instead of the ecliptic plane; second, its angular velocity on the equator is constant, equal to the real sun The average angular velocity of the sun. We call this false sun the flat sun. The time system established on the basis of the earth's rotation and the above-mentioned mean solar center as a reference point is called mean solar time. That is to say, the time interval between the hypothetical mean sun passing through the meridian circle of a certain place twice in succession is called a mean solar day. After being evenly divided based on it, the "hour", minute and "second" in the mean solar time system can be obtained. Mean solar time is numerically equal to the hour angle of the mean sun, plus 12 h 12 \mathrm { ~h}12 h 。
Since the mean sun is a hypothetical invisible celestial body, the mean solar time is actually obtained by observing the stars or the real sun and then calculating according to the mathematical relationship between different time systems.
4. Universal Time and Zone Time
Mean solar time is a local time. At the same moment, the mean solar time of two places located on different longitudes is different. For the convenience of daily life and work, a unified standard time is needed. The International Meridian Conference held in Washington in 1884 decided to divide the world into 24 standard time zones. From the zero meridian of Greenwich, 7. 5 ∘ 7.5^{\circ} to the east and west7.5∘ is 0 time zone, then eastward every1 5 ∘ 15^{\circ}15∘ is a time zone, recorded as1 , 2 , ⋯ , 23 1,2, \cdots, 231,2,⋯,23 time zones. In the same time zone, the mean solar time on the central meridian of the time zone is uniformly adopted, which is called zone time. The territory of Liaoge in China spans 5 time zones from west to east. At present, the district time of the East Eighth District is used, which is called Beijing time. After adopting zone time, the time used in a local area is relatively uniform, and different time intervals can also be easily converted.
The mean solar time at the meridian from Greenwich is called universal time. Universal time is based on the earth's rotation period as the time reference. With the development of science and technology and the improvement of observation accuracy, people have gradually discovered: (1) The speed of the
earth's rotation is not uniform. , and there are seasonal changes and short-period changes, the situation is more complicated;
(2) The position of the poles on the earth is not fixed, but is constantly moving, that is, there is a phenomenon of pole shift. This means that universal time no longer strictly meets the basic conditions of a time system, because it is actually not a completely uniform time system. In order to make the universal time as uniform as possible, since 1956, a pole shift correctionΔ λ \Delta \lambdaΔ λ and the seasonal correction of the earth's rotation speedΔ T \Delta TΔT . _ If we call the universal time measured directly based on astronomical observations as UT0, the universal time after pole shift correction is called UT1, and the universal time after seasonal correction of the earth’s rotation speed is called UT2, then: UT 1
= UT 0 + Δ λ UT 2 = UT 1 + Δ T = UT 0 + Δ λ + Δ T \begin{aligned} &\mathrm{UT} 1=\mathrm{UT} 0+\Delta \lambda \\ &\ mathrm{UT} 2=\mathrm{UT} 1+\Delta T=\mathrm{UT} 0+\Delta \lambda+\Delta T \end{aligned}UT1=UT0+D lUT2=UT1+ΔT=UT0+D l+ΔT
In the formula, the pole shift correction Δ λ \Delta \lambdaΔ λ infinity:
Δ λ = 1 15 ( X p sin λ − Y p cos λ ) tan φ \Delta \lambda=\frac{1}{15}\left(X_p \sin \lambda- Y_p \cos \lambda\right) \tan \varphiD l=151(Xpsinl−Ypcosl )tanIf
,X p, Y p X_p, Y_{\mathrm{p}}Xp、Ypare the two components of the pole shift, measured and published by IERS; λ , φ \lambda , \varphiλ and φ are the longitude and latitude of the station. The seasonal correction of the earth's rotationΔ T \Delta TDetermine the Δ T value:
Δ T = 0.022 s sin 2 π t − 0.012 s cos 2 π t − 0.006 s sin 4 π t + 0.007 s cos 4 π t (2-8) \Delta T= 0.022 \mathrm{~s} \sin 2 \pi t-0.012 \mathrm{~s} \cos 2 \pi t-0.006 \mathrm{~s} \sin 4 \pi t+0.007 \mathrm{~s}\ cos 4 \pi t \quad \text { (2-8) }ΔT=0.022 s sin2πt−0.012 s cos2πt−0.006 ssin4πt+0.007 s cos4πttt
in formula (2-8) t is the Bessel year. t = ( \mathrm{t}=(t=( MJD-51544.03)/ 365.2422 / 365.2422/365.2422 . After the above corrections, the stability of UT2 has improved (about1 0 − 8 10^{-8}10− 8 ), but still contains the long-term term, short-period term and some irregular terms in the inhomogeneity of the earth's rotation, so they are not a uniform time system, and cannot be used in high-precision application fields such as GPS measurement.
It should be pointed out that since UT1 reflects the real situation of the earth's rotation and is directly related to the earth's rotation angle, it is an important parameter in the coordinate transformation between GCRS and ITRS (WGS-84) coordinate system.
5. Atomic Time, Coordinated Universal Time and GPS Time
5.1. Atomic time
With the development of productivity and the improvement of science and technology, people have higher and higher requirements for the accuracy and stability of time and frequency. Sidereal time and peace solar time based on the rotation of the earth, and the revolution of planets and moons Almanac has been difficult to meet the requirements. Since the 1950s, people have gradually focused their attention on establishing the atomic time based on the atomic motion inside the material.
When the electrons in an atom jump from one energy level to another, they emit or absorb electromagnetic waves. The frequency of this electromagnetic wave is very stable, and the above phenomenon is easy to reproduce, so it is a good time reference. In 1955, the British National Physical Laboratory NPL cooperated with the US Naval Observatory USNO to accurately measure the oscillation frequency of the electromagnetic wave signal emitted by the ground state of the cesium atom when it transitions between two hyperfine energy levels in a zero magnetic field. In October 1967, the Thirteenth International Conference on Planning and Design adopted the following resolution: cesium 133 ( C s 133 ) 133\left(\mathrm{Cs}^{133}\right) located at sea level133(Cs133 )The world in which the 9192631770 cycles of transition radiation oscillation between two hyperfine energy levels in the ground state of the atom lasts for 9192631770 cycles is defined as the atomic time is 1s. And the starting point of atomic time is specified as January 1, 19580 h 0 \mathrm{~h}0 h , at this time, the atomic time is aligned with the universal time, but due to technical reasons, it was later found that the atomic time AT and the universal time UT were not aligned accurately at this instant, and there was 0.0039 s 0.0039 \mathrm{ ~s}0.0039 s difference, namely:
( AT − UT ) 1958.0 = − 0.0039 s (\mathrm{AT}-\mathrm{UT})_{1958.0}=-0.0039 \mathrm{~s}(AT−UT)1958.0=− 0.0039 s
From this the atomic time can be established. It should be noted that many different types of atomic clocks appeared later, such as rubidium atomic clocks, hydrogen atomic clocks, etc., and their transition signal frequencies were precisely determined to be 6834682605 Hz 6834682605 \mathrm{~Hz}6834682605 Hz and1420405757.68 Hz 1420405757.68 \mathrm{~Hz}1420405757.68 Hz , so the definition of atomic time is extended to a time system based on the stable frequency of atomic transition.
5.2. International Atomic Time
Atomic time is determined and maintained by atomic clocks, but due to differences in electronic components and external operating environments, the time given by each atomic clock is not strictly the same at the same moment. In order to avoid confusion, it is necessary to establish a more reliable, more accurate, and more authoritative unified time system that can be accepted by all countries in the world——International Atomic Time TAI. TAI was established by the International Time Bureau in 1971 and is now maintained by the time department of the International Bureau of Weights and Measures (BIPM). BIPM is based on the data given by about 240 free-running atomic clocks in about 60 time laboratories around the world, and the international atomic time is given after unified data processing.
5.3. Coordinated Universal Time
Atomic time with good stability and reproducibility can meet the requirements of high-precision time interval measurement, so it is adopted by many departments. However, there are many fields, such as astronomical navigation and terrestrial astronomy, which are closely related to the rotation of the earth and cannot be separated from universal time. Since atomic time is a uniform time system, and the earth's rotation has a long-term trend of slowing down, this means that the second of universal time will become longer and longer, so the difference between atomic time and universal time will become more and more obvious, and it is estimated that by the end of this century, the difference between the two will reach 2 min 2 \mathrm{~min}2 min 左右。为同时兼顾上述用户的要求, 国际无线电科学协会于 20 世纪 60 年代建立了协调世界时 UTC。协调世界时的秒长严格等于原子时的秒长, 而协调世界时与世界时 UT 间的时刻差规定需要保持在 0.9 s 0.9 \mathrm{~s} 0.9 s 以内, 否则将采取闰秒的方式进行调整。增加 1 s 1 \mathrm{~s} 1 s 称为正闰秒,减少 1 s 1 \mathrm{~s} 1 s 称为负闰秒。闰秒一般发生在 6 月 30 日及 12 月 31 日。闰秒的具体时间由国际计量局在 2 个月前通知各国的时间服务机构。
为了使用方便、及时, 各时间实验室通常都会利用本实验室内的多台原子钟来建立和维持一个局部性的 UTC 系统, 供本国或本地区使用。为加以区分, 这些区域性的 UTC 系统后要加一个括号, 注明是由哪一个时间实验室建立和维持的。例如, 由美国海军天文台建立和维持的 UTC 系统, 写为 UTC(USNO)。GPS 导航电文中给出了 UT1 与 UTC(USNO) 之间的差异 。而 BIPM 利用全球各个实验室的资料而建立起来的全球统一的协调世界时, 则直接标注为 UTC, 后面不加括号。
原子时的秒长是根据 1900.0 1900.0 1900.0 is defined by the second length of ephemeral time, that is, the length of an atomic time second defined by the 13th International Conference on Weights and Measures is the same as1900.0 1900.0The length of 1 second of ephemeris time is the same at 1900.0 . Due to the long-term slowing trend of the earth's rotation, that is to say, the seconds of universal time will become longer and longer. After more than 100 years, there is an obvious difference between the universal time second and the atomic time second, so the jumping seconds become more and more frequent (now about 1 s needs to be adjusted every year) 1 \mathrm{~s})1 s ) , which brings a lot of inconvenience to use. Some people suggest redefining the second length of atomic time so that it is as consistent as possible with the second length of the current universal time, so as to reduce the number of jumping seconds and keep UTC continuous in a long period of time. But "second" is a very important basic physical quantity. After its definition changes, it will cause a series of parameters such as the speed of light to change. Therefore, there are many opposing opinions, and it needs to be carefully considered and discussed in the long run.
In December 1979, UTC has replaced Universal Time as the standard time in radio communications. At present, many countries have adopted UTC as their own time system, and broadcast time numbers according to UTC time. Users who need to use universal time can obtain UT1 indirectly according to UTC and (UT1-UTC).
5.4. GPS time
GPS time is a time system used by the Global Positioning System, GPS. It is an atomic time established and maintained by the GPS ground monitoring system and the atomic clocks in GPS satellites, and its starting point is 0 h 00 m 00 s 0 \mathrm{~h} 00 \mathrm{~ on January 6, 1980 m} 00 \mathrm{~s}0 h 00 m 00 s . At the initial moment, GPS time is aligned with UTC, and the time given by these two time systems is the same. Due to the existence of jumping seconds in UTC, after a period of time, there will be a difference ofnnn whole seconds,nnn is the accumulated jumping seconds of UTC during this period, which will change with time. Since the starting moment of GPS time is January 6, 1980, the difference between UTC and TAI is19 s 19 \mathrm{~s}19 s , so there will always be 19 s between GPS time and international atomic time19 \mathrm{~s}19 s difference, ie TAI-GPST= 19 s =19 \mathrm{~s}=19 s . Theoretically speaking, both TAI and GPST are atomic time and do not jump seconds, so the difference between these two time systems should be strictly19 s 19 \mathrm{~s}19 s whole. But TAI (UTC) is a time system jointly maintained by BIPM based on about 240 atomic clocks around the world, and GPST is a localized atomic time maintained by dozens of atomic clocks in the Global Positioning System. In addition to the difference of several whole seconds between systems, there will also be small differences (several or tenths of nanoseconds)C 0 C_0C0, TAI − GPST = 19 s + C 0 ; UTC − GPST = n \mathrm{TAI}-\mathrm{GPST}=19s+C_0 ; \mathrm{UTC}-\mathrm{GPST}=nTHIS−GPST=19s+C0;UTC−GPST=n whole seconds+++ C 0 C_0 C0. Thanks to GPSGPSGPS has been widely used in time comparison, and users can obtain high-precision UTC or TAI time through the above relationship. There are special units in the world to measure and publishC 0 C_0C0value, its value can generally be kept at 10 ns 10 \mathrm{~ns}Within 10ns .
6. A time system based on the framework of the theory of relativity
Before 1984, almanac time was used in calculating the positions of natural and man-made celestial bodies, compiling astronomical ephemeris and satellite ephemeris. Ephemeris time is a time system based on classical Newtonian mechanics. According to Newtonian mechanics, time ttt is an independent variable in the equation of motion of a celestial body, which has nothing to do with the position of the celestial body in space and the gravitational potential it receives. It can be used not only for the motion of satellites around the earth, but also for the motion of planets around the sun. With the improvement of observation technology and the continuous improvement of the precision of timing tools, the contradiction between this classical theory and observation results began to appear, and became more and more obvious. It is urgent to use a new theory and model to explain and process data.
For this reason, in 1976, the 16th IAU General Assembly made a resolution to officially introduce the relativistic time scale in the field of astronomy, and gave specific definitions of geodynamic time TDT and solar system barycentric dynamic time TDB (however, geodynamic time and solar system barycentric dynamic time These two names were officially determined at the 17th IAU General Assembly in 1979). At the 21st IAU General Assembly held in 1991, it was decided to change the geodynamic time TDT to the earth time TT, and introduced the geocentric coordinate time TCG and the solar system barycentric coordinate time TCB. Concepts such as TDT (TT) and TDB will be involved in the new GPS navigation message.
6.1. Geodynamic Time (TDT)
Geodynamic time is a time system used to solve the equations of motion of celestial bodies (such as artificial satellites) moving around the center of mass of the earth, and to calculate the ephemeris of satellites. TDT is based on the international atomic time TAI, and its second length is equal to the second length of the international atomic time. But there are 32.184 s between the starting points 32.184 \mathrm{~s}A difference of 32.184 s , ie
TDT = TAI + 32.184 s \mathrm{TDT}=\mathrm{TAI}+32.184 \mathrm{~s} \quad \text {}TDT=THIS+32.184 s
This is because TDT starts at January 1, 1977 0 h 0 \mathrm{~h}0 h is the same as the ephemeral time ET (this is done to maintain the continuity of the celestial body's position), and at this time the difference between ET and TAI is32.184 s. 32.184 \mathrm{~s}_{\text{. }}32.184s 。 And TAI and GPS \mathrm{GPS}There are 19 s between GPS time19 \mathrm{~s}19 s difference, so there is theoretically51.184 s between TDT and GPS time 51.184 \mathrm{~s}The difference of 51.184 s :
TDT = GPST + 51.184 s \text { TDT }=\text { GPST }+51.184 \mathrm{~s} TDT = GPST +51.184 s
The above formula does not take into account the slight difference between TAI and GPS timeC 0 C_0C0, so it is only a theoretical value. It should be noted that the time when a certain time system was established and started to be used is not the same as the starting point of the time system, and the starting point is often earlier than the time when it was started to be used.
In the resolution of the 16th IAU General Assembly, the basic unit of TDT was changed from "second" in atomic time to "day" in astronomy, and 1 day of TDT was defined = 86400 s =86400 \mathrm { ~s}=86400 s (SI). This change has no substantive significance, but only for the convenience of astronomical calculations. In 1991, the 21st IAU General Assembly decided to rename TDT as Earth Time TT in order to avoid using the controversial term Dynamical.
At present, the earth time TT is used in the calculation of the motion equation of the GPS satellite and its ephemeris. Earth time TT can be regarded as an idealized atomic time consistent with SI seconds realized on the geoid.
6.2. The dynamic time TDB of the center of mass of the solar system
The center-of-mass dynamic time of the Paleosystem is simply called the center-of-mass dynamic time. This is a time system used to solve the equations of motion whose origin of coordinates is located at the barycenter of the solar system, and to compile planetary catalogs.
When the IAU introduced TDT (TT) and TDB, in order to prevent a large difference between the two time systems, it was artificially stipulated that no long-term change items are allowed between the two time systems, but only periodic item. That is, there are only slight periodic changes between TT and TDB, but the "average clock speed" of the two time systems is the same within a cycle. Under the constraints specified above, the following relationship exists between TT and TDB:
TDB − TT = 0.001658 s sin M + 0.000014 s sin 2 M + ν e ⋅ ( x − x 0 ) c 2 \mathrm{TDB}- \mathrm{TT}=0.001658\mathrm{s} \sin M+0.000014 \mathrm{s} \sin 2M+\frac{\nu_e \cdot\left(\boldsymbol{x}-\boldsymbol{x}_0\right) }{c^2}TDB−TT=0.001658ssinM+0.000014ssin2 M+c2ne⋅(x−x0)
where, MMM is the mean anomaly angle when the earth revolves around the sun;ve v_eve, is the revolution velocity vector of the earth's barycenter in the barycentric coordinate system of the solar system; x 0 \boldsymbol{x}_0x0is the position quantity of the center of the earth in the barycentric coordinate system of the solar system; x \boldsymbol{x}x is the position vector of the ground clock in the barycentric coordinate system of the solar system;( x 0 − x ) \left(x_0-\boldsymbol{x}\right)(x0−x )is actually the position vector of the ground clock in the geocentric coordinate system;c \boldsymbol{c}c is the speed of light in vacuum.
There is actually a scale ratio between TT and TDB, that is to say, the length of 1 second in TT is not equal to the length of 1 second in TDB, and the relationship between the two is as follows: Δ TDB Δ TT
= 1 + LB \frac{\Delta \mathrm{TDB}}{\Delta \mathrm{TT}}=1+L_BΔTTΔTDB=1+LB
In the formula, LR = 1.55051976772 × 1 0 − 8 L_R=1.55051976772 \times 10^{-8}LR=1.55051976772×10−8 。
This means that in the earth-centered coordinate system and the barycentric coordinate system of the solar system, due to the difference in the moving speed of the coordinate system and the gravitational potential received, under the influence of the theory of relativity, the time units of TT and TDB actually contain a systematic scale ratio LB L_BLBHowever, in order not to allow too large a difference between the two time systems, the International Astronomical Union (IAU) artificially defined TDT (TT) and TDB so that no systematic time scale ratio exists between them. , and only allow the existence of periodic variation items (let the average time intervals be equal), in order to keep the speed of light ccc is constant, so there can only be a scale ratio between the length unit in the earth-centered coordinate system and the length unit in the barycentric coordinate system of the solar system, that is,
LTDH = LTT 1 − LB L_{\mathrm{TDH}}=\frac{L_ {\mathrm{TT}}}{1-L_B}LTDH=1−LBLTT
That is to say, 1 meter in the barycentric coordinate system of Taiyou system is longer than 1 meter in the earth-centered coordinate system.
6.3. TCG in geocentric coordinate time and TCB in solar system barycentric coordinate time
Since introducing TDT ( TT ) \mathrm{TDT}(\mathrm{TT})After TDT ( TT ) and TDB, many people raised objections, such as:
- How to interpret the word Dynamical:
- The IAU specifies that only small periodic variations between TDB and TDT(TT) are allowed. However, when the time period is short, it is difficult to strictly distinguish the periodic item from the long-term item, and the periodic item is also equivalent to the long-term item;
- In order to get rid of the long-term term between TDB and TDT, it is necessary to artificially introduce a scale ratio between the geocentric coordinate system and the barycentric coordinate system of the solar system, thus resulting in different astronomical constants in different coordinate systems, and also making Some concepts became vague, so in 1991, at the 21st IAU General Assembly, it was decided to introduce the geocentric coordinate time TCG and the solar system barycentric coordinate time TCB.
Geocentric coordinate time TCG is the fourth dimension coordinate used in the celestial coordinate system whose origin is located at the center of the earth: time coordinate. It is a time-like variable that transforms TDT from the geoid to geocentric time through relativity.
The solar system barycentric time TCB is the fourth dimensional coordinate in the solar system barycentric celestial coordinates. It is the time variable in the equations of motion used to calculate the motion of planets around the sun, and it is also an independent variable when compiling planetary catalogs.
In the time system, we usually refer to the time that can be directly determined by the standard clock as the original time. The original time can be directly measured with precise timing tools, such as atomic time. The time derived under the framework of the theory of relativity is called coordinate time or class time, such as TDB, TCG, TCB, etc. The coordinate time cannot be realized by measurement, but needs to be obtained indirectly through calculation according to the mathematical relation given by the space-time metric, and the space-time law can be obtained through the Einstein field equation. Below we directly give the relationship between TT and TCG without derivation:
TCG − TT = LG ( MJD − 43144.0 ) × 86400 s \text { TCG }-\mathrm{TT}=L_G(\mathrm{MJD}- 43144.0) \times 86400 \mathrm{~s} \quad TCG −TT=LG( M.J.D−43144.0)×86400 s
where, LG L_GLGis a constant, its value is equal to 6.969290134 × 1 0 − 10 6.969290134 \times 10^{-10}6.969290134×10−10 . _ The starting time of TT and TCG is defined as January 1, 1977 at0 h 0 \mathrm{~h}0 h , expressed as 2443144.5 2443144.5in Julian day2443144.5 days, expressed as 43144.0 43144.0with simplified Julian day MJD43144.0 , it is stipulated that TCG = TTat the starting time\mathrm{TCG}=\mathrm{TT}_{\text {. }}TCG=TT。 。
And there is the following relationship between TCB and TCG:
TCB − TCG = L c ( MJD − 43144.0 ) × 86400 s + 0.001658 s × sin M + 0.000014 s × sin 2 M + vec 2 ( x − x 0 ) \ begin{aligned} \mathrm{TCB}-\mathrm{TCG}=& L_c(\mathrm{MJD}-43144.0) \times 86400 \mathrm{~s}+0.001658 \mathrm{~s} \times \sin M \ \ &+0.000014 \mathrm{~s} \times \sin 2 M+\frac{v_e}{c^2}\left(\boldsymbol{x}-\boldsymbol{x}_0\right) \end{aligned}TCB−TCG=Lc( M.J.D−43144.0)×86400 s +0.001658 s×sinM+0.000014 s×sin2 M+c2ve(x−x0)
In the formula, L c = 1.48082686741 × 1 0 − 8 L_c=1.48082686741 \times 10^{-8}Lc=1.48082686741×10− 8 , the meanings of other symbols are the same as before.
The first term in the above formula is a long-term term, which will increase with the increase of the time interval. On September 4, 20070 h 0 \mathrm{~h}At 0 h , this item has reached14.3335 s 14.3335 \mathrm{~s}14.3335 s ; The second term is a periodic term related to time, the maximum value can reach0.001658 s 0.001658 \mathrm{~s}0.001658 s ; The third term is the periodic term related to the spatial position of the atomic clock, the maximum value is only2.1 μ s 2.1 \mu \mathrm{s}2.1μs 。
L 2 C , L 5 L_2 C , L_5 in GPSL2C 、L5The new navigation messages up-modulated will involve concepts such as TDT (TT), TDB, etc., but due to space limitations, this chapter will not introduce in detail the derivation of various time systems and mutual conversion relations established under the framework of the theory of relativity. Interested students Refer to relevant resolutions of the IAU and reference materials such as space geodesy.
7. Some long time timing methods involved in GPS
In GPS navigation and GPS measurement, some timing methods and timing units for measuring long-term intervals will also be encountered, such as year, month, day, Julian day, simplified Julian day, yearly cumulative day, etc. Some of them involve the calendar, some It is some terms in astronomy. Although strictly speaking, these contents are beyond the scope of the time system, but because they are often used, they are also introduced together.
7.1. Calendar
The calendar is a set of rules that stipulate the length of the year, month, and day and the relationship between them, and formulate a time sequence. Since the period of the earth's revolution around the sun and the period of the moon's revolution around the earth are not the number of days, but the length of the year and month stipulated in the calendar can only be the number of days, so it is necessary to have a suitable method to arrange them. At present, the calendars used in various countries mainly include the solar calendar, the lunar calendar and the lunar calendar.
(1) The Gregorian calendar (Solar Calendar),
also known as the Gregorian calendar, is based on the annual apparent movement of the sun. The time interval between the solar center passing through the vernal equinox twice is a tropical year, and its length is:
1 tropical year = 365.24218968 − 0.00000616 × t ( =365.24218968-0.00000616 \times t(=365.24218968−0.00000616×t ( day) ))
where,ttt is fromJ 2000.0 \mathrm{J} 2000.0The number of Julian centuries since J 2000.0
, that is , t = JD − 2451545.0 36525 t=\frac{\mathrm{JD}-2451545.0}{36525}t=36525JD−2451545.0
The length of the regression year corresponding to January 1, 2009 is 365.24218913 365.24218913365.24218913 days.
The Julian Calendar
The Julian Calendar is a Gregorian calendar established by the Roman Emperor Julius Caesar in 46 BC. The calendar divides the year into 12 months. Among them, 1 , 3 , 5 , 7 , 8 , 10 , 12 1 , 3 , 5 , 7 , 8 , 10 , 121 , 3 , 5 , 7 , 8 , 10 , 12 are big months, 31st of each month;4, 6, 9, 11 4, 6, 9, 11April , June , September and November are small months with 30 days in each month; February has 28 days in normal years and 29 days in leap years. A year that is divisible by 4 is considered a leap year, and a year that is not divisible by 4 is considered an ordinary year. According to the above stipulations, the length of an ordinary year is 365 days, and the length of a leap year is 366 days, and the average length is365.25 365.25365.25 days. A Julian century is 36525 days. In astronomy and space geodesy, when calculating some parameters that change very slowly, the Julian century is often used as the unit.
The Gregorian Calendar The Gregorian
calendar is the current Gregorian calendar and is widely adopted by countries all over the world. In order to make the average length of each year as consistent as possible with the length of the regression year, in 1582, Pope Gregory modified the regulations for setting leap years in the Julian calendar, stipulating that for century years, only centuries divisible by 400 year is a leap year. In this way, years such as 1700, 1800, and 1900 are all leap years in the Julian calendar, but they all become normal years in the Gregorian calendar, and 2000 is a leap year. Thus, every 400 years in the Gregorian calendar has 3 days less than the 400 years in the Julian calendar. That is, 400 years in the Julian calendar has 365.25 × 400 = 146100 365.25 \times 400=146100365.25×400=There are 146,100 days, and there are only 146,097 days in the 400 years of the Gregorian calendar. The average length of each year is365.2425 365.2425365.2425 days, which is closer to the length of the tropical year.
(2) The lunar calendar (Lunar Calendar)
The lunar calendar is a calendar formulated according to the change cycle of the moon phase (synodic month). The calendar stipulates that a single month has 30 days, a double month has 29 days, and the average of each month is 29.5 29.529.5 days, and the length of the synodic month29.53059 ⋯ 29.53059 \cdots29.53059 …The day is approaching. With the beginning of the new moon as the beginning of the month, 12 months make up a year, with a total of 354 days. And the length of 12 synodic months is354.36708 ⋯ 354.36708 \cdots354.36708⋯ Day, 0.36708 more than the lunar calendar⋯ 0.36708 \cdots0.36708... day. 30 years is11.0124 more than 11.012411.0124 days. Therefore, every 30 years in the lunar calendar, 11 lunar years should be set, and the2nd, 5th, 7th, 2nd, 5th, 7th,2、5、7、 10 、 13 、 16 、 18 、 21 、 24 、 26 、 29 10 、 13 、 16 、 18 、 21 、 24 、 26 、 29 Add one day to the end of December in 10 , 13 , 16 , 18 , 21 , 24 , 26 , and 29 , that is, there are 355 days in a leap year. The Hijri calendar used by Islamic countries is a lunar calendar.
(3) Luni-Solar Calendar (Luni-Solar Calendar)
The Luni-Solar Calendar is a calendar that takes into account the characteristics of both the Gregorian and Lunar calendars. The year in the Luni-Solar calendar is based on the return year, while the month is based on the synodic month. The day, the small month is 29 days, the average monthly is 29.5 29.529.5 days. In order to make the average length of the middle year of the lunar calendar close to the length of the tropical year, the calendar stipulates that 7 of every 19 years are leap years. One month added to a leap year is called a leap month. my country has used the lunar calendar for a long time, and adopted the solar calendar after 1912, but the lunar calendar was not abolished, and it is still widely used among the people, which is called the lunar calendar.
7.2. Julian day and simplified Julian day
(1) Julian Day (Julian Day, JD)
Julian Day is a long-term continuous calendar method that does not involve concepts such as year and month. It is often used in astronomy, space geodesy, and satellite navigation and positioning. This method was proposed by JJScaliger in 1583, named Julian Day in honor of his father Julian. This method is especially convenient when calculating the interval between two moments spanning many years. The starting point of the Julian day is 12h, January 1, 4713 BC, and it is added up day by day. In China's astronomical calendar, there is the Gregorian calendar in this year × × \times \times× × month× × \times \timesThe comparison table between × × day and Julian day is for users to check. In addition, users can also use the following formulas for calculation.
(1) Calculate the corresponding Julian day JD according to the year (Y), month (M) and day (D) of the Gregorian calendar Formula 1: JD
= 1721013.5 + 367 × Y − int { 7 4 [ Y + int ( M + 9 12 ) ] } + d + h 24 + int ( 275 × M 9 ) \begin{aligned} \mathrm{JD}=& 1721013.5+367 \times Y-\operatorname{int}\left\{\ frac{7}{4}\left[Y+\operatorname{int}\left(\frac{M+9}{12}\right)\right]\right\} \\ &+d+\frac{h}{ 24}+\operatorname{int}\left(\frac{275 \times \mathrm{M}}{9}\right) \end{aligned}JD=1721013.5+367×Y−int{
47[Y+int(12M+9)]}+d+24h+int(9275×M)
In the formula, constant 1721013.5 1721013.51721013.5 is January 1, 1 AD0 h 0 \mathrm{~h} Julian day at 0 h ; Y , M , DY , M , DY , M , D are the year, month, and day numbers in the Gregorian calendar,h \mathrm{h}h is the hour in universal time, and int is the rounding symbol.
公式 2:
J D = int ( 365.25 × y ) + int [ 30.6 + D + h 24 + 1720981.5 \begin{aligned} \mathrm{JD}=& \operatorname{int}(365.25 \times y)+\operatorname{int}[30.6\\ &+D+\frac{h}{24}+1720981.5 \end{aligned} JD=int(365.25×y)+int[30.6+D+24h+1720981.5
Current month number M > 2 M>2M>2 , there isy = Y , m = M y=Y, m=My=Y,m=M;
M ⩽ 2 M \leqslant 2 M⩽2 , there isy = Y − 1 , m = M + 12 y=Y-1, m=M+12y=Y−1,m=M+12 。
(2) 根据儒略日反求公历年 、月、日
a = int ( J D + 0.5 ) b = a + 1537 c = int [ b − 122.1 365.25 ] d = int ( 365.25 × c ) e = int ( b − d 30.600 ) D = b − d − int ( 30.6001 × e ) + FRAC ( J D + 0.5 ) M = e − 1 − 12 × int ( e 14 ) Y = c − 4715 − int ( 7 + M 10 ) \begin{aligned} &a =\operatorname{int}(\mathrm{JD}+0.5) \\ &b =a+1537 \\ &c =\operatorname{int}\left[\frac{b-122.1}{365.25}\right]\\ &d=\operatorname{int}(365.25 \times c) \\ &e=\operatorname{int}\left(\frac{b-d}{30.600}\right) \\ &D=b-d-\operatorname{int}(30.6001 \times e)+\operatorname{FRAC}(\mathrm{JD}+0.5) \\ &M=e-1-12 \times \operatorname{int}\left(\frac{e}{14}\right) \\ &Y=c-4715-\operatorname{int}\left(\frac{7+M}{10}\right) \end{aligned} a=int(JD+0.5)b=a+1537c=int[365.25b−122.1]d=int(365.25×c)e=int(30.600b−d)D=b−d−int(30.6001×e)+FRAC(JD+0.5)M=e−1−12×int(14e)Y=c−4715−int(107+M)
In the formula, the symbol FRAC ( a ) \mathrm{FRAC}(a)FRAC ( a ) means to take the valueaaThe fractional part of a .
The IAU decided to use J2000.0 (that is, Ruyi day 2451545.0 ) 2451545.0) in the calculation of precession, nutation, and compilation of celestial bodies and star catalogs from 19842451545.0 ) as the standard epoch. any timettThe time interval from t to the standard epoch is JD( t ) − 2451545.0 ( (t)-2451545.0((t)−2451545.0 ( day) )) . (2) Simplified Julian Day (Modified Julian Day, MJD) The starting point of Julian Day has been more than 67 centuries, and the current time expressed by Julian Day has a large value and is inconvenient to use. For this reason, in 1973, the IAU adopted a simpler continuous timekeeping method, the simplified Julian day. The relationship between it and the Julian day is:
MJD = JD − 2400000.5 \text { MJD }=\mathrm{JD}-2400000.5 MJD =JD−2400000.5
MJD is the midnight of November 17, 1858 ( JD= 2400000.5 =2400000.5=2400000.5 ) is a continuous timing method used as the starting point of timing. It is convenient to use MJD to indicate the most recent time.
(3) Annual accumulation day
Annual accumulation day is a continuous counting method used only in one year. Every year, January 1 is counted as day 1, February 1 is counted as day 32, and so on. December 31st in an ordinary year is the 365th day, and December 31st in a leap year is the 366th day. It can be used to easily calculate the two moments t 1 t_1 in one yeart1and t 2 t_2t2time interval between.
From: Chapter Two of "GPS Measurement and Data Processing".