EHILLE Crescent Visibility: Key Factors and Criteria

An Analysis of EHILLE Crescent Visibility Calculations Determining the first visibility of the lunar crescent (hilal) is a foundational task in Islamic astronomy, dictating the commencement of lunar months for the global Hijri calendar. Historically, this practice relied entirely on direct visual observation, leaving it vulnerable to human error and regional atmospheric fluctuations. In the modern era, the integration of advanced computational tools has shifted the field toward predictive mathematics. Among these innovations is EHILLE, a specialized scientific analysis software developed by researcher ⁠Abdurrahman Özlem. Named after the Arabic word ahillah (the plural form of hilal, meaning crescent moons), the ⁠EHILLE simulator models and maps the exact geographic thresholds where a new crescent becomes visible. This article analyzes the theoretical foundations, astronomical parameters, and algorithmic mechanisms that underpin the EHILLE system. The Theoretical Framework: Beyond Simple Geometry

Early visibility criteria, dating back to Babylonian astronomy, relied on a single geometric parameter, such as the time lag between sunset and moonset. As astronomy matured, criteria evolved to incorporate dual-parameter metrics, such as the fixed altitude and elongation limits adopted by religious bodies across Southeast Asia. However, static geometric constraints often fail to account for the physical reality of the twilight sky.

EHILLE departs from static limits by utilizing the Extended Crescent Visibility Criterion. The theoretical foundation of this model relies on contrast threshold physics. For an observer to detect a thin waxing crescent, the intrinsic brightness of the illuminated lunar disc must overcome the ambient sky brightness at dusk. Because sky brightness drops exponentially as the Sun sinks lower beneath the horizon, visibility is highly dynamic. EHILLE calculates this evolving contrast ratio topocentrically, ensuring that variables unique to the observer’s location—including horizon refraction and atmospheric extinction—are mathematically integrated. Core Parameters of the EHILLE Model

The software evaluates lunar visibility by calculating a series of interconnected celestial mechanics: Nusantara: Journal of Law Studies

The Role of Islamic Astronomy in Determining the Hijri Calendar