TEMPUS: Relativistic coordinate time scales for any solar-system body from arbitrary ephemerides

Abstract

Precise time-scale transformations between solar-system bodies are an essential requirement for deep-space science and solar system navigation. The post-Newtonian relativistic expression relating a body-centered coordinate time TCX to the Barycentric Coordinate Time TCB depends on the gravitational environment and velocity of the target body, and must be evaluated consistently with the chosen planetary ephemerides. So far only INPOP has provided such a solution as part of its ephemerides releases, albeit only for Earth with TCG-TCB. We present TEMPUS, a tool that numerically integrates the IAU 2000 time-transformation for any solar-system body using positions and velocities from an arbitrary ephemerides. We provide a validated, ephemerides-agnostic implementation of TCX-TCB and assess its accuracy against published independent solutions. The rate $d\,\mathrm{TCX}/d\,\mathrm{TCB}$ is integrated with an Adams-Moulton order-12 predictor-corrector. The gravitational potential sum tested here includes the Sun, eight planets, Pluto, up to 343 main-belt asteroids, and 30 trans-Neptunian objects. Outputs can be stored in readable format tables of sampled values or as Chebyshev coefficient files. Comparisons are performed against the TU Dresden Klioner time solutions, the TCG-TCB solution provided with INPOP19a and INPOP21a, and the LTE440 lunar solution. For the planetary bodies TEMPUS agrees with Klioner at the $10^{-21} s\,s^{-1}$ level over 200 yr. Against the INPOP19a released TCG-TCB we also agree to the same level. The main-belt asteroids as well as the trans-Neptunian objects shift the planetary time scales at the $10^{-18} s\,s^{-1}$ level, and the choice of planetary and lunar ephemerides contributes differences on the $10^{-18} s\,s^{-1}$ level as well. TEMPUS provides a validated, ephemeris-agnostic post-Newtonian time-transformation for any solar-system body.