Time ephemerides for the major solar system bodies

Sergei A. Klioner
Lohrmann Observatory, Technische Universität Dresden, 01062 Dresden, Germany

The time ephemerides for each body represent the time transformation between the coordinate time TCX of the local GCRS-like relativistic reference system of the corresponding body X and the coordinate time TCB of the BCRS.

The original GCRS (Geocentric Celestial Reference System) was defined for the Earth and adopted by the IAU back in 2000. For the Moon, the GCRS-like coordinate system is called LCRS (Lunar Celestial Reference System) and it was recommended by the IAU Resolution II of 2024 "to establish a standard Lunar Celestial Reference System (LCRS) and Lunar Coordinate Time (TCL)": https://iau.org/Iau/Publications/List-of-Resolutions. For the Moon then, the time ephemeris published here represents a numerical transformation between TCL and TCB evaluated in the center of gravity of the Moon.

As it was always intended for the GCRS and as the cited IAU Resolution states, similar GCRS-like relativistic reference systems and coordinate times can be defined for any body of the Solar System. This framework is assumed here. Analogous to TCG and TCL, the numerical transformations between between the coordinate times TCX of other solar system bodies are computed. The notation used for these coordinate time are given in the tables below.

The physical background of the relativistic reference systems on the example of BCRS and GCRS can be found in (Soffel, Klioner, Petit et al. 2003) and references therein. The description of the formulas used in the calculations of the time ephemerides are published in (Klioner, Gerlach, Soffel, 2010, Section 6) or, in much more details, in the publicly accessible Technical Note (Klioner, 2025) discussing the time framework of Gaia. In particular, two functions for each body are given here:

• Function deltaTCB(TCB) from the transformation from TCB to TCX: TCX = TCB + deltaTCB(TCB)
  
  
• Function deltaTCX(TCX) from the transformation from TCX to TCB: TCB = TCX − deltaTCX(TCX)

https://www.imcce.fr/recherche/equipes/asd/inpop/download19a

In particular, the short version of INPOP19a was used here which is valid for approximately 200 years.

Since the export version of the INPOP19a ephemeris was used, the overall accuracy of the time ephemerides published here are somewhat lower than that of the time ephemerides that could be computed directly by the ephemeris providers using their numerical integration framework and dynamical models. This is being done already now for the transformation between TCB (or TT) and TCB (or TDB) for the Earth. Those latter time ephemerides are part of the standard INPOP delivery.

Nevertheless, to demonstrate the accuracy of the time ephemerides provided here the transformation between TCG and TCB at the geocenter was computed using our framework and is also published here. One can show that the differences between the TCG ephemeris at the geocenter published here and that published as a part of INPOP19a is 6.2×10⁻¹⁸ in the linear trend and a non-linear (quasi-periodic) deviation of about 0.15 nanosecond within the validity period of about 200 years. The difference most probably originates from the extended dynamical models (asteroids and Kuiper belt objects) used in INPOP19a and missing in the framework used here. Numerical noise in the time ephemerides published here is estimated at the level of a few picoseconds.

The time ephemerides are represented via Chebyshev polynomials as it is done for all solar system ephemerides. The ASCII files below are in the same standard format that is used e.g. by the INPOP team.