Construction of an autonomous lunar timekeeping system: The "Yuekun Wangshuo Calendar" model and its applications

Abstract: The establishment of an autonomous lunar timekeeping system is fundamental for sustainable deep space exploration. This paper addresses the core calendrical challenge: how to define the fundamental units of a “day,” “month,” and “year” on the Moon and reconcile their inherent incommensurability. Inspired by the classical Chinese calendrical wisdom of “Pingqi Dingxu” (evenly spacing the solar terms and fixing their sequence), we propose the “Hou-Level Tolerance” theory, defining the “Hou” (≈5 Earth days) as the basic tolerance unit, and design a “Multi-Level Tolerance” linkage algorithm. Based on this, a dual-track calendar system named the “Yuekun Wangshuo Calendar” is constructed. This system first establishes a temporal reference framework with the Earth-Moon synodic period as the “day,” the Earth phase cycle as the “month,” and the lunar orbital revolution period as the “year.” It then enables the long-term stable compilation of both a lunar “solar calendar” and a “lunar calendar,” achieving seamless mapping to Earth's time system. Mathematical modeling and simulations show that the system confines key astronomical phase errors to within one lunar day and remains robust against orbital perturbations. This work provides the first computable, culturally coherent, and engineering-ready solution for a lunar calendar. Its paradigm of “active tolerance” management offers a universal reference for constructing time systems on other celestial bodies. Furthermore, the calendrical framework and harmonization logic proposed in this study also provide a novel theoretical prototype for contemplating the evolution of Earth’s future timekeeping system. Keywords: astronomy; autonomous time system; incommensurable period harmony; lunar calendar model; earth-moon synodic cycle; Yuekun Wangshuo Calendar