Mathematical Analysis of 5° + 8° Parameters in the Unified Global Hijri Calendar

Muhammad Hidayat : Universitas Muhammadiyah Sumatera Utara
Submitted: 03-01-2025 || Accepted: 20-07-2026 || Published: 20-07-2026

Abstract


This research departs from the need to strengthen the scientific basis of the criteria of the Unified Global Hijri Calendar (KHGT), especially the criteria for the height of the hilal 5° and elongation of 8° guided by Muhammadiyah. So far, official documents on the origin of these criteria have not been widely publicized, raising questions among astronomers, astronomers, and religious institutions. The main objective of the study was to explain the mathematical analysis behind the selection of the 5° + 8° parameters. The research method was carried out with a theoretical approach using basic astronomical equations to analyze the moon's height, elongation, and azimuth difference, as well as assess its correlation with the possible visibility of the hilal. The results of this study show that the minimum hilal height of 5° and the minimum elongation of 8° have a strong scientific foundation, and do not appear arbitrarily, but are closely related to Bruin's theoretical analysis in 1977 which mapped the relationship between the height of the Moon, ARCV, the depression of the Sun, the width of the moon while the elongation parameter of 8° has a strong correlation with the theory of the visibility limit of the hilal proposed by André Danjon in 1936 the determination of 8° elongation in the KHGT can be It is understood as a form of scientific refinement that combines the theoretical limits of Danjon with an approach to optimal visibility of Bruin's analysis.


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DOI: https://doi.org/10.30596/jam.v12i1.22595

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