A Time Tutorial

This chapter aims at collecting brief definitions of the various time systems in use, as well as simple formulae for doing transformations. Information was gleaned from a number of sources, like the *Explanatory Supplement to the Astronomical Ephemeris (1992)*, a paper by Soffel and Brumberg in *Celestial Mechanics and Dynamical Astronomy 52, 355 (1991)*, and several papers in the

The last section describes the time as it is kept in the *Chandra* FITS tables.
Information is available on absolute time calibration.

See also the USNO Time Scales page.

**TAI (International Atomic Time):**Based on the SI second and derived from a large number of clocks all over the world. Analyzed and published by by BIPM. Reduced to mean sea level.**UTC (Universal Time, Coordinated):**Based on the SI second, it knows days of 86400 and 86401 seconds. The latter are days with a so-called leap second. The objective is to keep UTC within a second of UT1, which is based on the earth's rotation. The offset from TAI is always an integer number of seconds (the accumulated leap seconds).**TT (Terrestrial Time):**An idealized time, for all practical purposes based on TAI, but with a constant offset to provide continuity with Ephemeris Time. Defined on the rotating geoid.**TB (Barycentric Time):**Also known as TDB (Barycentric Dynamical Time). This is basically TT transformed to the solar system barycenter.**TCG (Geocentric Coordinate Time):**A properly relativistic coordinate time, referred to the geocenter. The coordinate time equivalent of TT.**TCB (Barycentric Coordinate Time):**The coordinate time equivalent of TB.**JD (Julian Date):**Number of days since Greenwich mean noon on January 1, 4713 B.C. Note that JD may be used in conjunction with all of the above time systems; whenever the required accuracy dictates this, the time system used should be indicated: e.g., JD (TT).**MJD (Modified Julian Date):**Equals JD - 2400000.5. The same note applies as for JD concerning the time system in use. We shall continue to use MJD notwithstanding the IAU's recent decision not to recognize MJD anymore as an official time unit.

**JD - MJD:****TT - TAI:****TAI - UTC:**Since 1972, an integer number of seconds. Please consult this USNO document for the history of the leap seconds.**TCB - TCG:**The vectors

and**xe**denote the barycentric position and velocity of the earth's center of mass, and**ve**is the barycentric position of the observer. The quantity**x***P*represents periodic terms which can be evaluated using analytical formulae. For observers on the Earth's surface, these are diurnal, with a maximum amplitude of 2.1 microseconds; for spacecraft, they presumably depend solely on the orbit.The origins of coordinate times have been arbitrarily set so that these times all coincide with TT at the geocenter of 1977.0 (TAI).

**TB - TT:****TCG - TT:****TCB - TB:**

**Relation between time on the geoid (***t'*) and time on a Low Earth Orbit spacecraft (*tL*):This approximates to:

At an altitude of 500 km, the clock would loose approximately 8.5 ms per year, unless its frequency were adjusted.

The time stamps presented by *Chandra* FITS tables as generated by XFF will be in TT.

It has been agreed that the **Spacecraft Clock Seconds (SCCS)**, or
**Mission Elapsed Time (MET)**, will represent true elapsed seconds
since January 1, 1998, at 0h0m0s TT, which corresponds to MJD = 50814.0 (TT).
At this time, the leapsecond value (TT - UTC) was 63.184 s. Hence:

MJD (Jan 1, 1998, 0h TT) = 50814.0 (TT) = 50813.999268703704 (UTC)

Raw time stamps in the FITS tables created by XFF will be on this
(SCCS or MET) time system. However, FITS times are to be taken as the
sum of a Time value and the values of the `MJDREF` and
`TIMEZERO` keywords.

The `TIMEZERO` keyword will provide a nominal clock correction
that ensures an absolute accuracy of TBD (nominally 1) ms for the time
stamps. The exact value of the tolerance will be based on experience
in orbit; the goal is to provide reasonably accurate absolute time
with a minimum effort.

To summarize the times in the FITS tables:

- Raw time stamps are in SCCS.
- Time stamps plus
`TIMEZERO`plus`MJDREF`provides absolute time in TT. - Time stamps plus
`TIMEZERO`plus`MJDREF`minus 32.184 s provides absolute time in TAI. - Time stamps plus
`TIMEZERO`plus`MJDREF`minus 63.184 s minus the number of leap seconds since 1998 provides absolute time in UTC. - All time-related quantities are in seconds, except for
`MJDREF`which is in days.

Keyword Value Unit Comment TTYPE1 'TIME' s Column 1 contains raw time in SCCS TIMESYS 'TT' Defines TT as fundamental time system MJDREF 50814.0 d 1998.0 (TT) TIMEZERO <nominally 0.0> s Clock correctionVarious transformations between MET, TT, and UTC in a variety of formats (seconds, calendar date/time, year-day-time, JD, MJD) can be performed using the tools axTime or axTime3.

Code to handle time is available from the CDA FTP site:

*XTime*is a C++ time conversion library, including axTime3*bary*contains a C library and tools to handle barycenter corrections and pulsar data

*A Time Tutorial* was written by Arnold Rots of the *Chandra* Data Archive
Operations team.