Time

Table 1: Time-scales relevant in space science [see A. B4]

UT1	universal time, defined by the mean solar day
TAI	international atomic time, defined by SI seconds
UTC	coordinated universal time, TAI - leap seconds, broadcast standard
TT	terrestrial time, TT=TAI+$32^s.184$, basis for geocentric ephemeris
TDB	barycentric dynamical time, defined by the mean solar day at the
	solar system barycentre, basis for solar system ephemeris

The time-scales relevant for coordinate transformations are defined in Tab.1. Formulae in the J2000.0 reference system are in ephemeris time $T_{eph}$ [S. 2.26, but see also Standish (1998b)], but for most purposes of space data analysis one may neglect the difference of less than 2 msec between $T_{eph}$, Barycentric Dynamical Time (TDB) and Terrestrial Time (TT) [A. B5] and less than 0.1s between the two Universal Times (UTC, UT1) ⁸. A difference between Atomic Time (TAI) and Coordinated Universal Time (UTC) is introduced by leap-seconds tabulated in Tab.2 [A. K9 for current table] ⁹.

Table 2: Leap seconds $\Delta A$ = TAI-UTC [see A. K9]

1972/1/1 +10s	1972/7/1 +11s	1973/1/1 +12s
1974/1/1 +13s	1975/1/1 +14s	1976/1/1 +15s
1977/1/1 +16s	1978/1/1 +17s	1979/1/1 +18s
1980/1/1 +19s	1981/7/1 +20s	1982/7/1 +21s
1983/7/1 +22s	1985/7/1 +23s	1988/1/1 +24s
1990/1/1 +25s	1991/1/1 +26s	1992/7/1 +27s
1993/7/1 +28s	1994/7/1 +29s	1996/1/1 +30s
1997/7/1 +31s	1999/1/1 +32s.

Thus TDB or TT can be approximated from UTC by TDB=UTC+ $32^s.184+\Delta A$ where $\Delta A$ is the number of elapsed leap seconds to date. For earlier dates Meeus (2000) gives different approximation formulae for UTC-TDB. Spacecraft data are usually given in UTC. Relative velocities of solar system objects are small enough ($<100$ km/s) to neglect the difference in time systems. Care must only be taken for problems of relative timing. If high precision timing ($<$ 0.1s) is requested the reader should refer to McCarthy (1996) and to the documentation of the SPICE system (see above). The reference points in time (epochs) for the ephemeris are given in Tab.3. Before 1984 the ephemeris referred to B1950.0 and many spacecraft trajectory data are still given in the older system (see Appendix). The actual position of solar system objects and spacecraft is usually given in an epoch of date system which means that coordinates refer to the orientation of the Earth equator or ecliptic at the time of measurement. We give formulae to convert from the reference epoch to the epoch of date in the following section 2.1.

Table 3: Epoch definitions [S. Table 15.3, A. B4]

J1900.0 =	1899 December 31, 12.00TDB =	JD 2415020.0
J1950.0 =	1950 January 1, 00.00TDB =	JD 2433282.5
J2000.0 =	2000 January 1, 12.00TDB =	JD 2451545.0
B1950.0 =		JD 2433282.42345905

The Julian Day Number ($JD$) starts at Greenwich mean noon 4713 Jan. 1, B.C. [S. 2.26]. The epoch day number is defined in this paper as the fractional number of days of 86400 seconds from the epoch:

$$d_0 = (JD - 2451545.0) .$$ (1)

Formulae from S. and A. use Julian centuries ($T_0$) from J2000.0. One Julian century has 36525 days, one Julian year has 365.25 days, s.t. [S. T3.222.2]

$$T_0 = d_0/36525.0 \hspace{1cm} \mbox{ and }\hspace{1cm} y_0 = d_0/365.25$$ (2)

We use this notation throughout the paper. When the astronomical reference systems eventually switch to the next epoch (presumably J2050.0) formulae given in this paper have to be adapted.