Astronomical Calculations Research Articles

Exploring the Legacy of Ancient India Cultural, Scientific, and Socio-Political Contributions to World Civilization

This study explores the remarkable achievements of ancient India, focusing on its enduring impact on global thought and practices. From the philosophical insights enshrined in the Vedas and Upanishads to the revolutionary scientific advancements in mathematics, astronomy, and medicine, ancient India emerged as a beacon of intellectual brilliance. Concepts such as zero, the decimal system, and advanced astronomical calculations influenced civilizations across Asia, the Middle East, and Europe, forming the foundation for modern science and technology. Culturally, ancient India introduced transformative ideas of spirituality, yoga, and meditation, which continue to inspire holistic health and mental well-being worldwide. The philosophical principles of dharma, karma, and non-violence, as seen in Hinduism, Buddhism, and Jainism, have resonated globally, shaping ethical and moral frameworks across cultures. The socio-political structures of ancient India, including democratic assemblies and the Varna system, offered models of governance and societal organization, albeit evolving over time.This exploration reveals how ancient India's legacy transcends time, fostering intercultural exchanges and providing timeless wisdom that addresses contemporary challenges, from sustainability to global harmony. By examining this rich heritage, we celebrate ancient India's unparalleled contributions to humanity's collective progress.

Deep learning-based prediction approaches of binary star parameters

The precise computation of binary star parameters is crucial for understanding their formation, evolution, and dynamics. However, large datasets of available astronomical measurements require substantial effort for computing using classic astronomical methods. Deep learning (DL) is a promising approach that can provide a proper solution for estimating the parameters and reducing the burden of the lengthy procedures of astronomical computations. This study proposes two DL-based models for estimating binary star parameters. The first is the well-known multi-layer perceptron (MLP) model, whereas the second is based on long short-term memory (LSTM). We rely on databases, such as large sky multi-object fiber spectroscopic telescope area (LAMOST), to train the proposed models. In addition, we verify the training ratio showing that the performance of both models at a low training ratio of 30%, based on the mean square error (MSE), results in acceptable performance. Furthermore, the LSTM-based DL model outperforms the conventional MLP for different training ratios. Eventually, the two models have superiority compared to the benchmark methods.

Evolution and Significance of Sine Function in Ancient Indian Mathematics

This research article delves into the historical and mathematical intricacies of the construction of sine functions, particularly focusing on ancient Indian mathematical concepts and their evolution. It begins by highlighting the significance of sine (jya) as a fundamental trigonometric function in Indian mathematics, alongside its synonyms in Sanskrit. The historical journey of the term “sine” is traced back to ancient Indian mathematical texts, which were later translated into Arabic and then into Latin, ultimately leading to the adoption of the term “sine” in modern mathematics. The article elaborates on the definitions and interpretations of sine (ज्या), cosine (कोटिज्या), versed sine (उत्क्रमज्या), and co-versed sine (कोट्युत्क्रमज्या) in Indian mathematical traditions. It explains how these functions were conceptualized and utilized in astronomical calculations, emphasizing their geometric and trigonometric significance. Furthermore, the article discusses the division of a circle into quadrants (Vṛttapādas) and the concept of Trijyā (radius), highlighting the mathematical sophistication and terminology used by ancient Indian mathematicians. Several mathematical formulas related to the construction and calculation of sine functions are presented, including formulas for finding sine values at specific angles such as 45 degrees, 18 degrees and 72 degrees. These formulas showcase the mathematical ingenuity and problem-solving skills of ancient Indian mathematicians. Overall, this research article provides a comprehensive overview of the historical development and mathematical foundations of sine functions in ancient Indian mathematics, shedding light on their enduring legacy and contributions to modern trigonometry.

Modelling of Control Strategy for Sun Tracking of Concentrated Photovoltaic (CPV) Systems and Performance Analysis of Optical Losses Due to Tracking Errors.

Abstract Among the wide range of solar energy technologies, CPV remains a promising technology worldwide. The photovoltaic concentrator maximizes its efficiency through the use of optical concentration systems. But since optical concentration depends on direct solar radiation, maximizing the quantity of useful solar radiation received requires using a solar tracker that tracks the direction of the sun. To maximize collector efficiency, it’s crucial to choose tracking systems that align with the optical concentration factor. Inadequate focusing of direct solar radiation on the concentrator’s receiver can result in high optical losses, regardless of quality. This paper focuses on improving the accuracy and lowering the cost of the tracker trajectory generation strategy. A sun tracker simulator is first developed, allowing for the investigation of the impact of sun tracking performance a traditional control strategy is initially implemented that uses an astronomical calculation to follow the path of the sun. This strategy uses a sun position algorithm from the National Renewable Energy Laboratory to generate the tracker trajectory and track the sun’s path. When tested on the simulator, as a result, this strategy demonstrated a level of accuracy that ensured a good balance between intricacy and accuracy. Then, An investigation study was conducted to determine how this solar tracker’s precision might affect its optical efficiency. the optical losses resulting from the tracking were calculated using the provided location, The optical loss calculated for this collector’s maximum tracking error is approximately 9%. The research methodology showed that the tracker precision satisfied the requirements of the optical system under study.

The Concept of Maslahah in the Dynamics of the Rukyah and Hisab Methods for Determining the Beginning of the Lunar Month

Determining the beginning of the lunar month is a significant issue in Islamic tradition, especially in establishing the timing of religious observances such as Ramadan and Eid al-Fitr. The methods used for this determination, namely rukyah (moon sighting) and hisab (astronomical calculation), often lead to differing opinions among Muslims. This paper aims to analyze the dynamics between the rukyah and hisab methods through the lens of the maslahah theory, which emphasizes the achievement of good and the prevention of harm for the community. The analysis shows that the rukyah method is more relevant for determining the beginning of months related to major religious observances, as it aligns with sharia tradition and helps maintain the unity of the Muslim community. Conversely, the hisab method is more efficient for determining the start of months not directly related to religious observances, such as 1 Muharram, as it provides certainty and ease in planning. The conclusion of this paper is that integrating both methods, with an emphasis on their respective contexts, can optimize the maslahah for Muslims, ensure the smooth execution of religious practices, and support unity within the community.

The Level of Compliance of Muhammadiyah Citizens to The Decision of The Muhammadiyah Central Leadership Number 01/MLM/1.0/E/2024

This study aims to examine the level of compliance among Muhammadiyah members in Banjarnegara with the Decree of the Muhammadiyah Central Leadership Number 01/MLM/1.0/E/2024, which establishes the Eid al-Fitr holiday on 1 Shawwal 1445 Hijri, corresponding to April 10, 2024. This research employs a qualitative approach, collecting data from Muhammadiyah branches and sub-branches in Banjarnegara. The data were analyzed using techniques of classification, coding, editing, and interpretation. The results show that all Muhammadiyah members in Banjarnegara (100%) comply with the decree, indicating a high level of adherence to organizational rules. The study also found that Muhammadiyah uses the hisab wujudul hilal method, which combines astronomical calculations and moon sighting, to determine the beginning of the lunar month.

Facing Interdisciplinary Research In Syariah Researches, Findings From Applied Falak Sience

This working paper aims to describe the use of interdisciplinary studies in the application of Sharia, especially Islamic astronomy (Ilmu Falak). The benefit is strengthening holistic insight in applying Islamic astronomy in everyday life. This broadening of insight is assisted by the study of exact sciences which can scientifically impact the accuracy of astronomical calculations. Through a literature review, it can be found that interdisciplinary research in Sharia, especially astronomy in determining the direction of the Qibla, cannot avoid the use of science and technology that is currently developing to strengthen its fiqh norms.

Was the Supernova of 1054 CE Recorded in Constantinople? A Historical and Astronomical Reassessment

This paper critically reexamines two candidate records of the supernova of 1054 CE (SN 1054) that allegedly came from Constantinople, integrating historical and astronomical analyses. East Asian records documented SN 1054 in detail and formed the basis for astronomical discussions. In contrast, few reports of SN 1054 from Western Eurasia (Europe and West Asia) are known. The majority of such alleged reports have been rejected on the basis of philological and astronomical discussions. This study scrutinizes two potential accounts of SN 1054. The first is Ibn Buṭlān’s account, as cited in a later work. The second is a specific class of Byzantine gold coin issued in Constantinople, which may have commemorated SN 1054. Our reanalysis of Ibn Buṭlān’s record questions its connection to Constantinople. We also challenge speculation regarding the Byzantine coin, analysing contemporary historical and numismatic backgrounds. The paper also compares these accounts with the reconstructed SN light curve and modern astronomical calculations to assess the astronomical aspect of these records.

Digital Hilal Observation: Evaluating the Authenticity of Hilal Testimonials in Indonesia Using the Digistar-6 Planetarium System

This article aims to provide supporting data to test the authenticity of testimonial claims of sighting the hilal (new moon) that have been received and decided by the Ministry of Religious Affairs of the Republic of Indonesia (RI) from 1962-2021 during the isbat session for the determination of the beginning of the months of Ramadan, Shawwal, and Dhu al-Hijjah. Building upon the results of the author's previous research that revealed inconsistencies in the application of the minimum visibility criteria for the hilal known as imkan al-rukyat by the Ministry of Religious Affairs Indonesia. Approximately 45.5% of the hilal testimonial claims found in the Minister of Religious Affairs' decisions are doubted for their authenticity due to various reasons, including the absence of elongation data and the presence of hilal altitude data below the Ministers of Religious Affairs of Brunei Darussalam, Indonesia, Malaysia, and Singapore (MABIMS) criteria. To substantiate the old data, this article employs the Digistar-6 planetarium system to provide a scientifically accurate 3D visualization of the hilal observation process through a full-dome planetarium. Using a qualitative descriptive approach, this article examines all the testimonial claims data after classifying them based on the application of the imkan al-rukyat theory in MABIMS in Indonesia. The findings show several key points: First, there is no elongation data available in all of these decisions. Second, there is a variation in the use of astronomical calculations for hilal data, especially before the implementation of MABIMS criteria. Third, there is astronomical data on hilal claims post the implementation of MABIMS criteria that are accepted with altitudes below 2°. Fourth, the tendency is that the hilal can be seen with optical aids during hilal altitudes above 3° and elongations exceeding 6°.

Milanković Forcing in Deep Time

AbstractAstronomical (or Milanković) forcing of the Earth system is key to understanding rhythmic climate change on time scales ≳104 y. Paleoceanographic and paleoclimatological applications concerned with past astronomical forcing rely on astronomical calculations (solutions), which represent the backbone of cyclostratigraphy and astrochronology. Here we present state‐of‐the‐art astronomical solutions over the past 3.5 Gyr. Our goal is to provide tuning targets and templates for interpreting deep‐time cyclostratigraphic records and designing external forcing functions in climate models. Our approach yields internally consistent orbital and precession‐tilt solutions, including fundamental solar system frequencies, orbital eccentricity and inclination, lunar distance, luni‐solar precession rate, Earth's obliquity, and climatic precession. Contrary to expectations, we find that the long eccentricity cycle (LEC) (previously assumed stable and labeled “metronome,” recent period ∼405 kyr), can become unstable on long time scales. Our results reveal episodes during which the LEC is very weak or absent and Earth's orbital eccentricity and climate‐forcing spectrum are unrecognizable compared to the recent past. For the ratio of eccentricity‐to‐inclination amplitude modulation (recent individual periods of ~2.4 and ~1.2 Myr, frequently observable in paleorecords) we find a wide distribution around the recent 2:1 ratio, that is, the system is not restricted to a 2:1 or 1:1 resonance state. Our computations show that Earth's obliquity was lower and its amplitude (variation around the mean) significantly reduced in the past. We therefore predict weaker climate forcing at obliquity frequencies in deep time and a trend toward reduced obliquity power with age in stratigraphic records. For deep‐time stratigraphic and modeling applications, the orbital parameters of our 3.5‐Gyr integrations are made available at 400‐year resolution.

The Temple of Apollo in Didyma

The Temple of Apollo in Didyma, located on the Aegean coast of southwestern Turkey, is not aligned towards the cardinal directions: GPS measurements and satellite imagery indicate that the azimuth of the temple is 55.117°. Lack of prominent geological features in the surrounding landscape raise the idea of a probable celestial orientation. Various orientation studies have suggested bright stars of Gemini, sunrise direction during the summer solstice or the heliacal rising direction of Cygnus and Lyra during the winter solstice as potential vantage directions, and we propose that the temple is aligned towards the heliacal rising direction of Castor (a Geminorum). During the Hellenistic period Castor’s heliacal rise also coincided with the summer solstice, and we believe this alignment serves calendrical and symbolic purposes. We rest our case on astronomical computations, classical texts, archaeological evidence and the unique architectural plan of the temple.

The Point of Views of Indonesian Mufassir (M. Quraish Shihab and Hamka) on Polygamy and its Relevance to Legislation in Indonesia

Asr prayer is one of the obligatory prayers performed at specific times among the five daily prayers. However, in the literature of fiqh, there is a division of Salat Asar into fadīlah (preferred time), ikhtiyār (permissible time), and jawāz (allowable time). This is closely related to the virtue of performing the prayer in its early time, as mentioned in the sayings of the Prophet Muhammad, and the discouragement of delaying Asr prayer until its later time. It is essential to establish a precise time, specifying the exact hour and minute for fadīlah, ikhtiyār, and jawāz in Asr prayer. There are two methods for determining the timing of fadīlah, ikhtiyār, and jawāz: firstly, through a fiqh approach, which involves observing the phenomena of the Sun’s movement, and secondly, through a scientific approach, using mathematical and astronomical calculations. Both the fiqh and scientific methods are integrated and mutually beneficial in the development of a formulation, providing ease in determining the timing of fadīlah, ikhtiyār, and jawāz in Salat Asar.
 Keywords: Asr prayer, Fadīlah, Ikhtiyār, Jawāz, fiqh, science

Formulation of Faḍīlah, Ikhtiyār, and Jawāz Times of Asr Prayer of Fiqh and Science Perspectives

Asr prayer is one of the obligatory prayers performed at specific times among the five daily prayers. However, in the literature of fiqh, there is a division of Salat Asar into faḍīlah (preferred time), ikhtiyār (permissible time), and jawāz (allowable time). This is closely related to the virtue of performing the prayer in its early time, as mentioned in the sayings of the Prophet Muhammad, and the discouragement of delaying Asr prayer until its later time. It is essential to establish a precise time, specifying the exact hour and minute for faḍīlah, ikhtiyār, and jawāz in Asr prayer. There are two methods for determining the timing of faḍīlah, ikhtiyār, and jawāz: firstly, through a fiqh approach, which involves observing the phenomena of the Sun’s movement, and secondly, through a scientific approach, using mathematical and astronomical calculations. Both the fiqh and scientific methods are integrated and mutually beneficial in the development of a formulation, providing ease in determining the timing of faḍīlah, ikhtiyār, and jawāz in Salat Asar. Keywords: Asr prayer, Faḍīlah, Ikhtiyār, Jawāz, fiqh, science

Астрономические и календарные вычисления Ефрема Сирина в 6-м гимне «О Распятии» в вавилонском, иудейском и христианском контексте

The paper is focused on the astronomical and calendrical lore which the Syriac poet-theologian Ephrem the Syrian abundantly uses in his 6th hymn De crucifixione. In this hymn devoted to the interpretation of three days problem of Jesus’ resurrection, the Syriac poet and theologian employs some astronomical data, i.e., the duration of solar and lunar years, the duration of the lunar months, the necessity of the intercalations in the calendars etc. The author analyses this lore in the context of the astronomical knowledge existing to Ephrem’s epoch. On the one hand, the article pays attention to the similar use of the astronomical data in a lot of Jewish and Christian works of the 3rd and 4rd centuries. In this period the astronomical calculations have been used actively both in Christian and Jewish milieux. On the other hand, the calculations by Ephrem mirror the peculiarities of the region of the north Mesopotamia where he lived and created his works. For example, the author demonstrates that Ephrem could be influenced by the old Babylonian astronomical theory and use in his computations the Babylonian “double hour”. In the article is also demonstrated that the calculations by Ephrem are striking similar to the ones in the “Panarion” by Epiphanius of Salamis. Epiphanius seems to be acquainted with Ephrem’s works or to use the similar tradition stretching back to the Babylonian one. The author draws a conclusion that the calculations in the hymns are used to express Ephrem’s self-presentation as the scribe and the sage who obtains the cosmic “secrets”. This picture is deep rooted as in the old Mesopotamian literature as in Jewish Aramaic writings. The author points out that Ephrem uses the astronomical lore in the liturgical context and not in the theological “scientific’’ tractate. Hence, Ephrem constructs a new religious and poetic “myth” about the Crucifixion and feast of Pascha upon the astronomical dimensions it has both in the Christian and in the Jewish traditions.

Digital Transformation in Hisab Rukyat: A Sociological Perspective on Integrating Information Technology in Islamic Astronomical Tradition

This research investigates how the integration of Information Technology (IT) in the practice of Hisab Rukyat, a traditional method in Islamic astronomy for determining prayer times, is transforming the social and cultural landscape in Muslim communities. Employing a qualitative approach, the study collected data through in-depth interviews, participatory observations, and analysis of documents related to the Hisab Rukyat bodies in various countries. Findings indicate that the adoption of IT not only enhances accuracy and efficiency in astronomical calculations but also sparks sociological debates over balancing technological innovation with tradition. Furthermore, the study identifies shifts in community dynamics, where younger generations are more receptive to technological use, while older ones tend to adhere to traditional methods. These findings suggest that while IT provides a more efficient means for calculations, an intergenerational dialogue is also necessary to maintain cultural continuity in this digital transition. The implications of this study are significant for policymakers, religious communities, and academics interested in the interplay between technology, society, and religious traditions.

PyMsOfa: A Python Package for the Standards of Fundamental Astronomy (SOFA) Service

The Standards of Fundamental Astronomy (SOFA) is a service provided by the International Astronomical Union that offers algorithms and software for astronomical calculations, which was released in two versions for FORTRAN 77 and ANSI C, respectively. In this work, we implement the Python package PyMsOfa for SOFA service by three ways: (1) a Python wrapper package based on a foreign function library for Python (ctypes), (2) a Python wrapper package with the foreign function interface for Python calling C code (cffi) and (3) a Python package directly written in pure Python codes from SOFA subroutines. The package PyMsOfa has fully implemented 247 functions of the original SOFA routines released on 2023 October 11. In addition, PyMsOfa is also extensively examined, which is exactly consistent with those test examples given by the original SOFA. This Python package can be suitable to not only the astrometric detection of habitable planets from the Closeby Habitable Exoplanet Survey mission, but also for the frontier themes of black holes and dark matter related to astrometric calculations and other fields. The source codes are available via http://pypi.org/project/PyMsOfa/ and https://github.com/CHES2023/PyMsOfa.

The Problems of Implementing Imkan Rukyat in the Case of an Invisible Hilal (Crescent): A Perspective of Syafi�i Scholars

Imkan rukyat refers to the conditions under which the new moon (hilal) can likely be sighted based on specific criteria. When the hilal is visible, the following day can be confirmed as the start of the new lunar month. However, if the hilal is not seen during the rukyat observation, a dilemma arises between two choices: whether the next day should be declared as the first day of the new lunar month based on the criteria of imkan rukyat, or whether the current month should be completed (istikmal) to a full 30 days. All Islamic mazhabs including Hanafi, Maliki, and Hanbali generally advocate for istikmal if the hilal is not sighted. However, within the Syafi�i Mazhab, there is a divergence of opinion, with some scholars advocating for istikmal and others for hisab (astronomical calculations). This duality of opinion is particularly relevant in Indonesia, a country with a majority of Syafi�i followers. The aim of this research is to analyze the views of Syafi�i scholars on this matter. This study is a type of library research, focusing on the decisions of the Ministry of Religious Affairs of the Republic of Indonesia's isbat meetings regarding the start of the lunar month and the moon sighting data provided by Nahdlatul Ulama. The research is grounded in the Quran, Hadith, and Syafi�i jurisprudence (fiqh) texts. The findings of this study indicate that the majority of Syafi�i scholars hold that if the hilal is in a position of imkan rukyat but is not sighted, the month should be completed to 30 days (istikmal). However, some Syafi�i scholars permit the determination of the start of the new lunar month the next day based on hisab imkan rukyat, provided that the calculation is done by at least seven qualified astronomers who are unlikely to err, and that the non-sighting of the hilal is due to technical or natural factors. These results can serve as a reference for determining the start of the lunar month when the hilal is not visible due to cloudy conditions

Date Of Easter Sebagai Reformasi Kalender Masehi

This research discusses the history of the calculation of the date of Easter as part of the reform of the Gregorian calendar using a historical approach. It examines the history of the determination of the date of Easter by the Council of Nicaea in 325 AD and the use of the ecclesiastical full moon method to calculate the date of Easter. This research also discusses the differences in the dating of Easter in the Julian and Gregorian calendars and the relationship between the dating of Easter and the astronomical vernal equinox. The results of this research show that the date of Easter is calculated based on mathematical calculations, taking into account the ecclesiastical full moon and is no longer related to accurate astronomical calculations. This research provides a clear overview of the history and methods of determining the date of Easter and can serve as a reference for scientists and researchers to further study the reform of the Gregorian calendar and the calculation of the date of Easter.

North Atlantic Drift Sediments Constrain Eocene Tidal Dissipation and the Evolution of the Earth‐Moon System

AbstractCyclostratigraphy and astrochronology are now at the forefront of geologic timekeeping. While this technique heavily relies on the accuracy of astronomical calculations, solar system chaos limits how far back astronomical calculations can be performed with confidence. High‐resolution paleoclimate records with Milankovitch imprints now allow reversing the traditional cyclostratigraphic approach: Middle Eocene drift sediments from Newfoundland Ridge are well‐suited for this purpose, due to high sedimentation rates and distinct lithological cycles. Per contra, the stratigraphies of Integrated Ocean Drilling Program Sites U1408–U1410 are highly complex with several hiatuses. Here, we built a two‐site composite and constructed a conservative age‐depth model to provide a reliable chronology for this rhythmic, highly resolved (<1 kyr) sedimentary archive. Astronomical components (g‐terms and precession constant) are extracted from proxy time‐series using two different techniques, producing consistent results. We find astronomical frequencies up to 4% lower than reported in astronomical solution La04. This solution, however, was smoothed over 20‐Myr intervals, and our results therefore provide constraints on g‐term variability on shorter, million‐year timescales. We also report first evidence that the g4–g3 “grand eccentricity cycle” may have had a 1.2‐Myr period around 41 Ma, contrary to its 2.4‐Myr periodicity today. Our median precession constant estimate (51.28 ± 0.56″/year) confirms earlier indicators of a relatively low rate of tidal dissipation in the Paleogene. Newfoundland Ridge drift sediments thus enable a reliable reconstruction of astronomical components at the limit of validity of current astronomical calculations, extracted from geologic data, providing a new target for the next generation of astronomical calculations.

射电脉冲星搜索的优化方法

The connection between astronomy and high-performance computing is becoming stronger with the development of innovative observing facilities such as the Square Kilometre Array (SKA) and the proposed innovative platform for big data and high-performance computing. Astronomical computation is characterized by a large data volume and massive parallelism, particularly for pulsar search, a leading scientific direction of the SKA. In this study, we present an approach for accelerating the pulsar search pipeline based on OpenMP and multiprocessing techniques. We propose a method for solving the load imbalance problem and have successfully installed the pipeline on x86 and ARM compute nodes on the China SKA Regional Centre prototype (CSRC-P). The performance evaluation from tests on the Murchison Widefield Array (MWA) VCS observations shows that our optimization method works well on the x86 and ARM nodes, improving the relative speedup by factors of 10.4–12.2 and 24.5–25.8, respectively, compared with the original single-thread approach. The ARM platform was 1.1–1.3 times faster than the x86 platform in the tested cases, showing its great potential for SKA data processing. This optimized pulsar search pipeline deployed on the CSRC-P will be used for the pulsar survey of the southern-sky MWA rapid two-meter program for various scientific goals, including pulsar timing arrays for gravitational wave detection.