On Astronomical Materials in Buddhist Scriptures

Abstract

There are many foreign astronomical materials that were preserved in the Chinese translation of Buddhist canons. From the content, these astronomical materials include cosmology theories, lunar mansion systems, calendrical data, etc. These astronomical materials are important evidence for the exchange and dissemination of astronomy between ancient civilizations. This paper aims to sort out and analyze the astronomical materials preserved in the Chinese translation of Buddhist canons, classifying and differentiating the content of astronomy, which was foreign to China, tracing the origins of these astronomical knowledge, discussing their impact on local astronomy in China, and evaluating the preservation form, characteristics, reliability, functionality, and limitations of these astronomical materials. Through the above discussion, this paper will demonstrate the core meaning of the historical view of transcultural transmission of sciences and technology, which is ‘knowledge progresses through dissemination and civilization thrives through communication’.

1. Introduction

In the ancient history of Chinese astronomy, there were three major waves of significant foreign astronomical inputs: (1) Indian astronomy, along with Babylonian–Greek astronomy, brought to China with the spread of Buddhism from the late Eastern Han Dynasty to the early Northern Song Dynasty (c. 3–10); (2) Arabian astronomy introduced to China during the Yuan and early Ming Dynasties (c. 13–15) with the spread of Islam; (3) Western classical astronomy brought to China during the late Ming and early Qing Dynasties with the spread of Christianity (c. 16–17). Among these, the first wave of Buddhist astronomy lasted the longest and had the most extensive influence.

Although all three instances of foreign astronomical knowledge entering China were associated with religion, the latter two instances were not as closely tied to religion in terms of the content and form of transmission. However, the Buddhist canons, serving as religious scriptures, preserved a large amount of Indian astronomical data. Therefore, the Buddhist canons have become extremely important primary sources for studying the introduction of Indian astronomy to China.

In recent years, scholars have conducted research on astronomical materials in Chinese translated Buddhist scriptures from the following aspects.

Firstly, scholars have sorted out and interpreted the content of Indian astronomy accompanying the translation of Buddhist scriptures into Chinese. Makoto Zenba (Zenba 1952, pp. 171–213; 1956, 1957, 1968), Toru Aoyama (Aoyama 1982), Michio Yano (Yano 1986b, 1987), Chen Meidong (Chen 1998), Zhou Liqun (Zhou 2015), Akira Sadakata (Sadakata 1997), and others have interpreted and verified the specific content of Indian astronomy in the Chinese-translated Buddhist scriptures from the ephemerides to cosmological theories. Jeffrey Kotyk conducted extensive research on Buddhist astrology in the Tang Dynasty using various translated Buddhist scriptures as materials (Kotyk 2017a).

Secondly, research on the introduction and impacts of foreign astronomy and astrology in China using Buddhist scriptures has been conducted by many scholars. Michio Yano discussed the Japanese Sukuyoudou 宿曜道which originated from the “Xiuyao Jing” and translated or compiled in the Tang Dynasty (Yano 1986a). Li Hui specifically discussed the Xiuyao Shu 宿曜術introduced to China through the translation of Buddhist scriptures into Chinese (Li 2011). Niu Weixing takes Rāhu and Ketu, which accompanied the translation of Buddhist scriptures into Chinese, as the starting point to explore how foreign astronomical concepts were absorbed and melted into the process of becoming a part of the local culture (Niu 2010). Song Shenmi further paid attention to the inheritance, transformation, and integration of foreign astrology into the local culture (Song 2014). She also investigated the dissemination and sinicization process of the twelve zodiac signs in China based on the various literature records, including Buddhist scriptures (Song 2021). Jin Zhijia paid attention to the study of foreign astrology and its influence during the Tang and Song Dynasties using Buddhist and Daoist scriptures (Jin 2020).

Thirdly, scholars have examined factors such as dissemination intermediary and pathways in the exchange and dissemination of ancient Chinese and foreign astronomy. Niu Weixing discussed the issue of transmission intermediaries and pathways for Indian astronomy to China (Niu 2004b). Zhou Liqun analyzed an Indian astrological dissemination text in three languages: Sanskrit, Tibetan, and Chinese (Zhou 2013). Bill M. Mak explored the Central Asian factors that influenced the spread of Buddhist astronomy from India to East Asia (Mak 2015). Jeffrey Kotyk sorted out the Iranian elements in Tang Dynasty Buddhist astrology (Kotyk 2017b).

The above mentioned research centered on astronomical materials in Buddhist scriptures has achieved a large number of research results, but there are still many issues that need to be further explored. In this article, I attempt to provide a comprehensive classification, organization, and interpretation of astronomical materials in Chinese Buddhist scriptures, as well as an analysis and judgment of their preservation, reliability, limitations, etc., in order to provide a panoramic overview for a comprehensive understanding of astronomical materials in Chinese Buddhist scriptures.

2. The Distribution, Classification, and Interpretation of Astronomical Data in the Buddhist Canons

The astronomical data preserved in the Buddhist canons can be classified into eight categories based on their content: 1. Cosmology; 2. Lunar Mansions System; 3. Seasons, Calendars, and Divisions of Day and Night; 4. Length of Shadows; 5. Solar and Lunar Eclipses; 6. Five Planets (wuxing 五星) and the Seven Luminaries (qiyao 七曜); 7. Rāhu (Luohou 羅睺), Ketu (Jidu 計都), and Navagraha (Jiuzhi 九執); and 8. Planetary Tables.

Below, we will organize, analyze, and interpret the distribution of these astronomical contents in the Buddhist canons.

2.1. Cosmological Knowledge in the Buddhist Canons

Among various astronomical knowledge, cosmological knowledge is closely linked with other human thought domains such as religion and philosophy. The cosmological theories in Buddhist scriptures are intricately related to Buddhist philosophical systems and encompass three theoretical aspects: firstly, theories concerning the formation of the universe, describing the causes and processes of cosmic formation; secondly, descriptions of the structure of the heavens and earth in Buddhist scriptures; and thirdly, descriptions of the operation of the universe. Although these Buddhist cosmological theories are relatively ancient, they provide coherent explanations for basic astronomical phenomena such as diurnal variations, annual variations in day length and sunrise azimuth, and seasonal changes.

In Buddhist scriptures, the term shijie 世界 (world) is often used instead of yuzhou 宇宙 (universe). According to the explanation in the Lengyan jing 楞嚴經 [Skt. Śūraṃgama-sūtra], shi 世 refers to the passage and change in time in the past, present, and future; jie 界 means boundary, delineating space.1 Buddhism divides the world into two dimensions: the world of sentient beings, also known as the ‘world of the sentient’ (youqing shijie 有情世界), and the world of objects, which is the land where all sentient beings dwell. The world of objects has more materialistic implications and is therefore closer to the astronomical concept of the universe.

The Abidamo jushe shilun 阿毗達磨俱舍釋論 [Skt. Abhidharmakośa-bhāṣya] uses a verse-by-verse commentary format to interpret the theory of the world of objects. From this, we understand that the world was roughly formed as follows: At the beginning of a kalpa, there was a great wind that could shatter and disperse everything, making all things formless and invisible, without a trace of dust remaining. All the states and mountains in the world were blown apart. After undergoing an extremely long period of time, a great black cloud arose, covering the entire world, followed by heavy rain that poured continuously for millions of years. The water accumulated and formed the bottom sea, which was eleven lakṣas2 and twenty thousand yojanas deep and twelve lakṣas and three thousand four hundred and fifty yojanas wide. The water from the bottom sea surged upward, coalescing into gold, like cream solidifying on the surface of boiled milk, forming the Golden Earth Wheel. The Golden Earth Wheel was three lakṣas and twenty thousand yojanas thick and had the same width as the water wheel (the bottom sea), which was diminished to eight thousand yojanas thick. The circumferences of the Golden Earth Wheel and the water wheel were three times their width,3 totaling thirty-six thousand lakṣas and ten thousand three hundred and fifty yojanas. Above the Earth Wheel, heavy rain poured down again, forming the Great Ocean. Under the agitation of the wind wheel, the essence gathered and formed Mount Sumeru, with superior essence forming seven golden mountains, middle essence forming seven silver mountains, inferior essence forming a mountain ring, and miscellaneous essence forming the four great continents.4

After the formation of the world, it acquired a certain internal structure. Descriptions of this world structure can be found in various Buddhist scriptures, among which the descriptions in several Abhidharma texts are more systematic and quantitative. In the Abidamo jushe lun 阿毗達磨俱舍論 [Skt. Abhidharmakośa-bhāṣya, hereafter Jushe lun], a combination of verses and commentary is used to depict the quantitative structure of the world.5 It is believed that all things in the universe exist on a vast and boundless wind wheel, with a water wheel above it. The surface of the water wheel solidified into the Golden Earth Wheel. At the top of the Golden Earth Wheel lies Mount Sumeru, surrounded by seven mountains including Yugamdhara (Ch. Yujiandaluo 踰健達羅). Mount Sumeru’s water level and depth are both eighty thousand yojanas.6 The remaining seven mountains are all made of gold. Beyond the seven mountains are the continents, namely the four great continents: Jambudvipa, Pūrva-videha, Avara-godānīya, and Uttara-kuru. The shapes of the four great continents are as follows: Jambudvipa is shaped like a chariot, with two thousand yojanas on each of the east, west, and north sides, and only three and a half yojanas on the south side; Pūrva-videha is shaped like a half-moon, with a length of three hundred and fifty yojanas on the east side and two thousand yojanas on the other three sides; Avara-godānīya is shaped like a full moon, with a diameter of two thousand five hundred yojanas and a circumference three times the diameter, i.e., seven thousand five hundred yojanas; and Uttara-kuru is square, with each side being two thousand yojanas. Additionally, there are eight subcontinents attached to each of the four great continents. These continents and subcontinents are inhabited places.

The operation of the Buddhist universe is closely related to the dynamics of Buddhist cosmological evolution and the structure of the world of objects: the sun, moon, and stars revolve around Mount Sumeru under the support and propulsion of the wind wheel. The height of the sun and moon’s orbit is half the height of Mount Sumeru, which is forty-two thousand yojanas. The sun revolves around Mount Sumeru, causing day and night alternations and seasonal changes on the four great continents.

Including the four great continents, the sun, moon, stars, Mount Sumeru, and the heavenly realms collectively are called one Small Thousand World. A thousand Small Thousand Worlds make up one Middle Thousand World. A thousand Middle Thousand Worlds constitute one Great Thousand World. Everything in the Great Thousand World is generated and destroyed together in one great kalpa and regenerated at the beginning of a new great kalpa, reflecting a typical cyclical cosmological idea.

From the depiction of the Buddhist world structure in the Jushe lun, it can be seen that the structure of this world is quite refined. Whether it is the structure of the heavens and earth, the movement of the sun and moon, the shape of the four great continents, or the magnificent abodes of the heavenly beings atop Mount Sumeru, as well as the heights and lifespans of the gods, humans, and ghosts, all have a set of quantitative models, involving arithmetic and geometric progressions. At the same time, the world structure in Buddhist scriptures is not completely divorced from experience. For example, the description of the shape of Jambudvipa roughly matches the north-wide and south-narrow shape of the Indian subcontinent. In summary, from the Buddhist scriptures, we can understand a quantified ancient Indian cosmological model.

2.2. Lunar Mansions System in the Buddhist Canons

Lunar mansions are a very common concept in Buddhist scriptures. However, a considerable portion of the discourse on lunar mansions is not directly related to astronomy and is sporadic and incomplete. Classical texts that provide relatively comprehensive descriptions of the lunar mansions system include the Da fangdeng daji jing 大方等大集經 [Skt. Mahāvaipulya-mahāsaṃnipāta-sūtra, T no. 397], the Wenshushili pusa ji zhuxian suoshuo jixiong shiri shan’e xiuyao jing 文殊師利菩薩及諸仙所說吉凶時日善惡宿曜經 [Sūtra Spoken by Bodhisattva Mañjuśrī and Various Devas on Auspicious and Inauspicious Times and Days and Good and Evil Nakṣatras and Planets; T no. 1299; hereafter Xiuyao jing], the Modengjia jing 摩登伽經 [Skt. Mātangī-sūtra, T no. 399], the Shetoujian taizi ershiba xiu jing 舍頭諫太子二十八宿經 [Skt. Śārdūlakarṇāvadāna; T no. 1301; hereafter Shetoujian jing], and the Qiyao rangzai jue 七曜攘災訣 [Formulae for Averting Disaster by the Seven Luminaries; T no. 1308). Most of these sutras belong to the Esoteric Buddhist tradition. The descriptions of the Indian lunar mansions system7 in these Buddhist scriptures generally include six aspects: the names of the lunar mansions, the number of lunar mansions, the width of lunar mansions, the number of stars in each lunar mansion, the shape of each lunar mansion, and the astrological significance of each mansion.

The Fomu da Kongque Mingwang jing 佛母大孔雀明王經 [Skt. Mahāmāyūrī-vidyārājñī; T no. 982], translated by Bukong 不空 (Amoghavajra, 705–774), is listed as the first text in the ‘Esoteric’ category of the Taishō canon. In this sutra, the names of the 28 lunar mansions are listed, and the Chinese names for the Indian lunar mansions are used for translation, which is a common practice in Buddhist scriptures. However, it is worth noting that the Chinese lunar mansions do not strictly correspond to the Indian lunar mansions in terms of specific stellar compositions. The Foshuo da Kongque zhouwang jing 佛說大孔雀咒王經 [Skt. Mahāmāyūrī-vidyārājñī; T no. 985], translated by Yijing 義淨 (635–713), is an alternate version of the Mahāmāyūrī-vidyārājñī. Similarly, it lists the names of the 28 lunar mansions, but Yixing used phonetic translations for the names of the Indian lunar mansions.

The Da fangguang pusa zang Wenshushili genben yigui jing 大方廣菩薩藏文殊師利根本儀軌經 [Skt. *(Ārya)Mañjusrīmūlakalpa; Ritual Manual Sūtra on the Fundamentals of the Mañjuśrī in the Vaipulya-bodhisattva-storehouse; T no. 1191; hereafter Genben yigui] translated by Tianxizai 天息災 (Skt. Devaśāntika, fl. 980–1000) during the Northern Song Dynasty (960–1127), lists the phonetic names of the twenty-seven lunar mansions excluding the Ox mansion. Influenced by Babylonian–Greek astronomy, Indian astronomy adjusted the number of lunar mansions to twenty-seven to match the imported zodiacal twelve houses. Additionally, considering the precession of the equinoxes, the first lunar mansion was changed from the older Krittikā to Rohini, also known as Aśvinī (Ch. Ashiweimi 阿濕尾儞). This sutra was translated by Tianxizai in the early years of the Northern Song Dynasty, relatively late in terms of translation date. Hence, the adjustment of the first lunar mansion to accommodate the precession of the equinoxes was necessary.

The Genben yigui, in juan 14, describes the fate of individuals born under the twelve zodiacal signs and establishes a correspondence between the twelve zodiacal signs and the twenty-eight lunar mansions. After the concept of the twelve zodiacal signs entered India, it inevitably raised questions about how to match them with the twenty-eight lunar mansions. Here, we see an example of such coordination. In the Nanmijishipaluo tian shuo zhilun jing 難儞計濕嚩囉天說支輪經 [*Nandikêśvara-deva Teaches the Zodiac Sūtra; T no. 1312, hereafter Zhilun jing], a similar correspondence between the twelve zodiacal signs and the twenty-eight lunar mansions is given. The correspondence between the twelve zodiacal signs and the twenty-eight lunar mansions provided in the Zhilun jing is more detailed than that given in juan 14 of the Genben yigui. Each lunar mansion is first divided into several sections and then matched with the twelve zodiacal signs, with some mansions divided into two parts, each matched with neighboring signs, and each zodiacal sign nominally paired with three mansions. Similar methods of matching zodiacal signs and lunar mansions can also be found in the Xiuyao jing.

The Modengjia jing and the Shetoujian jing are different translations of the same sutra, each with its own characteristics in translating the names of the twenty-eight lunar mansions. In the Modengjia jing, in the fifth chapter ‘Shuo xingtu pin’ 說星圖品 [Discourse on Star Charts], the names of the Indian lunar mansions are translated entirely according to the Chinese names of the lunar mansions, with the first mansion being Krittikā, which is evidently a relatively ancient system. The Shetoujian jing, on the other hand, uses a completely different translation method, translating the names of the Indian lunar mansions into Chinese using a method of paraphrasing. By examining the literal meanings of the Sanskrit names of the Indian lunar mansions, it can be seen that almost all of the paraphrased names correspond to the original Sanskrit meanings. This method of translating the names of lunar mansions is unique among all Buddhist scriptures.

The twenty-eight (or twenty-seven) lunar mansions encircle the heavens, with each mansion occupying a certain celestial area. In ancient China, the widths of the twenty-eight lunar mansions varied, with some being over thirty degrees wide, while others were only a few degrees wide or even just one degree wide. The width of the lunar mansions in ancient India differed. In the Da fangdeng daji jing it is said that Krittikā (Maoxiu 昴宿) ‘travels the four continents through thirty shi (時) in one day and one night’ (一日一夜, 歷四天下, 行三十時).8 The ancient Indian lunar mansions, also called Nakṣatras (Yuezhan 月站), were closely related to the movement of the moon, and the width of each mansion was expressed in terms of the time it took for the moon to stay in the mansion, from entering to leaving. Here, thirty shi is the width of Krittikā. The ‘Shuo xingtu pin diwu’ 說星圖品第五 [Fifth Discourse on Star Charts] in the Modengjia jing also provides the widths of the twenty-eight lunar mansions. The Shetoujian jing is a different version of the Modengjia jing and also lists the widths of the twenty-eight lunar mansions, but with slight variations compared with the Modengjia jing.

From the records of the three Buddhist scriptures mentioned above, it can be understood that the widths of the Indian lunar mansions are classified into three categories, large, medium, and small, based on the time the moon stays in each mansion. The width of the large mansion is three times that of the small mansion, while the medium mansion is twice the width of the small one. In ancient China, there was no consistent pattern for the widths of the lunar mansions. The widths of the lunar mansion given in the three scriptures are particularly narrow for the Ox mansion and do not fall into the categories of large, medium, or small widths. This further illustrates the uniqueness of the Ox mansion in the Indian lunar mansion system and helps to understand why the Ox mansion is excluded from the Indian system of twenty-seven mansions. For the same mansion, the values given by the three scriptures are mostly the same, with few differences. The time unit in the Daji jing is shi; in the Shetoujian jing, the time unit is a ‘moment’ (xuyu 須臾).9 The time unit in the Modengjia jing is not strictly defined, where ‘day’ (ri 日) refers to daytime, and one day and one night are equivalent to thirty shi.

2.3. The Division of Seasons, Calendar Days, and Day and Night Hours in the Buddhist Canon

The content related to calendars and seasons in the Buddhist canon is quite rich, mainly involving the division of seasons, the insertion of intercalary months, the arrangement of lunar months, the concepts of black and white months, day and night hours, and the determination of time segments.

In ancient India, the year was divided into 12 months, which were further divided into three or six seasons. These concepts are mentioned in many Buddhist scriptures. In ancient India, the name of the lunar mansion where the moon appeared on the night of the full moon determined the name of the month. The arrangement of days in a month and the division of hours in a day in ancient India also had their unique characteristics, as will be described below.

As the performance of rituals in Esoteric Buddhism requires precision in timing, Esoteric Buddhist scriptures often contain records related to calendar days and time segments. In the Suxidi jieluo jing 蘇悉地羯羅經 [Skt. Susiddhikara-mahātantra-sādhanopāyika-paṭala], within the ‘Apizhelujia pin di shiwu’ 阿毘遮嚕迦品第十五 [Fifteenth Chapter of Ābhicāra], it is mentioned that a ritual called abhiṣeka (apizhelujia 阿毘遮嚕迦)10 should be performed at noon on the eighth or fifteenth day of the dark moon to more effectively subdue demons and monsters.11 In the ‘Gongyang cidi fa pin di shiba’ 供養次第法品第十八 [Eighteenth Chapter on the Stages of Offering] of the same sutra, it is also mentioned that appropriate rituals should be performed at different times of the day. From this passage, we know that ancient India had a division of six time segments: three during the day and three during the night.12

In juan fourteen of the Da fangguang pusa zang Wenshushili genben yigui jing 大方廣菩薩藏文殊師利根本儀軌經 [Sūtra of the Fundamental Rites for the Great Bodhisattva Cundi’s Treasury], there is also a discussion on seasons, calendar days, and day and night hours. It mentions that the first to fifteenth days belong to the white month, while the sixteenth to thirtieth days belong to the black month. Both white month and black month are Indian time units called a paksa (half-month); two paksas make up one month, twelve months make up one year, and one year is divided into six or three seasons.13 In juan four of the Da Piluzhe’na chengfo jing shu 大毘盧遮那成佛經疏 [Commentary on the Mahāvairocana Sūtra], it is also mentioned that the first, third, fifth, seventh, and thirteenth days of the white month are auspicious and suitable for mandala (mandaluo 漫荼羅) rituals. Among them, the eighth, fourteenth, and fifteenth days are particularly auspicious, and performing rituals on these days can have twice the effect with half the effort.14 The text further reminds that in the case of a short lunar month, there are only fourteen days in the white months, the fifteenth day is actually the first day of the black months, so it is no longer an auspicious day. Due to the variation in the moon’s speed, the calendar typically uses the average speed of the moon. The actual occurrences of the new moon and full moon, known as ‘true new moon’ (dingshuo 定朔) and ‘true full moon’ (dingwang 定望), may differ by a day from the calculated new moon and full moon.15 From this, it can be seen that the rituals in Esoteric Buddhism should be determined based on the true new moon and true full moon, which is referred to as the ‘fixed day’ (dingri 定日).

The ‘Mingshi fenbie pin diqi’ 明時分別品第七 [Seventh Chapter on Understanding the Time Segments] in the Modengjia jing introduces the rules of the annual changes in the length of day and night recognized in ancient India, as well as the specific names of the 30 time segments of day and night. The same content is also mentioned in the variant translation of the Shetoujian jing, but the two texts have different methods of translating the names of the 30 time segments of day and night. Interestingly, both the Modengjia jing and the Shetoujian jing mention the use of human observation of the length of the shadow cast by their own body to determine the fifteen time segments of daylight, which is equivalent to using a person as a horizontal sundial.

2.4. The Length of Sunlight Shadow Data in Buddhist Texts

The Modengjia jing and the Shetoujian jing both mention the method of using ‘self-measurement’ to determine the fifteen time segments of daylight, which cleverly utilizes the sun’s projection. However, this involves the diurnal changes in the length of the shadow. Generally, astronomy focuses on the annual changes in the length of the noonday shadow. Such data are also mentioned in Buddhist scriptures, such as in the Da fangdeng daji jing and the Shi feishi jing 時非時經 [Sūtra of Timeliness and Untimeliness].

In the Modengjia jing, in the ‘Mingshi fenbie pin diqi’ section, the character Emperor Triśaṅku (Di Tengjia 帝勝伽) explains to the Brahmin ‘Lotus Fruit’ (Lianhua shi 蓮華實) the changes in the length of day and night and the variation in the length of the noonday shadow, which is measured using a noonday shadow chart with a height of 12 units.16 Based on the monthly records of the length of the noonday shadow in the scripture, it can be inferred that the location where the data were obtained was approximately near 39 degrees north latitude. From this, it can be further inferred that the astronomical knowledge reflected in the Modengjia jing was transmitted from India to Central Asian countries first and stayed there for a period. The noonday shadow data in the Modengjia jing were measured at that time and place, and then transmitted to the Central Plains.

The Shi feishi jing consists mainly of a data table with a few descriptive texts.17 Through analysis and interpretation of the scriptures and references to similar data in other Buddhist scriptures, it is not difficult to determine that these data are about the annual changes in the length of the shadow cast by the sun.

Regarding the concepts of ‘timeliness’ (shi 時) and ‘untimeliness’ (feishi 非時), although they occasionally have other meanings in Buddhist scriptures, in the vast majority of cases they are associated with ‘time for eating’ (shishi 時食) and ‘untime for eating’ (feishi shi 非時食). According to the ‘Shishi bu diwu’ 食時部第五 [Fifth of the Dining Time Sections] in juan 42 of Fayuan zhulin 法苑珠林 [Forest of Gems in the Garden of the Dharma] it is stated that ‘Noon is the time for the Dharma, that is, the time for eating. Beyond this time, when the shadow moves a hair’s with by a second, it is considered untimeliness’ (午時為法，即是食時. 過此午時影一髮一瞬，即是非時).18 Thus, ‘timeliness’ and ‘untimeliness’ are strictly divided based on noon, which is very precise.

From a passage of the seventeenth juan of the Mohe sengqi lü 摩訶僧祇律 [Skt. Mahāsaṅghika Vinaya], we can roughly understand how the early Buddhists determined the time of noon. At that time, the mealtime for monks was not fixed and was ridiculed by the public. The Buddha then prescribed that meals should be taken in the first half of the day and taught the monks the method of ‘taking time’ (qushi 取時), which involved making a foot shadow and using a water clock (kelou 刻漏).19 In other words, on clear days, the exact moment of noon can be determined by observing the shadow of the sun, while on cloudy or rainy days, water clocks can be used to ascertain the time of noon. This term ‘foot shadow’ (jiaoying 脚影) corresponds exactly to the unit of shadow length ‘foot’ mentioned in the Shi feishi jing. Combining the narrative description at the beginning of the Shi feishi jing, it can be inferred that the Buddha obtained the length of the noonday shadow for twenty-four half-months in a year in advance and then informed the monks. As long as the monks observed the length of the shadow during the corresponding half-month, they could eat when the length of the shadow reached the ‘timeliness’ (shi 時) corresponding to that half-month. If it slightly exceeded the length corresponding to ‘un timeliness’ (feishi 非时), they could not eat that day. Therefore, the Shi feishi jing provides the ‘technical parameters’ for determining the time of noon. Buddhists had to rely on this ‘technical manual’ to determine the time for eating, ensuring that it was ‘timeliness for eating’ and not ‘untimeliness for eating.’

A complete set of shadow length data should include two important parameters: the height of gnomon measuring the length of shadow H, and the latitude of the measuring location φ. However, the Shi feishi jing does not provide these two parameters. Nevertheless, using certain spherical astronomy knowledge and necessary mathematical methods, it is not difficult to calculate these two parameters, shown as follows (Niu 2004a):

φ = 36.2° ± 2.42°, H = 5.99 feet ± 0.57 feet

According to the description at the beginning of the Shi feishi jing, the Sūtra was preached by the Buddha Śākyamuni when he resided in the Jeta Grove Monastery (Jialantuo zhulin yuan jingshe 迦蘭陀竹林園精舍) in Śrāvastī (Wangshe cheng 王舍城)20, so the data on the length of the noonday shadow should theoretically be applicable to the geographical latitude of Śrāvastī. Śrāvastī was the capital of the ancient Indian kingdom of Kosala (Mojietuo guo 摩揭陀國), located south of the Ganges River in the present-day Bihar state, at about 25 degrees north latitude. However, according to the calculation results, the applicable latitude for the length of the noonday shadow data in the Shi feishi jing is around 36 degrees north. Since the ‘untimeliness’ shadow length data were not measured in Śrāvastī, the ‘untimeliness’ shadow length data in the Shi feishi jing did not originate from the mouth of the Buddha. The latitude where these data are applicable belongs to the region of ancient Gandhāra, present-day eastern Afghanistan, northwestern Pakistan, and the Kashmir region controlled by Pakistan. This region was part of the ancient Gandhāra (Jibin guo 罽賓國) mentioned in Chinese historical records, a region where ancient Indian Buddhist culture flourished and the starting point for the spread of Buddhism to China via land routes. The translation of the Shi feishi jing was carried out in Khotan, which is also within the latitude range obtained. Therefore, the two sets of shadow length data provided by this sutra provide quite reliable technical support for Buddhists around 36 degrees north latitude to eat at the right time and avoid eating at the wrong time. At the same time, the Shi feishi jing is evidence of the spread of Buddhism from its place of origin to northwest India and the ancient western regions, and it is also important evidence of the transmission of Indian astronomical calendar knowledge along with Buddhism to China.

2.5. Sun, Moon, and Solar and Lunar Eclipses in the Buddhist Texts

The sun and the moon are undoubtedly the two most prominent celestial bodies, and Buddhist scriptures contain extensive descriptions of the sun, the moon, and related phenomena. These descriptions can generally be categorized as follows: (1) characteristics of the sun itself—sunlight, sun diameter, sun path, etc.; (2) characteristics of the moon itself—moon diameter, moon shape, moon substance, moon path, etc.; (3) phenomena of daily changes; (4) phenomena of annual changes; (5) changes in lunar phases; and (6) solar and lunar eclipses.

2.5.1. Origin, Material, Shape, and Size of the Sun and Moon

The sun and the moon are two essential celestial bodies, and how they are generated and what they are composed of is detailed in the ‘Shi benyuan pin’ 世本緣品 [Chapter on the Original Conditions of the World] of juan 22 of the Chang ahan jing 長阿含經 [Skt. Dīrgha-agama], which states that the sun and the moon are brought forth by a great storm from the original continent (golden land wheel 金地輪) located beneath the ocean, which is eighty-four thousand yojanas deep. The sun and the moon can move in the sky without falling, being supported by the so-called ‘five winds.’ Wind was a fundamental force in ancient Indian cosmology, and it played a role in the formation of the world and the generation of the sun and moon.

According to the Chang ahan jing, the sun and moon are composed of different materials. The sun is made of two parts ‘heavenly gold’ (Tianjin 天金) and one part glass (poli 頗梨)21, while the moon is made of two parts heavenly silver and one part crystal (liuli 琉璃). Both the sun and moon are square-shaped because they ‘appear round from a distance’ 遠見故圓.22 The length and width of the sun and moon are each fifty-one yojanas.23

The ‘Riyuexing pin dijiu’ 日月行品第九 [The Ninth Chapter on Sun and Moon’s Path] in juan 5 of the Lishi apitan lun 立世阿毗曇論 [Skt. Sarvastivada Abhidharma] offers similar views to the Chang ahan jing regarding the composition of the sun and moon. However, it differs in its description of the shape and size, stating that the sun and moon are cylindrical. According to this text, the sun is fifty-one yojanas thick and wide, with a circumference of one hundred and fifty-three yojanas; the moon is fifty yojanas thick and wide, with a circumference of one hundred and fifty yojanas.24 Clearly, the circumference is calculated using the formula ‘radius 1 diameter 3’ 徑一週三. Juan 10 of Qishi jing 起始經 [Sūtra on the Arising of Worlds] also mentions the sun being fifty-one yojanas long and wide,25 and the moon being forty-nine yojanas long and wide. The Yujia shidi lun 瑜伽師地論 [Skt. Yogācārabhūmi Śāstra] states that the sun’s diameter is fifty-one yojanas, while the moon’s diameter is one yojana smaller than the sun’s.26

Ancient Indians believed that the sun and moon emitted light themselves. According to the Chang ahan jing, the reason the sun and moon emit light is that the deities of the sun and moon themselves shine; their light first illuminates their golden and crystal palaces and then the solar and lunar abodes. The Chang ahan jing also explains ten reasons why sunlight becomes hot.27

2.5.2. Path of the Sun and Moon

According to the Chang ahan jing, ancient Indians believed that the sun and moon revolved around Mount Sumeru at half its height. The ‘Riyuexing pin dishijiu’ in juan 5 of Lishi apitan lun also mentions a similar view: the sun and moon travel at a height of forty thousand yojanas above Jambudvipa, which is half the height of Mount Sumeru.28

The description of the movement of the sun and moon here is particularly noteworthy. Ancient Indians believed that the rotation of the sun and moon was a form of rotation around Mount Sumeru, which stands upright on the ground. In ancient Chinese cosmology, the Huntian 渾天 (chaotic heavens) theory advocated that the sun and moon revolve around the earth, but the Gaitian 蓋天 (covering heavens) theory in the Zhoubi suanjing 周髀算經 [Calculation Classic of the Zhou Gnomon] proposed a similar movement of the sun and moon to that of ancient India’s viewpoint.

The model of the sun orbiting Mount Sumeru can explain the alternating changes in seasons and day and night. In the ‘Riyuexing pin dishijiu’ in juan 5 of Lishi apitan lun, there is a detailed description of the sun’s annual movement, stating that the sun’s path consists of 180 routes, while the moon’s path consists of 15 routes. Within half a year, the sun transitions consecutively from one daily path to the next, until it reaches the outermost path, then gradually returns to the innermost path. This annual variation in the azimuth of sunrise and the length of daylight can be fully explained in this manner. As for the moon’s movement, each lunar path is equivalent to 12 solar paths. Between the southernmost and northernmost routes of the 180 solar paths lies a distance of 290 yojanas, and the sun and moon travel back and forth within this range. The southernmost solar path is called the outer path (wailu 外路), with a diameter of 481,380 yojanas and a circumference of 1,444,140 yojanas. The northernmost solar path is called the inner path (neilu 內路), with a diameter of 488,000 yojanas and a circumference of 1,442,400 yojanas.29 Here, the value of π is taken as 3, making it easy to calculate the difference of 290 yojanas in radius between the outer and inner paths.

Continuing in the ‘Riyuexing pin dishijiu’ in juan 5 of Lishi apitan lun, the text further introduces the speed and direction of the sun and moon’s movements, their relative movements, and the changes in lunar phases.30 Similar descriptions can also be found in juan 22 of the Chang ahan jing31 and juan 5 of Qishi jing32, which are essentially consistent with the records in the Lishi apitan lun. However, in juan 11 of Lishi apitan lun there is a different explanation for the process and causes of the waxing and waning of the moon phases.33 It can be seen that ancient Indians already recognized the relationship between lunar phase changes and the variations in sunlight and its position.

2.5.3. Sunlight Coverage

The ‘Riyuexing pin dishijiu’ in juan 5 of Lishi apitan lun mentions that the diameter of sunlight coverage is 721,200 yojanas34 with a circumference of 216,3600 yojanas. When the sun rises in the southern Jambudvipa, it sets exactly in the northern Uttarakuru (Bei Yudanyue zhou 北鬱單越洲), reaches noon in the eastern Pubbavideha (Dong Fupoti zhou 東弗婆提洲), and midnight in the western Jambudvipa. The different seasons throughout the day are formed by the sun’s movement.35 Although the concept of sunlight having a certain coverage range is only found in one place in the Buddhist scriptures, it is highly significant. In the ancient Indian cosmological model, the sun’s path revolves around Mount Sumeru and is parallel to the earth’s surface. In this model, if the radius of sunlight were infinite, it would not be possible to have alternating changes between day and night. Therefore, the Buddhist scriptures explicitly state that the diameter of sunlight coverage is 721,200 yojanas, which means the radius is 360,600 yojanas. As such, within the spherical range centered on the sun with a radius of 360,600 yojanas, it is daytime, while beyond that is nighttime.

As the radius of sunlight coverage is smaller than the inner path diameter of the sun’s orbit around Mount Sumeru (480,800 yojanas), it is determined that when the sun travels along its ‘route’, it cannot shine on the opposite side of its position. For example, when sunlight shines on the southern Jambudvipa, it cannot reach the northern Uttarakuru. The alternation of day and night on the four continents can be explained based on the two premises of ‘the sun revolves around Mount Sumeru’ and ‘the limited coverage range of sunlight’.

2.5.4. Solar and Lunar Eclipses

Regarding the cause of solar eclipses, ancient Indians also had unique understandings. In the form of the Buddha Śākyamuni preaching to the various celestial beings, such as in the fourteenth chapter, ‘Yinyang shan’e zhengying pin’ 陰陽善惡征應品 [The Chapter on the Divine Signs of the Good and Evil and Yin and Yang] found within juan 18 of Da fangguang pusa zang Wenshushili genben yigui jing, it explains the cause of solar eclipses, attributing them to Rāhu Asura, the king of the Asuras. Asura is the fifth class of the eight transmundane beings led by the devas (gods) and nagas (Dragons)36 in Indian Buddhism, originally a kind of deity in the Indian Buddhist world, often at war with Indra, the king of the gods. Rāhu is the king of the Asuras. During a battle with Indra, Rāhu blocked the sun with one hand because it was too dazzling, causing a solar eclipse. Due to this relationship between Rāhu and eclipses, in ancient Indian astronomy, the ascending node of the ecliptic and the celestial equator, which is closely related to eclipses, was named Rāhu. In the Qiyao rangzai jue, detailed instructions and tables are given for Rāhu’s movements.

The fourteenth chapter, ‘Yinyang shan’e zhengying pin’ found within juan 18 of Da fangguang pusa zang Wenshushili genben yigui jing, also mentions a six-month period of eclipses. Modern astronomy tells us that eclipses must occur near the points where the ecliptic intersects the celestial equator, and the time it takes for the sun to move from the ascending node to the descending node is precisely six months. In fact, concerning lunar eclipses, including penumbral lunar eclipses, they occur at least twice a year, about every six months, and regarding solar eclipses, they also occur at least twice a year, about every six months.

In many more Esoteric Buddhist scriptures, solar and lunar eclipses appear more as signals of disasters or as special moments for conducting rituals. After explaining the cause of eclipses, as in the aforementioned Da fangguang pusa zang Wenshushili genben yigui jing, the text lists the constellations associated with solar eclipses and the disasters expected in various regions of ancient India, which is similar to the theory of divisions in ancient China.

From various descriptions in Esoteric Buddhist scriptures, it seems that ancient Indians believed that performing certain rituals during solar and lunar eclipses would have special positive effects. For example, the Xukongzang pusa nengman zhuyuan zuishengxin tuoluoni qiu wenchi fa 虛空藏菩薩能滿諸願最勝心陀羅尼求聞持法 [Vajrasattva Mantra for Fulfilling All Wishes and Empowering the Most Excellent Mind] describes a method for preparing a divine medicine, which must be prepared during a solar or lunar eclipse.37 The entire process described in the text is highly ritualistic, with detailed instructions. This divine medicine seems to primarily enhance people’s understanding and memory. In the Foshuo Da Molizhi pusa jing 佛說大摩里支菩薩經 [Sūtra of the Great Maudgalyāyana], another process for preparing a divine medicine is described. This medicine is even more miraculous: it is refined during a solar or lunar eclipse, and when ingested, it can make a person invisible.38 The Shengjiani fennu jin’gang tongzi pusa chengjiu yigui jing 聖迦柅忿怒金剛童子菩薩成就儀軌經 [Ritual Manual for the Holy Vajraketu Fierce Vajra Youth Bodhisattva] also describes a process for preparing a divine medicine that enables one to fly in the sky. The phrase ‘waiting for the time of the lunar eclipse, fast for three days from the thirteenth to the fifteenth day’ (候月蝕時，從十三日至十五日三日斷食)39 reveals that one must have the ability to predict the day of the lunar eclipse in advance, otherwise fasting cannot begin on the thirteenth day. Indian astronomy, which was introduced to Tang Dynasty China, excelled in predicting eclipses, so this was probably not difficult during the flourishing period of Esoteric Buddhism in 7th and 8th century India.

Similar descriptions of conducting rituals during solar and lunar eclipses to enhance spiritual practice effectiveness are found in other Buddhist scriptures as well. All these descriptions illustrate that ancient Indians had a thorough understanding of solar and lunar eclipses, and their astronomical knowledge enabled them to accurately predict the occurrence of eclipses, thereby providing support for the religious practices of Esoteric Buddhism, allowing these rituals to be conducted smoothly.

2.6. The Five Planets and the Seven Luminaries in the Buddhist Canon

Without exception, various ancient civilizations recognized the existence of five major planets. In Buddhist scriptures, the names of these five major planets can generally be divided into two categories. First, the use of the common names of the five planets in ancient China: Suixing 歲星 (Saturn), Yinghuo 營惑 (Jupiter), Zhenxing 鎮星 (Mars), Taibai 太白 (Venus), and Chenxing 辰星 (Mercury), or alternatively, Muxing 木星 (Jupiter, Wood star), Huoxing 火星 (Mars, Fire star), Tuxing 土星 (Saturn, Earth star), Jinxing 金星 (Venus, Metal Star), and Shuixing 水星 (Mercury, Water star); second, the transliteration of the names of the five planets from India and western regions into Chinese.

The names Suixing, Yinghuo, Zhenxing, Taibai, and Chenxing were the formal designations for the five major planets in ancient Chinese astronomy. Later, these five planets were associated with the five elements, and they were arranged in the order of the Five Phases, which is the sequence of Wood generating Fire, Fire generating Earth, Earth generating Metal, and Metal generating Water.

In Buddhist scriptures, there are various arrangements for the sequence of the five planets. The Renwang huguo bore boluomiduo jing 仁王護國般若波羅蜜多經 [Perfection of Wisdom Sūtra for Humane Kings Protecting Their Countries] lists the names of the five planets in the order of Wood, Fire, Metal, Water, and Earth.40 The Sheng yaomu tuoluoni jing 聖曜母陀羅尼經 [Sūtra of the Holy Mother of the Luminaries] also arranges them in the same order. The Qiyao rangzai jue gives the names and sequence of the five planets as Suixing, Yinghuo, Zhenxing, Taibai, and Chenxing.

In the Da weide jinlun foding chisheng guang Rulai xiaochu yiqie zainan tuoluoni jing 大威德金輪佛頂熾盛光如來消除一切災難陀羅尼經 [Sūtra of the Great Radiant Light of the Vajra Summit Buddha, the Extinguisher of All Calamities], the sequence of the five planets given is Metal, Wood, Water, Fire, and Earth. This sequence does not follow the Five Phases sequence, nor the sequence of the Five Phases generating and overcoming each other. However, it is the most commonly used sequence in colloquial speech for the five major planets, and it is actually arranged according to the average visual brightness of the five planets from brightest to darkest.41

In the Xiuyao jing, another different sequence for the five planets is given from fastest to slowest, namely Chenxing, Taibai, Yínghuo, Suixing, and Zhenxing, arranged in sequence. Here, the speed of the five planets refers to their apparent motion against the background of the fixed stars, for example, Jupiter orbits the sky once every 12 years, Mars orbits the sky once every 2 years, etc.42 Arranging the sequence of the five planets based on their speed of motion from fastest to slowest is essentially arranging them according to their distance from the sun, from nearest to farthest. In Esoteric Buddhist scriptures, various other arrangements of the sequence of the five planets are also found, but it is not necessary to elaborate on them here.

There are many details about the orbits and sizes of the five planets in the Qiyao rangzai jue. The astronomical table of the five planets in this Buddhist scripture is the most detailed description of the orbits of the five planets among many Buddhist scriptures. Before each section of the planetary tables, there is a general description of the names, sizes, and orbits of the respective planets. The Modengjia jing also provides a simple description of the orbital periods of the five planets. Except for the claim that Venus orbits the sky once every one and a half years, which is questionable—usually ancient beliefs consider Venus and Mercury to orbit the sky once a year—the orbital periods of the other four planets are consistent with those given in the Qiyao rangzai jue.

Regarding the diameters of the five planets, the Xiuyao jing provides the following: Taibai is ten yojanas in diameter, Suixing is nine yojanas, Chenxing is eight yojanas, Yinghuo is seven yojanas, and Zhenxing is six yojanas.43 Although the numerical values of the planetary diameters given in the Qiyao rangzai jue are different, they correspond to the sequence of the visual brightness of the planets in terms of Metal, Wood, Water, Fire, and Earth. The Fantian huoluo jiuyao 梵天火羅九曜 [*Skt. Brahmā Hora Navagraha; The Nine Luminaries of Indian Heaven] provides that the circumference of Saturn is ninety li, Mercury one hundred li, Venus one hundred li, the sun one thousand five hundred li, Mars seventy li, the moon one thousand five hundred li, and Jupiter one hundred li,44 which differs from the Qiyao rangzai jue, and provides the circumference values instead of the diameter values.

The diameter values of the five planets given in the Buddhist scriptures do not reflect the actual size of the planets but rather to some extent reflect their apparent brightness. In the Xiuyao jing, the five planets are arranged from ‘large’ to ‘small’, which corresponds to the usual verbal sequence of the five planets: Metal, Wood, Water, Fire, and Earth. These statements about the size of the planets indicate that ancient India noticed the different brightness of different planets and believed that the difference in brightness was due to the different sizes of the stars themselves. However, it is worth noting that in the Fantian huoluo jiuyao, the circumference of Saturn is greater than that of Mars, which seems to imply that size is not simply judged according to brightness.

The five major planets plus the sun and the moon are the most prominent seven celestial bodies in the sky, collectively referred to as the ‘seven luminaries’ (qiyao 七曜). The term ‘seven luminaries’ within Buddhist sūtras first appeared in ‘Shuo xingtu pin’ contained within juan 1 of Modengjia jing, translated by Zhu Lüyan 竺律炎 (d.u.) and Zhi Qian 支謙 (fl. 223–253) during the Wu 吳 Dynasty of the Three Kingdoms 三國 (222–280).45 It also mentioned the seven luminaries in the section ‘Mingshi fenbie pin’ within the second juan of the same scripture.46 In addition, the meaning of the seven luminaries was explicitly stated in the Da fangdeng daji jing (T no. 397), translated by the Indian trepiṭaka Naliantiyeshe 那連提耶舍 (Narêndrayaśas; 517–589) during the Northern Qi Dynasty 高齊 (550–577): ‘The so-called luminaries, there are seven kinds, namely the sun, the moon, Venus, Jupiter, Mercury, Mars, and Saturn’ (言曜者，有於七種，一者日、二者月、三者營惑星、四者歲星、五星鎮星、六者辰星、七者太白星).47

In the Xiuyao jing, it is mentioned that the stars of the sun, moon, and five planets take turns in presiding over good and bad events, which is the origin of the still prevailing system of the week.48 During the Tang Dynasty, due to the developed communication between China and the West, the Western system of a seven-day week had already been introduced to China. In Chang’an, there were also areas where Persians, Indians, and Central Asians lived together, and it was common to hear them referring to the days of the week by the names of the seven luminaries.

Additionally, the Fantian huoluo jiuyao also provides alternative names for the seven luminaries, namely: Tuxing 土星, Jihuan 雞緩; Shuixing 水星, Dixing 滴星; Jinxing 金星, Najie 那頡; Taiyang 太陽, Mi 密; Huoxing 火星, Xuhan 虛漢; Taiyin 太陰, Mu 暮; and Muxing 木星, Womosi 嗢沒斯. These are the names for the seven luminaries used by the Central Asian peoples during the Tang Dynasty.

As a collective term for the sun, moon, and five planets, the seven luminaries also frequently appear as a whole recitation name in Esoteric Buddhist scriptures. In most ritual and mantra scriptures, there are mantras related to the seven luminaries, and reciting such mantras can achieve specific purposes of salvation or supplication.

2.7. Rāhu, Ketu, and the Nine Luminaries in the Buddhist Canon

In addition to the sun, moon, and five planets, Rāhu and Ketu together constitute the so-called nine ‘grabbing’ (Jiuzhi 九執) (or nine luminaries [Jiuyao 九曜]). Juan 4 of Da piluzhe’na chengfo jing shu 大毗盧遮那成佛經疏 [Commentary on the Mahāvairocana Sūtra], describes them as follows: the nine luminaries consist of the seven planets, namely, the sun, moon, Mars, Mercury, Jupiter, Venus, Saturn, and also Rāhu and Ketu, totaling nine luminaries.49 The same text in juan 17 also mentions that in Sanskrit, it is called Bālīka (Bolihe 檗哩何), translated as ‘nine grabbing’.50 In Sanskrit, nine grabbing is known as Navagraha, referring to the nine deities that influence celestial phenomena.

In fact, the ‘Shuo xingtu pin’ section of juan 5 of Modengjia jing, translated as early as the Eastern Wu period, had already defined the nine luminaries: ‘Now, I will explain to you the seven celestial bodies: the sun, moon, Mars, Jupiter, Venus, Saturn, and Mercury are called the seven, and Rāhu and the comet, together, are called the nine’ (今當為汝復說七曜：日、月、熒惑、歲星、鎮星、太白、辰星、是名為七，羅睺、彗星，通則為九) (see Note 45). The ninth celestial body among the nine luminaries was referred to as the ‘comet’ (hui 彗) The commentary on the Mahāvairocana Sūtra in juan 4 also lists Rāhu and the comet together.51 In the Beidou qixing humo fa 北斗七星護摩法 [Procedures for the Fire Ritual for the Seven Stars of the Big Dipper], the monk Yixing 一行 (683–727) explained it as follows: ‘Ketu, translated as a banner. A banner refers to a comet. Rāhu refers to the deity of conjunction and eclipse’ (計都者，翻為旗也。旗者，彗星也。羅睺者，交會蝕神也).52 Ketu is Sanskrit for ‘banner’ (qi 旗) and its original meaning in Sanskrit includes both ‘banner’ and ‘comet.’ Therefore, ‘Ketu’ is a transliteration, and ‘comet’ is a translation. The Qiyao rangzai jue mentions that Ketu is also known as ‘moon boli’ (Yue boli 月孛力), with ‘bo’ 孛 being a type of comet mentioned in ancient Chinese texts. In many Esoteric Buddhist scriptures, Ketu is translated as huixing 彗星 (comet), huibo 彗孛 (bo comet), or changwei xing 長尾星 (long tailed star), but they all refer to Ketu when listed as one of the nine luminaries.

Apart from descriptions of Rāhu and Ketu in texts such as the Qiyao rangzai jue that closely align with their astronomical meanings, in many other Esoteric Buddhist scriptures, when Rāhu, Ketu, or the nine luminaries are mentioned, they are mostly treated as one group of important celestial deities for chanting.

The Buddhist scriptures mentioned above that discuss Rāhu, Ketu, or the nine luminaries belong to the Esoteric Buddhist canon. Texts outside the Esoteric Buddhist canon rarely mention Rāhu, Ketu, and the nine luminaries. This indicates that the concept of the nine luminaries was introduced into China with the spread of Esoteric Buddhism, and in many cases, it was treated only as a symbol of astrology. The aforementioned Buddhist scriptures were translated during the middle to late Tang Dynasty and early Song Dynasty, suggesting that the concept of the nine luminaries was introduced on a large scale during the middle to late Tang Dynasty.

2.8. Planetary Ephemerides in the Buddhist Canon

Planetary ephemerides in Esoteric Buddhist scriptures primarily appear in the Qiyao rangzai jue. This scripture directly presents the tables of the five major planets (wuda xingxing 五大行星), Rāhu, and Ketu in numerical form. Each table provides the celestial coordinates for a heavenly body in a certain constellation and degree for each month. The tables also mark the dates and positions on the ecliptic for the planets’ invisibility, visibility, direct motion, and retrograde motion. The ephemerides for Jupiter span 83 years, for Mars 79 years, for Saturn 59 years, for Venus 8 years, for Mercury 33 years, for Rāhu 93 years, and for Ketu 62 years.53 Here, the length in years of a certain planetary ephemerides is equal to the sum of the planet’s sidereal periods and synodic periods. For Jupiter, as an example, there are 7 sidereal periods and 76 synodic periods in 83 years. This quantitative relationship can be traced back to Indian and Babylonian astronomy (Pingree 1981).

By utilizing modern accurate astronomical tables, an analysis of the precision in both position and time of the planetary tables and Rāhu and Ketu tables in the Qiyao rangzai jue yields the following results (

Table 1. The precision of the positions of the Five Star Calendar in Qiyao rangzai jue.

Planet	Mean Error of Stationary Point	Mean Square Error of Stationary Point	Mean Error of Concealing and Appearing Position	Mean Square Error of Concealing and Appearing Position
Jupiter	−0.41°	1.29°	−0.47°	1.89°
Mars	1.00°	6.34°	−2.45°	15.11°
Saturn	−0.39°	1.72°	−0.38°	1.70°
Venus	−0.98°	5.65°	0.23°	11.68°
Mercury	—	—	−1.13°	6.95°

and

Table 2. The precision of the times of the Five Star Calendar in Qiyao rangzai jue.

Planet	Mean Error of Stationary Point	Mean Square Error of Stationary Point	Mean Error of Concealing and Appearing Time	Mean Square Error of Concealing and Appearing Time
Jupiter	−3.14 days	6.25 days	−3.57 days	2.38 days
Mars	−1.61 days	6.71 days	−5.20 days	15.58 days
Saturn	−3.89 days	3.32 days	−2.93 days	1.94 days
Venus	−0.80 days	7.05 days	−3.85 days	6.72 days
Mercury	—	—	−1.04 days	7.50 days

):

Additionally, the mean positional error for Rāhu in the table is −3.4° with a mean square error of 1.2°, while for Ketu, the mean positional error is −5.7° with a mean square error of 1.3°.

The precision mentioned above generally aligns with the accuracy of planetary tables during the era of visual observation, supporting the functionality of the Qiyao rangzai jue as a practical astrological handbook.

3. The Preservation Characteristics of Astronomical Data in the Buddhist Canon

A prominent feature of the preservation of astronomical data in Buddhist scriptures is its integration with astrology. Astronomy and astrology have inherently intricate connections. Although early Buddhism generally prohibited the study of astrology among its followers, by the time Buddhism reached the stage of Esoteric Buddhism, this barrier had been completely eliminated. Some Buddhist scriptures, especially those classified as ritual texts and Esoteric scriptures in the Esoteric Buddhist tradition, serve the purpose of facilitating rituals for disaster relief, which essentially serves the broader objectives of astrology.

Some Esoteric Buddhist scriptures appear entirely as astrological documents based on their titles. For instance, the Qiyao rangzai jue conveys its purpose as utilizing the movements of the sun, moon, and the five planets to forecast and mitigate disasters. Regardless of its astrological purpose, the descriptions of the movements of the five planets and the tables provided for their positions, as well as the positions of Rāhu and Ketu, are invaluable to ancient Indian astronomical data. Similarly, the Xiuyao jing contains rich astronomical data, including information on the Indian constellation system, the twelve houses of the zodiac, and knowledge about the sun, moon, and five planets. However, the title of this scripture, ‘Wenshushili pusa ji zhuxian suoshuo jixiong shiri shan’e xiuyao jing’ 文殊師利菩薩及諸仙所說吉凶時日善惡宿曜經 [Sūtra Spoken by Bodhisattva Mañjuśrī and Various Devas on Auspicious and Inauspicious Times and Days and Good and Evil Nakṣatras and Planets], indicates its purpose of elucidating the auspiciousness and inauspiciousness of specific days and planets for human activities, undoubtedly making it a work of the astrological literature.

Under the overarching characteristic of serving astrology, the preservation of different astronomical content in Esoteric Buddhist scriptures also exhibits distinct features. Some scriptures directly preserve ancient astronomical data, while astronomical knowledge in certain Buddhist scriptures is embedded in the narrative more indirectly and subtly.

Astronomical knowledge in Buddhist scriptures often gets disseminated in a way that integrates with Buddhist principles. After all, the ultimate goal of Buddhist scriptures is to propagate the Dharma. Therefore, even when astronomical content is mentioned in Buddhist scriptures, it is often used to elucidate Buddhist principles more explicitly. For example, in juan five of Foshuo da bonihuan jing 佛說大般泥洹經 [Sutra on the Great Nirvana], a lunar eclipse is used to illustrate the unchanging nature of the Tathāgata’s dharmakāya (Rulai fashen 如來法身), emphasizing the permanence of the Tathāgata’s Dharma.54 Similarly, in the Xiangtou jingshe jing 象頭精舍經 [Sutra of the Elephant’s Head Hermitage], the lunar phases from the first to the fifteenth day are metaphorically used to describe the process of spiritual cultivation and the states attained.55

Of course, in the above examples, astronomical concepts are only used metaphorically for explanatory purposes. In some cases, astronomical content itself becomes part of Buddhist theoretical discussions, particularly in the integration of Buddhist cosmology with cosmological theories. For instance, in juan 16 of Abidamo zang xianzong lun 阿毗達磨藏顯宗論 [Skt. *Abhidharma-samayapradīpikā, *Abhidharma-piṭaka-prakaraṇa-śāsana-śāstra or *Abhidharmakośa-śāstra-kārikā-vibhāṣya; Treatise Clarifying the Tenets of the Abhidharma Treasury], a Buddhist cosmological diagram is described, starting from the movements of the sun and moon, discussing the alternation of day and night, the changes in the length of day and night, and extending to the abodes of celestial beings, accompanied by extensive descriptions of Buddhist cosmology.56 It presents a vividly Buddhist worldview, with astronomical content being an integral component. In Esoteric Buddhist scriptures, Buddhist theories are intricately combined with astrology and astronomy. From the distribution of astronomical data in Buddhist scriptures, it is evident that a substantial amount of data appears in Esoteric Buddhist scriptures.

4. The Reliability of Astronomical Data in the Buddhist Canon

We believe that the astronomical data in the Buddhist scriptures are reliable, and this reliability can be explained from two perspectives.

Firstly, from the perspective of textual preservation, the Chinese Buddhist canon has been well preserved. Although there may have been some transcription errors due to copying, the act of transcribing Buddhist scriptures was considered a meritorious deed by Buddhists, especially when they transcribed scriptures with devout faith, as the possibility of errors was minimized. Therefore, we can essentially affirm that the Chinese-translated Buddhist scriptures we see today are essentially the same as they were when they were originally translated.

Secondly, from the perspective of Buddhist scripture translation, many of the translators involved in the translation of Buddhist scriptures into Chinese had a good grasp of astronomical knowledge at that time. This can be inferred from some biographical materials about these translators. For example, from the Gaoseng zhuan 高僧傳 [Biographies of Eminent Monks], we see that An Qing 安清 (i.e., An Shigao 安世高, active during the 140s–160s) was proficient in knowledge of the ‘Seven Luminaries and Five Elements’ (Qiyao wuxing 七曜五行)57; Tankejialuo (Tankāra 曇柯迦羅; active in the 220s–250s) had a command of the study of ‘star maps and their changes’ (星宿圖讖運變)58; Kāng Senghui 康僧會 (?–280) was knowledgeable about ‘astronomical charts and diagrams’ (天文圖緯)59; Tanwuchen 曇無讖 (Dharmakṣema; 385–433) had a clear understanding of ‘mantras and incantations’ (明解咒術)60; Jiumoluoshi (Kumārajīva 鳩摩羅什; 344–413) was highly skilled in ‘yinyang astrology’ (陰陽星算)61; Qiunabatuoluo 求那跋陀羅 (Guṇabhadra; 394–468) had learned various treatises of Wuming 五明 (Five clarities) since childhood and was proficient in astronomy, arithmetic, medicine and incantations, etc.62; Qiunapidi 求那毗地 (Guṇavṛddhi; ?–502) had a clear understanding of ‘yinyang’ and was skilled in divination63; Junaluotuo 拘那羅陀 (Paramārtha or Zhendi 真諦, 499–569) was extremely knowledgeable and renowned for his expertise64; and Putiliuzhi 菩提流志 (Bodhiruci; 572–727) was well versed in ‘calendars, numerology, yinyang, and divination’ (曆數咒術，陰陽讖緯).65

The likes of Kumārajīva, Guṇabhadra, Paramārtha, etc., were renowned translators. The Gaoseng zhuan was written during the Southern Liang Dynasty, recording the early translation situation. Translation reached its peak during the Tang Dynasty. The famous monk Yi xing was proficient in both astronomy and calendar calculation, and the ‘Dayan Calendar’ (Dayan li 大衍曆) he constructed was one of the best calendars in the history of calendrics, and he translated a large number of Buddhist scriptures.

Due to the work of these translators who were knowledgeable in astronomy, it can be inferred that the astronomical data in the existing Chinese-translated Buddhist scriptures were accurately translated from the original texts.

5. Limitations of Astronomical Data in the Buddhist Canon

It is undeniable that the astronomical data in the Buddhist canon have their limitations. Astronomy in the Buddhist canon is either intertwined with Buddhist philosophy or associated with astrology. For example, the cosmological content in the Buddhist canon closely aligns with the propagation of Buddhist worldview. The astronomical content appearing in the Buddhist canon sometimes serves as a means to elucidate Buddhist doctrine, sometimes as a tool to determine the precise timing of religious rituals, and sometimes even as a subject of criticism. Therefore, the astronomical content in Buddhist scriptures is subject to certain restrictions. Serving astrology and elucidating doctrine is both the reason why astronomy can be preserved in the Buddhist canon and the reason why it is limited.

The limitations of astronomical data in the Buddhist canon are also related to the religious views of certain Buddhist sects. For example, in the Da boniepan jing 大般涅槃經 [Skt. Mahāparinirvāṇa-sūtra; Nirvana Sūtra], it is mentioned that some Buddhist monks at the time were knowledgeable in astronomy and astrology.66 However, some Buddhist sects believe that for Buddhist monks, practices such as astrology, crafts, and skillful activities are as sinful as eating fish and meat. Only by abstaining from these sinful activities can one be considered a true disciple of the Buddha.

Buddhism refers to other religious sects such as Brahmanism as ‘outsiders’. From the records in the Buddhist canon, it is known that most Brahmanic outsiders were knowledgeable in astronomy and calendrical calculation. For example, in the Lianhua mian jing 蓮花面經 [Sūtra of the Monk Lotus Face], it is mentioned that a Brahmanic disciple named Lotus Face 蓮花面 was intelligent and knowledgeable, mastering the knowledge of the twenty-eight constellations and the degrees of the five planets.67 Juan 2 of Genben shuoyiqieyoubu pi’naiye zashi 根本說一切有部毗奈耶雜事 [Skt. Mūlasarvāstivāda-vinayakṣudrakavastu] mentions the outsiders being ‘good at calendar calculating’ 善明曆數 at that time.68 The Buddha did not allow his disciples to engage with other disciplines such as astronomy and astrology in order to focus on Buddhism. This is explicitly stipulated in the Vinayas; for example, it is stated in the Da Aidao biqiuni jing 大愛道比丘尼經 [Sūtra on the Bhikṣuṇī Mahāprajāpatī] ‘throughout his life, he must not say whether the day is good or bad, and divining the auspiciousness and inauspiciousness, observing the sky, calculating the calendar and eclipse, fortunetelling through celestial phenomena, ......all of these are prohibited.’ (盡形壽，不得說道日好日不好，占視吉凶，仰觀曆數、推布盈虛、日月薄蝕、星宿變殞……一不得知).69 This regulation extensively prohibits bhikṣuṇīs engaging in astronomical and astrological activities, thus prohibiting the learning and dissemination of astronomical knowledge. This prohibition had a negative effect at the time. According to the first volume of Genben shuoyiqieyoubu nituona 根本說一切有部尼陀那 [Skt. Mūlasarvāstivāda Vinaya], the prohibition on studying astronomy and calendrical calculation resulted in Buddhist disciples not knowing the current date. When the Buddha allowed them to study these subjects, it caused a disturbance and diverted them from their practice of good deeds. Later, the Buddha came up with a compromise solution, specifying that only the chief monk should learn about the stars and calendar days, and others should not learn.70

In the Mohe sengqi lü da biqiu jieben 摩訶僧祗律大比丘戒本 [Skt. *Mahāsāṃghika-pratimokṣa-sūtra], the so-called ‘six memorization methods’ (liunian fa 六念法) are stipulated, among which the first method is ‘knowing the dates of the sun and moon, the first day, the second day, up to the fourteenth and fifteenth days, big month or small month, one should know them all’ (當知日數月，一日、二日及至十四日、十五日，月大月小悉應知).71 Although this somewhat relaxed the prohibition on studying astronomy, it was limited to learning the arrangement of calendars.

In the later period of Buddhism, as it gradually merged with Brahmanism to form Esoteric Buddhism, what was originally considered the study of outsiders by Buddhism was also accepted. The Da boniepan jing mentions books about ‘solar and lunar eclipses, and the changes in celestial phenomena’ (日月薄蝕、星宿運變) that were previously unseen but are now available.72

The introduction of Esoteric Buddhism into China can be said to have occurred almost simultaneously with the arrival of Buddhism in China. Many of the early translators who came to China were Brahmins or converted from Brahmanism to Buddhism. By the middle of the Tang Dynasty, Esoteric Buddhism had reached its peak in China. Esoteric Buddhist scriptures contain more astronomical content, which is fortunate for the preservation of Indian astronomical data.

6. Conclusions

Ancient civilizations around the world have developed distinct astronomy systems which served as important components in their respective cultures and facilitated exchanges and dissemination between different ancient civilizations. American historian of astronomy David Pingree (1933–2005) once likened ancient astronomy–astrology to a great tree, with its main roots deeply buried in the deserts of Mesopotamia, its secondary roots extending deeply into Egypt and China, and its branches branching out from Babylon to Egypt, Greece, Syria, Iran, India, and China. They were grafted onto the cultural trunks of different civilizations, growing different leaves, shoots, and flowers (Pingree 1992, p. 563). The astronomical data in the Buddhist canon discussed in this article aligns with Pingree’s depiction of the cultural exchange between eastern and western astronomy–astrology, confirming each other’s perspectives.

The astronomical knowledge in the Buddhist canon originates directly from Indian civilization, but some knowledge can be traced back to Babylonian and Greek civilizations. They spread to China through the Silk Road and interacted with indigenous Chinese astronomy. The study of astronomical data in the Buddhist canon helps us understand the position of ancient Chinese civilizations in the history of world civilization. It also provides concrete examples to illustrate that human civilization has never developed in isolation or in a closed state, revealing the core meaning of the historical view of technological and cultural exchange: knowledge advances through dissemination, and civilization flourishes through communication.