Geospatial Accuracy Evaluation of Napier's Analogy Method for Global Qibla Direction: Analyzing Quadrant Ambiguity at High Latitudes

Abstract

Accurate determination of the Qibla direction is fundamental to Muslim worship, requiring rigorous validation of various calculation methods. This study conducts a mathematical comparative study between Napier's Analogy Formula and Spherical Trigonometry. The method used is a qualitative analysis based on literature studies with modeling simulations at various global geographic locations. The results show that Napier's Analogy Formula has an identical level of accuracy to Spherical Trigonometry in tropical regions. However, an anomaly was found in the form of quadrant ambiguity that results in a constant deviation at locations with latitudes above 21° (North and South), which is a critical point related to the geographical position of the Kaaba (21°25′21.04′′ N). This finding confirms that Napier's Analogy has limited spatial scope. As a solution, this study proposes the implementation of quadrant correction logic to ensure the precision of results at extreme latitudes. Thus, the use of Napier's Analogy should be limited to tropical regions or followed by the correction parameters formulated in this study.