Sains Malaysiana 49(4)(2020): 859-870

http://dx.doi.org/10.17576/jsm-2020-4904-15

A New Crescent Moon Visibility Criteria using Circular Regression Model: A Case Study of Teluk Kemang, Malaysia

 (Kriteria Baru Kebolehnampakan Bulan Sabit menggunakan Model Regresi Berkeliling: Suatu Kajian Kes Teluk Kemang, Malaysia)

NAZHATULSHIMA AHMAD^1*, MOHD SAIFUL ANWAR MOHD NAWAWI², MOHD ZAMBRI ZAINUDDIN², ZUHAILI MOHD NASIR³­, ROSSITA MOHAMAD YUNUS³ & IBRAHIM MOHAMED³

¹Space Physics Laboratory, Department of Physics, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

 ²Islamic Astronomy Programme, Department of Fiqh and Usul, Academy of Islamic Studies, University of Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

³Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

 Diserahkan: 22 Oktober 2019/Diterima: 13 Januari 2020

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.

Keywords: Circular regression; crescent moon; lunar month; q-test; visibility criteria

ABSTRAK
Ramai ahli astronomi telah mengkaji kebolehnampakan bulan sabit sepanjang sejarah. Kepentingannya tidak dapat dipertikaikan, terutama dalam menentukan kalendar Islam tempatan dan tarikh peristiwa penting Islam. Kriteria yang berbeza telah digunakan untuk meramalkan kemungkinan kebolehnampakan bulan sabit semasa proses pencerapan. Walau bagaimanapun, setakat ini, model kebolehnampakan yang digunakan adalah berdasarkan teori statistik linear, sedangkan pemboleh ubah penting dalam kajian ini adalah dalam sukatan membulat. Oleh itu, dalam kertas ini, kami mencadangkan ujian kebolehnampakan baru menggunakan model regresi berkeliling, yang akan membahagikan data menjadi tiga kategori kebolehnampakan; dapat dilihat dengan mata kasar, mungkin memerlukan bantuan optik dan tidak kelihatan. Kami memformulasi prosedur tersebut untuk memisahkan kategori menggunakan sisa model regresi berkeliling yang sesuai. Kami mengaplikasikan model tersebut dalam 254 pemerhatian yang dikumpulkan di Baitul Hilal Teluk Kemang Malaysia, bermula dari Mac 2000 sehingga kini. Kami menunjukkan bahawa ujian kebolehnampakan dibangunkan berdasarkan pemanjangan bulan (pemboleh ubah bersandar) dan ketinggian bulan (pemboleh ubah bebas) memberikan kadar salah pengkelasan terkecil. Daripada analisis statistik, kami mencadangkan pemanjangan bulan pada 7.28°, ketinggian bulan 3.33° dan aras penglihatan 3.74° ketika matahari terbenam sebagai kriteria baharu kebolehnampakan bulan sabit. Kriteria baharu ini memberi kesan yang besar dalam meningkatkan peluang melihat bulan sabit dan menghasilkan kalendar Islam yang lebih tepat di Malaysia.

Kata kunci: Bulan lunar; bulan sabit; kriteria kebolehnampakan; regresi berkeliling; ujian q

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*Pengarang untuk surat-menyurat; email: n_ahmad@um.edu.my