the construction of a TTTDB transformation.

The following subsections describe the various steps involved in this process and the impact for the ephemeris users.
2.1.

The TCB-TCG transformation Two reference systems are defined: a global one, the Barycentric Celestial Reference System (BCRS), covering the whole Solar System and a local one, the Geocentric Celestial Reference System (GCRS), which is physically suitable for the modeling of processes in the vicinity of the Earth.

BCRS is particularly useful when one wants to model the light propagation or motion of celestial objects in the Solar System.

We can then, in the mass-monopoles approximation, write the equation of motion of bodies as well as the conservation laws satisfied by the Solar System barycenter (see Damour and Vokrouhlick´y 1995); all these features being already implemented in INPOP06. (Damour and Vokrouhlick´y 1995) gives the complete conservation equations based on (Damour,Soffel and Xu 1991) formalism including spin/spin, mass/mass and mass/spin couplings.

However, each fundamental reference system has its own time-scale: TCB for the BCRS and TCG for the GCRS.

The relation between TCB and TCG can be derived, but time transformations are only determined for specified space-time events (one coordinate time and three
spatial positions) so, at the geocenter, the transformation reads (Damour, Soffel and Xu 1991, Soffel et al. 2003):
� (1)
c2 α(T CB) + 1
dT CG dT CB = 1 + 1
c4 β(T CB) + O �1 c5
c being the speed of light in a vacuum and where
α(T CB) = −1
GMA
2v2 E − �
, (2)
rEA
A̸=E


�
GMA
β(T CB) = −1

8v4 E + 1
rEA
A̸=E
�
GMA
4vA.vE −3
2v2 E −2v2
+ �
A
rEA
A̸=E
�vA.rEA rEA
�2
+1
2aA.rEA + 1
�
GMB
. (3)
+ �
rAB
B̸=A
Capital latin subscripts A and B enumerate massive bodies, E corresponds to the Earth, MA is the mass of body A, rEA = xE −xA, rEA = |rEA|, vA = ˙xA, aA = ˙vA, a dot signifying time derivative with respect to TCB and xA being the BCRS position of body A.

Eqs. (1), (2) and (3) exhibit that the time transformation between TCB and TCG is explicitly related to the positions and velocities of Solar System bodies, so to the planetary ephemeris itself.

As stressed by Klioner (2008), if we are distributing a time transformation together with positions and velocities, we are building a four-dimensional planetary ephemeris.

This time transformation will be called in the following time ephemeris to be close to the terminology of Irwin and Fukushima (1999).

An issue remains.

The use of TCB in planetary ephemerides should induce important changes in numerical values of planet masses, initial conditions and astronomical unit commonly adopted by users.

Therefore, even if a TCB-based ephemeris and a TDBbased ephemeris are related linearly, caution has to be taken when one wants to shift from one ephemeris to an other as it will induce large changes for all users.

For a more complete discussion, see for instance (Klioner 2008).
2.2.

The TT-TCG transformation The IAU time realization is done by the International Atomic Time (TAI) with a service running since 1958 and attempting to match the rate of proper time on the geoid by using an ensemble of atomic clocks spread over the surface and low orbital space of the Earth.

TAI is conventionally related to the Terrestrial Time (TT) and the Universal Coordinate Time (UTC) by the two following relations:
T T (T AI) = T AI + 32.184s . (4)

and UT C = T AI −leap seconds , (5) leap seconds being added by the International Earth Rotation Service at irregular intervals to compensate for the Earth’s rotation irregularities.

Mainly, leap seconds are used to allow UTC to closely track UT1, which effectively represents the Earth rotation.