An Adjusted Julian Solar Calendar with an Optimized Leap-Year Structure

The construction of a civil solar calendar has long represented one of the most persistent problems in applied astronomy and mathematical chronology: the reconciliation of the non-integral, slowly varying tropical year with the discrete arithmetic structure required for civil timekeeping. From antiquity onward, this problem has been addressed not through direct astronomical observation but through fixed leap-year schemes that approximate the seasonal year by rational means, thereby ensuring predictability, continuity, and social stability. Within the Western tradition, this approach culminated in a sequence of Julian-derived reforms, most notably the Gregorian calendar of 1582 and the Revised Julian calendar proposed by Milutin Milanković in 1923. This paper introduces and analyzes an Adjusted Julian Solar Calendar (AJSC), conceived as a minimal arithmetic refinement of the classical Julian system. The proposed calendar preserves the traditional month structure and uninterrupted weekly cycle while achieving a mean year length exceptionally close to the modern mean tropical year near the J2000 epoch. From a physical perspective, the system may be described as a Mean Tropical Julian Calendar, that is, a fixed solar calendar explicitly optimized with respect to the mean tropical year at a defined epoch. From a mathematical standpoint, it constitutes an Optimized Julian Solar Calendar, illustrating the effect of higher-order divisibility corrections within a Julian framework. Using a unified mathematical formalism, the Julian, Gregorian, Revised Julian (Milanković), and Adjusted Julian calendars are compared under an identical metric. The analysis demonstrates that the AJSC achieves a substantially reduced residual drift relative to existing systems, while remaining conceptually conservative. At the same time, the study emphasizes the inherent physical limits of all fixed calendars imposed by the secular variability of the tropical year. The AJSC is therefore presented not as a proposal for immediate reform, but as a theoretical and historical contribution to the study of calendar optimization within the Julian tradition.