A new crescent moon visibility criteria using circular regression model: a case study of Teluk Kemang, Malaysia

Abstract

Many astronomers have studied lunar crescent visibility throughout history. Its importance is unquestionable, especially in determining the local Islamic calendar and the dates of important Islamic events. Different criteria have been used to predict the possible visibility of the crescent moon during the sighting process. However, so far, the visibility models used are based on linear statistical theory, whereas the useful variables in this study are in the circular unit. Hence, in this paper, we propose new visibility tests using the circular regression model, which will split the data into three visibility categories; visible to the unaided eye, may need optical aid and not visible. We formulate the procedure to separate the categories using the residuals of the fitted circular regression model. We apply the model on 254 observations collected at Baitul Hilal Teluk Kemang Malaysia, starting from March 2000 to date. We show that the visibility test developed based on elongation of the moon (dependent variable) and altitude of the moon (independent variable) gives the smallest misclassification rate. From the statistical analysis, we propose the elongation of the moon 7.28°, altitude of the moon of 3.33° and arc of vision of 3.74 at sunset as the new crescent visibility criteria. The new criteria have a significant impact on improving the chance of observing the crescent moon and in producing a more accurate Islamic calendar in Malaysia.