Lunar Time
Pascale Defraigne, Frédéric Meynadier, Adrien Bourgoin
TL;DR
The paper addresses how to establish a practical lunar time reference for precise navigation and PNT by comparing three options built around TCL: (1) use TCL directly, (2) apply a scale to approximate the lunar surface clock rate (TL), and (3) scale TL to minimize secular drift with TT while retaining only periodic terms. It develops the framework of coordinate vs proper time, detailing TCL’s role in a LCRS and quantifying steering requirements through clock performance and light-travel considerations, with explicit relations such as $[T - t]_{(t,\mathbf{x})} = - \frac{1}{c^{2}} \{ ... \} + \mathcal{O}(c^{-4})$ and $\frac{d \tau_l - d \mathcal{T}}{d \mathcal{T}} = -\frac{1}{2c^2}[\mathcal{V}_l^2 + 2\mathsf{W}(\mathcal{T}, \mathbf{\mathcal{X}}_l)]$. The key finding is that scaling TCL (options 2 or 3) introduces cross-scale complexity (mass parameters, distances) and larger steering requirements, whereas using TCL directly (option 1) remains the most natural and least constraining choice for lunar PNT; UTC alignment would still require clock steering and accurate time-transfer modeling. Overall, the work provides a principled trade-off and practical guidance for international standards and mission planning, favoring TCL as the lunar time reference to minimize operational complexity while enabling nanosecond-level synchronization through steering as needed.
Abstract
The regain of interest in Moon exploration has substantially grown in the last years. For this reason, the space agencies consider the development of a precise navigation and positioning service similar to the Earth GNSS. Aiming at some meter accuracy, this requires to set up a relativistic lunar reference frame, with an associated coordinate time. If the IAU already defined the Lunar Coordinate Time TCL, there is still some freedom in the choice of the coordinate timescale to be adopted as reference on or around the Moon. This paper proposes a trade-off analysis of different possible options for this reference time scale. It shows that TCL is the best option to be used as practical time reference on the Moon, without the need to define a new time scale based on a scaling of TCL.