# What direction does 0° in the J2000 epoch point towards on January 1, 2000?

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Is 0 degrees in the J2000 Epoch 'right ascension' is a line from Earth to the sun on January 1, 2000? Or is 0 degrees the direction towards the ascending node 'equinox'? Which is NOT towards the Sun on January first…

Or is 0 degrees the direction towards the ascending node 'equinox'? Which is NOT towards the Sun on January first…

The answer is yes, more or less. From JPL's HORIZONS, the location of the Sun at Noon Terrestrial Time on 1 Jan 2000 is, ignoring atmospheric effects, a right ascension of 18 hours, 45 minutes, and 9.36 seconds. This is nowhere close to a right ascension of zero hours (or 24 hours, same thing).

The right ascension of the Sun with respect to the center of the Earth is zero at the March equinox.

## What direction does 0° in the J2000 epoch point towards on January 1, 2000? - Astronomy

1. GEI: Geocentric Equatorial Inertial system. This system has X-axis pointing from the Earth toward the first point of Aries (the position of the Sun at the vernal equinox). This direction is the intersection of the Earth's equatorial plane and the ecliptic plane and thus the X-axis lies in both planes. The Z-axis is parallel to the rotation axis of the Earth, and y completes the right-handed orthogonal set (Y = Z * X). Geocentric Inertial (GCI) and Earth-Centered Inertial (ECI) are the same as GEI.

2. GEO: Geographic coordinate system. This system is defined so that its X-axis is in the Earth's equatorial plane but is fixed with the rotation of the Earth so that it passes through the Greenwich meridian (0 longitude). Its Z-axis is parallel to the rotation axis of the Earth, and its Y-axis completes a right handed orthogonal set (Y = Z * X).

3. GM: Geomagnetic coordinate system. Z-axis points to the Geomagnetic north pole (in Greenland). The positive X-axis points towards the great circle encompassing the North and South Geomagetic poles and lies in the geomagnetic equatorial plane in the segment that is in the western hemisphere. (The South GM pole is the antipode of the North GM pole.) Earth-centered Dipole is invoked. Y completes the triad.

4. GSE: Geocentric Solar Ecliptic system. This has its X-axis pointing from the Earth toward the Sun and its Y-axis is chosen to be in the ecliptic plane pointing towards dusk (thus opposing planetary motion). Its Z-axis is parallel to the ecliptic pole. Relative to an inertial system this system has a yearly rotation.

5. GSM: Geocentric Solar Magnetospheric system. This has its X-axis from the Earth to the Sun. The Y-axis is defined to be perpendicular to the Earth's magnetic dipole so that the X-Z plane contains the dipole axis. The positive Z-axis is chosen to be in the same sense as the northern magnetic pole. The difference between the GSM and GSE systems is simply a rotation about the X-axis.

6. SM: Solar Magnetic coordinates. In this system, the Z-axis is chosen parallel to the north magnetic pole and the Y-axis perpendicular to the Earth-Sun line towards dusk. The difference between this system and the GSM system is a rotation about the Y-axis. The amount of rotation is simply the dipole tilt angle. We note that in this system the X-axis does not point directly at the Sun. As with the GSM system, the SM system rotates with both a yearly and daily period with respect to inertial coordinates.

7. Invariant Latitude: For any point in space one can trace a B-field line to the Earth surface, assuming it is a centered dipole field. The GM latitude of this foot point is labelled as the Invariant Latitude along the entire field line. The dipole L-value is closely related to this invariant latitude L=1/(Cos(Lat))^2, and physically connotes the distance (in Earth radii) of the "top of the field line" from Earth center.

8. J2000: Geocentric Equatorial Inertial for epoch J2000.0 (GEI2000), also known as Mean Equator and Mean Equinox of J2000.0 (Julian date 2451545.0 TT (Terrestrial Time), or 2000 January 1 noon TT, or 2000 January 1 11:59:27.816 TAI or 2000 January 1 11:58:55.816 UTC.) This system has X-axis aligned with the mean equinox for epoch J2000 Z-axis is parallel to the rotation axis of the Earth, and Y completes the right-handed orthogonal set.

## Equinox and Epoch

The word epoch denotes a particular point in time. In this sense the word has the same meaning in astronomy as it has in day-to-day life. For example, epoch J2000 means the time corresponding to the Julian date 2451545.0 in the concerned time system. In the Gregorian calendar this is 2000/1/1 12:00:00.

If we record the coordinates of a comet on 2011/11/11 11:11:11 UTC in the Gregorian calendar, then the epoch of the coordinates is 2011/11/11 11:11:11 UTC, or equivalently the Julian date 2455876.966099537 UTC. At a different time i.e., epoch, say 2011/11/11 22:22:22, the comet would have moved some distance and will have a different set of coordinates.

Due to precession the reference point for celestial coordinates, the vernal equinox, is continuously changing. So when specifying coordinates of a body we need to specify the location of the vernal equinox, which then fixes the orientation of the coordinate system. We do this by mentioning that the coordinate system is defined by the location of the vernal equinox at a particular time. This time i.e., epoch is referred to as the equinox of the coordinates.

In catalogs, we usually find entries such as (RA, DE) equinox J2000 epoch J2000. This means that the given (RA, DE) is the coordinate of the star at the time J2000 (epoch J2000), in the coordinate system defined by the vernal equinox at the time J2000 (equinox J2000).

If the star has proper motion, then we need to apply proper motion from J2000 to the epoch of interest to get the position of the star at this time. If the epoch of interest is 2010/10/10, then the epoch of the coordinates after applying proper motion from J2000 to 2010/10/10, is 2010/10/10, but its equinox remains at J2000.

Going back to the example of the comet, assume that the coordinates were measured using the known equinox J2000 positions of stars in an image. In this situation, the equinox of the comet’s coordinates is J2000, but its epoch is the time of observation i.e., 2011/11/11 11:11:11.

Suppose we want to point a telescope at the comet, at the time 2011/11/11 12:00:00. Then we need to take the coordinates at equinox J2000 epoch 2011/11/11 11:11:11, apply proper motion to find the coordinates at equinox J2000 epoch 2011:11:11 12:00:00, then precess the equinox from J2000 to 2011:11:11 12:00:00 to get the position at equinox 2011/11/11 12:00:00 epoch 2011/11/11 12:00:00, and then convert (RA, DE) to (Azimuth, Elevation).

To flog a dead horse, we precess from one equinox to the next but we apply proper motion from one epoch to the next.

The modern celestial coordinate system, ICRS, does not refer to the vernal equinox, and its reference axes are fixed in space. Due to this coordinates in the ICRS system do not have an associated equinox. They only have an epoch.

## Standard epoch

Standard epoch: a date and time that specifies the reference system to which celestial coordinates are referred. Prior to 1984 coordinates of star catalogs were commonly referred to the mean equator and equinox of the beginning of a Besselian year (see year, Besselian).

standard epoch Particular date and time chosen as a reference point against which to measure astronomical data in order to remove the effects of precession, proper motion and gravitational perturbation. The standard epoch currently in use is called 2000.

The standard epoch in use today is Julian epoch J2000.0. It is exactly 12:00 TT (close to but not exactly Greenwich mean noon) on January 1, 2000 in the Gregorian (not Julian) calendar. Julian within its name indicates that other Julian epochs can be a number of Julian years of 365.25 days each before or after J2000.0.

The root mean square deviation from the arithmetic mean. [H76]

of observation for the catalog. The catalog data is most precise for this date, and becomes gradually less precise for dates in the past and future. Note that ALL THE POSITIONS ARE STILL IN THE J2000 COORDINATE SYSTEM.

Due to precession, this point moves over time, so positions of stars in catalogues and on atlases are usually referred to a "mean equator and equinox" of a specified

Right Ascension (RA) in hours and minutes, and Declination (DEC) in degrees and minutes, are given for the current

J2000.0, now used for new star-position catalogues and in solar-system-orbital calculations, means 2000 Jan. 1.5 Barycentric Dynamical Time (TDB) = Julian Date 2451545.0 TDB. When this dynamical, artificial "Julian year" is employed, a letter "J" prefixes the year.

declination of every star changes gradually, as the entire reference system rotates. For this reason, when citing the coordinates of a star, it is essential to specify the instant in time for which they are valid. This is known as the epoch of the coordinates. Star catalogues are usually compiled for a

basis"a small angle, but one that nevertheless must be taken into account in high-precision astronomical measurements. Rather than deal with slowly changing coordinates for every object in the sky, astronomers conventionally correct their observations to the location of the vernal equinox at some

## Geocentric systems

The following coordinate systems at the centre of the Earth.

## 1. Systems based on the Earth's rotation axis

#### 1.1 Geographic (GEO)

This system has its Z axis parallel to the Earth's rotation axis (positive to the North) and its X axis towards the intersection of the Equator and the Greenwich Meridian. Thus it is convenient for specifying the location of ground stations and ground-based experiments as these are fixed quantities in the GEO system.

A note of warning. When GEO coordinates are expressed in spherical form, the latitude component is identical what is termed geocentric latitude by astronomers and geographers. However, note that this is different to the system of geodetic latitude used in normal map-making. The geodetic latitude at any location is the angle between the equatorial plane and the local normal to the Earth's surface. In general that normal is NOT parallel to a radius vector because the shape of the Earth is an oblate spheroid and not a sphere.

#### 1.2 Geocentric equatorial inertial (GEI)

This system has its Z axis parallel to the Earth's rotation axis (positive to the North) and its X axis towards the First Point of Aries (the direction in space defined by the intersection between the Earth's equatorial plane and the plane of its orbit around the Sun (the plane of the ecliptic). This system is (to first order) fixed with respect to the distant stars. It is convenient for specifying the orbits (and hence location) of Earth-orbiting spacecraft as one can specify a Keplerian orbit in this frame.

However note that the GEI system is subject to second order change with time owing to the various slow motions of the Earth's rotation axis with respect to the fixed stars. Thus for GEI coordinates one must specify the date (normally termed the epoch ) to which the coordinate system applies. For space physics work one should use the epoch-of-date GEI system, i.e. the system applying at the same time as the data were taken. (Thus the rotation axis in GEI is identical with the GEO rotation axis.) On these pages the unqualified acronym GEI refers to the epoch-of-date system. See Hapgood (1995) for a more detailed discussion of this issue.

#### 1.3 Geocentric equatorial inertial for epoch J2000.0 (GEI 2000 )

Spacecraft orbits and locations are often made available in geocentric equatorial inertial coordinates for a fixed epoch, e.g. the standard astronomical epoch known as J2000.0 , which is 12:00 UT on 1 January 2000. We treat this as a separate coordinate system (with the qualified acronym GEI 2000 ) and specify how to transform from this to other systems.

## 2. Systems based on the Earth-Sun line

#### 2.1 Geocentric solar ecliptic (GSE)

This system has its X axis towards the Sun and its Z axis perpendicular to the plane of the Earth's orbit around the Sun (positive North). This system is fixed with respect to the Earth-Sun line. It is convenient for specifying magnetospheric boundaries. It has also been widely adopted as the system for representing vector quantities in space physics databases.

#### 2.2 Geocentric solar magnetospheric (GSM)

This system has its X axis towards the Sun and its Z axis is the projection of the Earth's magnetic dipole axis (positive North) on to the plane perpendicular to the X axis. The direction of the geomagnetic field near the nose of the magnetosphere is well-ordered by this system. Thus it is considered the best system to use when studying the effects of interplanetary magnetic field components (e.g. B z ) on magnetospheric and ionospheric phenomena.

## 3. Systems based on the dipole axis of the Earth's magnetic field

#### 3.1 Solar magnetic (SM)

This system has its Z axis parallel to the Earth's magnetic dipole axis (positive North) and its Y axis perpendicular to the plane containing the dipole axis and the Earth-Sun line (positive in direction opposite to the Earth's orbital motion). The direction of the geomagnetic field in the outer magnetosphere is well-ordered by this system. It is the preferred system for defining magnetic local time in the outer magnetosphere.

#### 3.2 Geomagnetic (MAG)

This system has its Z axis parallel to the Earth's magnetic dipole axis (positive North) and its Y axis is the intersection between the Earth's equator and the geographic meridian 90 degrees east of the meridan containing the dipole axis.

J2000_Ecliptic. The mean ecliptic system evaluated at the J2000 epoch. The mean ecliptic plane is defined as the rotation of the J2000 XY plane about the J2000 X axis by the mean obliquity defined using FK5 IAU76 theory. In the Vector Geometry Tool, this system is listed as SunMeanEclpJ200.

TrueEclipticOfDate. The true ecliptic system, evaluated at each given time. The true ecliptic plane is defined as the rotation of the J2000 XY plane about the J2000 X axis by the true obliquity defined using FK5 IAU76 theory.

## Appendix A. Background Material

The Toolkit directly supports three time systems. They are

1. Coordinated Universal Time (UTC)

2. Barycentric Dynamical Time (TDB) also called Ephemeris Time (ET)

3. Spacecraft Clock Time (SCLK---pronounced ess clock'')

## Coordinated Universal Time (UTC)

### International Atomic Time (TAI)

Before discussing Coordinated Universal Time we feel it is helpful to talk about International Atomic Time (TAI or atomic time). Atomic time is based upon the atomic second as defined by the oscillation of the undisturbed cesium atom.'' Atomic time is simply a count of atomic seconds that have occurred since the astronomically determined instant of midnight January 1, 1958 00:00:00 at the Royal Observatory in Greenwich, England. Atomic time is kept by the International Earth Rotation Service (IERS, formally the Bureau International L'Heure---BIH) in Paris, France. The National Bureau of Standards and the U.S. Naval Observatory set their clocks by the clock maintained by the IERS.

### Naming the seconds of TAI --- UTC

Coordinated Universal Time is a system of time keeping that gives a name to each instant of time of the TAI system. These names are formed from the calendar date and time of day that we use in our daily affairs. They consist of 6 components: year, month, day, hour, minutes and seconds. The year, month and day components are the normal calendar year month and day that appear on wall calendars. The hours component may assume any value from 0 through 23. The minutes component may assume any value from 0 to 59. The seconds will usually (but not always) range from 0 to 59.999. . The hour-minute-second string

is midnight and is the first instant of the calendar day specified by the first three components of the UTC time.

In the SPICE system UTC times are represented by character strings. These strings contain: year, month, day, hour, minute and second separated by delimiters (spaces or punctuation marks). The various delimiters and substrings between the delimiters are called the tokens of the string. A typical time string looks like

The tokens of the string and the associated UTC time components are

The link between any token and its corresponding UTC component is determined by examining the values of the tokens and comparing them to the other tokens. The precise rules used are spelled out in great detail in Appendix B. For now, simply be assured that the following five strings all mean the same thing and are interpreted in the same way by SPICE Toolkit software.

### Tying UTC to the Earth's Rotation

The names given to TAI instants by the UTC system are governed by the earth's rotation. Ideally, UTC strings having hours, minutes and seconds components all zero should correspond to Greenwich midnight as determined by the observations of the transits of stars (the time system known as UT1). However, since the rotation of the earth is not uniform, this ideal cannot be realized. The difference between Greenwich midnight observed astronomically and UTC midnight is almost never zero. However, to keep the difference from becoming too large, UTC is occasionally adjusted so that the difference between the two midnights never exceeds .9 seconds. Thus from a knowledge of UTC one can always compute UT1 to better than 1 second accuracy.

### Leapseconds

When Greenwich UT1 midnight lags behind UTC midnight by more than 0.9 seconds the IERS will announce that a leap second will be added to the collection of UTC names. This leap second has traditionally been added after the last normal'' UTC name of December 31 or June 30. Thus when a UTC second is added the hours-minutes-seconds portion of the UTC name progresses as shown here

Should Greenwich UT1 midnight run ahead of UTC midnight by more than 0.9 seconds the IERS will announce a negative leap second. In this case one of the usual UTC hours-minutes-seconds triples will be missing from the list of UTC names. In this case the progression will be:

Since 1972 when leap seconds and the UTC system were introduced, a negative leap second has not occurred.

### The Leapseconds Kernel (LSK)

The primary difficulty with UTC strings is that it is not possible to predict which atomic times will correspond to times during a UTC leap second. Thus algorithms for converting between UTC and time systems that simply use a continuous set of numeric markers require knowledge of the location of leap seconds in the list of names. This is the purpose of the LEAPSECONDS kernel supplied with the Toolkit. To convert between UTC times and any other system, you must first load the leapseconds kernel via a call to the routine FURNSH.

LSK files conform to a flexible format called NAIF text kernel'' format. The SPICE file identification word provided by itself on the first line of an LSK file is KPL/LSK''. Both the NAIF text kernel format and SPICE file identification word are described in detail in the Kernel Required Reading document, kernel.req.

## Ephemeris Time (ET)

Ephemeris time is the uniform time scale represented by the independent variable in the differential equations that describe the motions of the planets, sun and moon. There are two forms of ephemeris time: Barycentric Dynamical Time (TDB) and Terrestrial Dynamical Time (TDT). Although they represent different time systems, these time systems are closely related.

### Barycentric Dynamical Time (TDB)

Barycentric dynamical time is used when describing the motion of bodies with respect to the solar system barycenter.

### Terrestrial Dynamical Time (TDT)

Terrestrial dynamical time is used when describing motions of objects near the earth. As far as measurements have been able to detect, TDT and TAI change at the same rate. Thus the difference between TDT and TAI is a constant. It is defined to be 32.184 seconds. At the zero point of TAI, TDT has a value of 32.184.

### The Relationship between TDT and TDB

TDB is believed to be in agreement with the time that would be kept by an atomic clock located at the solar system barycenter. A comparison of the times kept by a clock at the solar system barycenter with a TDB clock on earth would reveal that the two clocks are in close agreement but that they run at different rates at different times of the year. This is due to relativistic effects.

At some times in the year the TDT clock appears to run fast when compared to the TDB clock, at other times of the year it appears to run slow. Let TDB0 be some fixed epoch on the TDB clock and TDT0 be a fixed epoch on the TDT clock (TDB0 and TDT0 do not necessarily have to be the same epoch). Any epoch, EPOCH, can be represented in the following ways: as the number of seconds TDB(EPOCH), that have elapsed since TDB0 on the TDB clock or as the number of seconds, TDT(EPOCH), that have elapsed since TDT0 on the TDT clock. If we plot the differences TDB(EPOCH) - TDT(EPOCH) against TDB(EPOCH) over all epochs, we will find that the graph is very close to a periodic function.

In SPICE the difference between TDT and TDB is computed as follows:

where K is a constant, and E is the eccentric anomaly of the heliocentric orbit of the Earth-Moon barycenter. This difference, which ignores small-period fluctuations, is accurate to about 0.000030 seconds. Thus to five decimal places the difference between TDT and TDB is a periodic function with magnitude approximately 0.001658 seconds and period equal to one sidereal year.

The eccentric anomaly E is given by

where EB and M are the eccentricity and mean anomaly of the heliocentric orbit of the Earth-Moon barycenter. The mean anomaly is in turn given by

where t is the epoch TDB expressed in barycentric dynamical seconds past the epoch of J2000.

The values K, EB, M0, and M1 are retrieved from the kernel pool. These are part of the leapseconds kernel. They correspond to the kernel pool variables'' DELTET/K, DELTET/EB, and DELTET/M. The nominal values are:

### In the Toolkit ET Means TDB

When ephemeris time is called for by Toolkit routines, TDB is the implied time system. Software that converts between the various time systems described here use TDB whenever ephemeris time is called for. We call this time ET. (You can convert a UTC time string to TDT times, but you must make two subroutine calls instead of one.)

Ephemeris time is given in terms of seconds past a reference epoch. The reference epoch used throughout the Toolkit is the epoch J2000 (roughly noon on January 1, 2000). Using the Toolkit software, you can find out how many seconds the J2000 epoch is from right now.

## Naming the Seconds of Ephemeris Time

Although ephemeris time is a formal time, within the limits of measurements it coincides with atomic time. As such we should be able to relate it to the expressions of time that we use everyday.

However, ephemeris time is described as a count of ephemeris seconds past the ephemeris reference epoch (J2000). For most of us the expression

bears little relationship to the time system we use to organize our lives. For this reason, it is common to give names to the various ephemeris seconds in a manner analogous to the UTC naming of the seconds of TAI---as a calendar date and time of day. The above string corresponds to

There is an important distinction between the names given to ephemeris seconds and the names used by the UTC system. The names assigned to ephemeris times never have leap seconds. The seconds' component of the name is restricted to and includes all values from 0 to 59.999. . Thus the time string above does not represent the same moment in time as does 1990 FEB 1 21:44:11 (UTC)'' There are two reasons. First, ephemeris time is ahead of atomic time by 32.184 seconds. Second, when a leap second occurs UTC strings fit an extra name into the sequence of valid UTC names. Thus it appears that UTC names fall behind ET names by a second after each leapsecond. At the present time UTC time strings appear to be 62.184 seconds behind ET time strings. This appearance is due to the fact that the two naming conventions are not the same. They simply have a lot of names in common.

It is both fortunate and unfortunate that there is a huge set of common names between calendar dates ET and calendar dates UTC. Since there are relatively few leapseconds, a time given by an ET name is always close to the time in the UTC system having the same name. Thus for planning observations, you can know what day the observation will take place, whether or not you are likely to need a coat and how to arrange your daily activities around the observation. But for precise work you must pay attention to the difference between the two times systems. If in planning the observation of a stellar occultation by an asteroid the difference between the two naming systems is neglected, it is likely that the observation will be missed.

The routine STR2ET will convert an ephemeris calendar date to seconds past the ephemeris epoch J2000.

### Some Consequences of Leapseconds

There is no way of predicting when future leapseconds will occur. Normally you can predict whether there will be a leapsecond in the next few months, but beyond this predictions of leapseconds are not reliable. As a result we cannot say with certainty when a particular future UTC epoch will occur. For example, suppose you have a timer that you can set to beep'' after some number of seconds have passed. If this timer counts seconds perfectly without loosing or gaining time over decades, you cannot set it today to beep at midnight (00:00:00) January 1 (UTC) ten years from now---the number of leapseconds that will occur in the next ten years is not known. On the other hand, it is possible to set the timer so that it will beep at midnight January 1 (TDB). The TDB system does not have leapseconds. It is only necessary to know an algorithm (such as STR2ET) for converting calendar epochs TDB to seconds past some reference epoch in order to determine how to set the timer to beep at the correct epoch.

Any given Leapseconds Kernel will eventually become obsolete. Sometime after the creation of any Leapseconds Kernel there will be new leapseconds. When future leapseconds occur the old Leapseconds Kernel will no longer correctly describe the relationship between UTC, TDT and TDB for epochs that follow the new leapsecond. However, for epochs prior to the new leapsecond, the old kernel will always correctly describe the relationship between UTC, TDT and TDB.

## Computing UTC from TDB (DELTET)

Below are a few epochs printed out in calendar format in both the TDT and UTC time systems.

At least in October 1996, it's clear that if you have either TDT or UTC you can construct the corresponding representation for the same epoch in the UTC or TDT system by simply subtracting or adding 62.184 seconds.

If you don't worry about what happens during a leapsecond you can express the above idea as:

For all epochs except during UTC leapseconds the above expression makes sense. DeltaTDT is simply a step function increasing by one after each leapsecond. Thus DeltaTDT can be viewed as a step function of either UTC or TDT.

If you rearrange this expression, you can get

Since, TDT can be expressed as seconds past J2000 (TDT), the above expression indicates the UTC can be expressed as some count of seconds. This representation is referred to by the dubious name of UTC seconds past J2000.'' If you write down the UTC calendar time string corresponding to an epoch and count the number of seconds between that calendar expression and the UTC calendar expression January 1, 2000 12:00:00'' and ignore leapseconds, you get the value of UTC in the expression above.

In practice this expression is broken down as follows:

The value DeltaTA is a constant, its value is nominally 32.184 seconds. DeltaTA is a step function. These two variables appear in the leapseconds kernel.

If we combine equation [6] above with equation [1] from the section The Relationship between TDT and TDB'' we get the following expression

This last value is called DeltaET and is computed by the SPICE routine DELTET. The various values that are used in the computation of DeltaET are contained in the Leapseconds Kernel. Indeed, a Leapseconds Kernel consists of precisely the information needed to compute DeltaET. Below is a sample Leapseconds kernel.

Although NAIF recommends against it, you could modify this file to alter the conversion. For example, until 1985 JPL's Orbit Determination Program (ODP) set used a value of 32.1843817 for DeltaTA, and some older CRS tapes were created using this value in the conversion from TAI to TDT. The value returned by DELTET can be made compatible with these tapes by replacing the current value (32.184, exactly) with the older value. Also, JPL'S Optical Navigation Program (ONP) set does not use the periodic term (K sin E) of the difference TDB-TDT. Setting the value of K to zero eliminates this term.

### Problems With the Formulation of DeltaET

As we pointed out above, the expression ( TDT - UTC ) is meaningful as long as you stay away from leapseconds. If you write down the TDT and UTC representations for an epoch that occurs during a leapsecond you will have something like this:

Given these two epochs, it is no longer clear what we should assign to the value TDT - UTC. Thus although equation [7] above provides a simple expression for computing the difference between UTC and TDB'', the expression fails to tell us how to convert between TDB (or TDT) and UTC during leapseconds. For this reason the SPICE system does not use DeltaET when converting between TDB (or TDT) and UTC. Instead, the table of offsets corresponding to DeltaAT in the leapseconds kernel is converted to an equivalent table as shown below.

where the day number associated with a particular calendar date is the integer number of days that have passed since Jan 01, 0001 A.D. (on the extended Gregorian Calendar).

Given an epoch to be converted between UTC and some other time system (call this other system S'), we decompose the conversion problem into two parts:

1. converting between UTC and TAI,

2. converting between TAI and system S.

To convert between TAI and UTC, we examine the above table to determine whether or not the epoch in question falls on a day containing a leapsecond or during a day that is 86400 seconds in length. Once the length of the day associated with the epoch has been determined, the conversion from UTC to TAI (or from TAI to UTC) is straight forward. (See the routine TTRANS for details.) Having settled the problem of converting between TAI and UTC, the conversion between TAI and system S is carried out using the analytic expressions (equations [1], [2] and [3]) given above.

## Spacecraft Clock (SCLK)

Most spacecraft have an onboard clock. This clock controls the times at which various actions are performed by the spacecraft and its science instruments. Observations are usually tagged with the spacecraft clock time when the observations are taken.

Each spacecraft clock can be constructed differently. For Galileo the SPICE spacecraft clock times looks like

When asking for the matrix which describes the pointing for some structure or instrument used to perform an observation, you will usually request this information by supplying the spacecraft clock string that was used to tag the observation. This string must usually be related to UTC or ET. Consequently it is necessary to load a file of spacecraft clock coefficients'' that enables SPICE software to transform the spacecraft clock string into one of the other time systems. This file of spacecraft clock coefficients is loaded with the routine FURNSH.

A more detailed discussion of Spacecraft Clock is contained in the Required Reading file sclk.req that is included with the SPICE Toolkit.

## Julian Date

The Julian date system is a numerical time system that allows you to easily compute the number of days between two epochs. NAIF recognizes two types of Julian dates. Julian Ephemeris Date (JED) and Julian Date UTC (JDUTC). As with calendar dates used for ephemeris time and calendar dates UTC, the distinction between the two systems is important. The names of the two systems overlap, but they correspond to different moments of time.

Julian Ephemeris Date is computed directly from ET via the formula

where J2000 is a constant function that returns the Julian Ephemeris Date of the reference epoch for ET, and SPD is a constant function that gives the number or seconds per day.

Julian Date UTC has an integer value whenever the corresponding UTC time is noon.

We recommend against using the JDUTC system as it provides no mechanism for talking about events that might occur during a leapsecond. All of the other time systems discussed can be used to refer to events occurring during a leap second.

### The abbreviation JD

Julian date is often abbreviated as JD.'' Unfortunately, the meaning of this string depends upon context. For example, the SPICE routine UTC2ET treats the string 2451821.1928 JD'' as Julian Date UTC. On the other hand, the SPICE routine TPARSE treats the same string as Julian Date TDB. Consequently, for high accuracy work, you must be sure of the context when using strings labeled in this way. Unless context is clear, it's usually safer to label Julian Date strings with one of the unambiguous labels: JDUTC, JDTDB, or JDTDT.

## Data Provider Groups

Data can be requested in a variety of coordinate systems, where the origin of the coordinate system is the object's central body. The available coordinate systems depend on the object's central body. Nominally, the systems Fixed, Inertial, J2000, TrueOfDate, and MeanOfDate are supported, although some central bodies (notably the Earth and Sun) have more.

The following lists the systems available for Earth.

NameDescription
ICRFInternational Celestial Reference Frame. The ICRF axes are defined as the inertial (i.e., kinematically non-rotating) axes associated with a general relativity frame centered at the solar system barycenter (often called the BCRF).
MeanOfDateThe mean equator mean equinox coordinate system evaluated at the requested time.
MeanOfEpochThe mean equator mean equinox coordinate system evaluated at the epoch of the object.
TrueOfDateThe true equator true equinox coordinate system evaluated at the requested time.
TrueOfEpochThe true equator true equinox coordinate system evaluated at the epoch of the object.
B1950The mean equator mean equinox coordinate system evaluated at the beginning of the Besselian year 1950 (31 December 1949 22:09:46.866 = JD 2433282.4234591).
TEMEOfEpochThe true equator mean equinox coordinate system evaluated at the epoch of the object.
TEMEOfDateThe true equator mean equinox coordinate system evaluated at the requested time.
AlignmentAtEpochThe non-rotating coordinate system coincident with the Fixed system evaluated at the object's coordinate reference epoch.
J2000The mean equator mean equinox coordinate system evaluated at the J2000.0 epoch (2000 January 1.5 TDB = JD 2451545.0 TDB).

## What direction does 0° in the J2000 epoch point towards on January 1, 2000? - Astronomy

The following conventions apply to facilitate the coordination of science planning, expedite the exchange of data between different instrument teams, and enhance the overall science activities.

The SOHO On Board Time (OBT) will use the CCSDS format, level 1 (TAI reference, 1958 January 1 epoch), as discussed in section 3.3.9 of the SOHO Experiment Interface Document Part A (Issue 1). The SOHO OBT is an unsegmented time code with a basic time equal to 1 second and a value representing the number of seconds from 1 January 1958 based on International Atomic Time. The OBT Pulse is adjusted to maintain the OBT within 20ms of the ground TAI.

The SOHO OBT is used to time tag the data packets sent to the EOF and to the Data Distribution Facility (DDF). The time tags for the spacecraft and instrument housekeeping packets are generated by the spacecraft on-board data handling system. The time tags for the instrument science data packets are inserted by the instruments generating the science data. The time tags will be provided in 6 bytes the first 4 bytes are TAI seconds (2 to 2 seconds) and the last 2 bytes are fractions of a second with the resolution of the On Board Time Pulse (2 seconds).

The SOHO Daily Pulse is generated every 86,400 seconds, and is synchronized to the TAI with an accuracy better than 100ms. The Daily Pulse will correspond to the beginning of a TAI day'', that is the Daily Pulse will occur at the zeros of TAI modulo 86,400. As of 1 January 1993, the difference between TAI midnight and 00:00 UTC was 27 seconds. Since July 1 1993 UTC-TAI = --28sec (TBC).

The helioseismology experiments plan to center one minute observations on the TAI minute, that is where TAI modulo 60 is zero.

Coordinated Universal Time (UTC) will be used as the operational time reference in the Experiment Operations Facility. The SOHO operations day'' is defined to begin at 00:00 UTC and the computer systems in the SMOCC and EOF will be synchronized to run on UTC.

The solar rotation axis will be calculated using the Carrington ephemeris elements. These elements define the inclination of the solar equator to the ecliptic as 7.25 degrees, and the longitude of the ascending node of the solar equator on the ecliptic as , where T is the time in years from J2000.0.

The solar rotation axis used for alignment of the SOHO spacecraft will be determined from the Carrington ephemeris elements. The Experiment Interface Document Part A (Issue 1, Rev 3) lists the longitude of the ascending node of the solar equator as 75.62 and the position of the pole of the solar equator in celestial coordinates as 286.11 right ascension and 63.85 declination. This definition is consistent with a solar rotation axis determined from the Carrington elements for a date of 1 January 1990. As mentioned in the EID Part A, this information must be updated for the actual launch date.

Heliographic longitudes on the surface of the Sun are measured from the ascending node of the solar equator on the ecliptic on 1 January 1854, Greenwich mean noon, and are reckoned from 0 to 360 in the direction of rotation. Carrington rotations are reckoned from 9 November 1853, 00:00 UT with a mean sidereal period of 25.38 days, and are designated as CR etc..

The spacecraft optical axes are defined with respect to the optical alignment cube of the Fine Pointing Sun Sensor, with the optical X axis (X ) nominally perpendicular to the spacecraft launcher separation plane and pointing from the separation ring through the spacecraft. The spacecraft optical Y axis (Y ) is along the direction of the solar panel extension with positive Y pointing from the interior of the spacecraft towards the UVCS instrument.

The orientation of the SOHO spacecraft is planned to have the spacecraft optical X axis (X ) pointing towards the photometric center of the Sun, and the spacecraft optical Z axis (Z ) oriented towards the north ecliptic hemisphere such that the (X ,Z ) plane contains the Sun axis of rotation. As such the Y axis will be parallel to the solar equatorial plane pointing towards the east (opposite to the solar rotation direction). ESA will be responsible for achieving this orientation with the misalignment margins defined in the EID-A.

A standard coordinate system is required for joint observations between instruments on the ground (for test purposes) and in space. This system, designated (X ,Y ), will be defined as follows: On the ground, the Y axis is parallel to the spacecraft Z axis and the X axis is anti-parallel to the spacecraft Y axis. In space, the (Y ,Z ) system is however no longer accessible. We will therefore define a virtual system (Y ,Z ), which is nominally coincident with (Y ,Z ) and where Y is perfectly aligned with the solar equator and its origin is at the Sun centre, and define (X ,Y ) in space as above using the virtual system (Y ,Z ).

The inter-instrument flag system (X ,Y ) thus has its origin at the Sun centre, its Y axis is in the plane containing the solar rotation axis pointing north, and its X axis positive towards the west limb. Each instrument participating in the flag exchange is reponsible for determining its orientation with respect to the (X ,Y ) system and report the coordinates of their observations in (X ,Y ) coordinates in units of 2 arcsec. Off-limb observations need special treatment if X , Y >1022''.

The Orbit data will describe the position and motion of the spacecraft, and it will be available in several coordinate systems including: geocentric inertial (GCI) coordinates for the J2000 system geocentric solar ecliptic (GSE) geocentric solar magnetospheric (GSM) coordinates and Heliocentric Ecliptic coordinate system.

The GSE coordinate system is defined as follows: The origin is Earth centered, with the X axis pointing from the center of the Earth to the center of the Sun the Y axis lies in the ecliptic plane and points in the opposite direction of the Earth's orbital motion the Z axis completes a right-handed orthogonal coordinate system and is parallel to the ecliptic pole. The Sun position is the true instantaneous'' position rather than the apparent'' (light-time delayed or aberrated) position. The ecliptic is the true ecliptic of date.

The Heliocentric Ecliptic coordinate system is defined as follows: the origin is Sun centered, with the Z axis parallel to the ecliptic pole with positive north of the ecliptic plane the X-Y plane lies in the ecliptic plane and the X axis points towards the first point of Aries the Y axis completes a right-handed orthogonal coordinate system.

The GCI coordinate system is defined as follows: Earth centered, where the X axis points from the Earth towards the first point of Aries (the position of the Sun at the vernal equinox). This direction is the intersection of the Earth's equatorial plane and the ecliptic plane --- thus the X axis lies in both planes. The Z axis is parallel to the rotation axis of the Earth and the Y axis completes a right-handed orthogonal coordinate system. As mentioned above, the X axis is the direction of the mean vernal equinox of J2000. The Z axis is also defined as being normal to the mean Earth equator of J2000.

The GSM coordinate system is defined as follows: again this system is Earth centered and has its X axis pointing from the Earth towards the Sun. The positive Z axis is perpendicular to the X axis and paralle to the projection of the negative dipole moment on a plane perpendicular to the X axis (the northern magnetic pole is in the same hemisphere as the tail of the magnetic moment vector). Again this is a right-handed orthogonal coordinate system.

## Epoch & Unix Timestamp Conversion Tools

The unix time stamp is a way to track time as a running total of seconds. This count starts at the Unix Epoch on January 1st, 1970 at UTC. Therefore, the unix time stamp is merely the number of seconds between a particular date and the Unix Epoch. It should also be pointed out (thanks to the comments from visitors to this site) that this point in time technically does not change no matter where you are located on the globe. This is very useful to computer systems for tracking and sorting dated information in dynamic and distributed applications both online and client side.