Nalanda, in eastern India's Bihar state, was once the most important Buddhist monastery in the world. The six excavated temples there are oriented approximately to the cardinal directions, but their east–west axes are tilted more than 4° south of east. Other key Buddhist temples within the same cultural milieu (Bodhgaya, Vikramasila, Somapura, and Samye) are similarly oriented a few degrees south of east. As M. B. Rajani and Viraj Kumar argue in Nalanda: A Tale in the Twist, this demands an explanation, because a method to orient structures to within 0.5° of the cardinal directions was known in the region for several centuries prior to the construction of these temples. Rajani and Kumar identify a temporal pattern in the orientation of Nalanda's temples; hypothesize that each temple was aligned with the rise of a specific star (Spica or Beta Librae), with the temporal pattern being a consequence of axial precession; propose a simple, unified explanation for the few exceptions to the pattern; and use this hypothesis to propose an approximate construction date for each temple based on its orientation.

Nalanda was a Buddhist residential monastery located in the ancient kingdom of Magadha, in modern-day Bihar state in northeast India, active from the fourth/fifth century CE until at least the end of the twelfth century.1 Although this site was not associated with the life of Buddha, its importance is evident from the fact that it attracted monks from as far away as China (e.g., Xuanzang spent some twelve years there in the seventh century) and received patronage not only from within India but also from such distant lands as Sumatra (whose king funded a monastic dwelling there).2 The Archaeological Survey of India has excavated and protected six temples, or chaityas, at this site: a row of four temples (T3, T12, T13, and T14) to the west, one (T2) to the east, and Sarai Temple further east (Figure 1).3 

Figure 1

Nalanda, Bihar, India, fourth–twelfth centuries CE, satellite view showing temple orientation angles (Google, CNES/Airbus).

Figure 1

Nalanda, Bihar, India, fourth–twelfth centuries CE, satellite view showing temple orientation angles (Google, CNES/Airbus).

When these structures are seen from the air, a slight skew in their orientations is immediately evident.4 This article is the first to measure that skew and attempt to explain it.5 We hypothesize that each temple was oriented prior to its construction through careful alignment of its east–west axis to the rise of a particular star: either Spica or Beta Librae.

Primary sources discussing the construction of ancient Indian monuments are generally quite scarce, and no ancient source of which we are aware records whether or how the temples at Nalanda were oriented. Further, no modern study has offered convincing dates for the construction of the temples. It is difficult to date these structures with precision for two reasons. First, extensive conservation work has obscured each monument's surfaces, making it difficult for researchers to collect samples of the original building material.6 Second, previously excavated material has not been documented well enough to allow for accurate dating or attribution to particular structures.7 An important consequence of our orientation hypothesis is that it allows us to calculate the approximate year in which each temple at Nalanda was oriented—presumably just prior to its construction.8 

There was a regular exchange of ideas—facilitated by monks, who often traveled long distances—between places of importance in South and Southeast Asia during the period from a few centuries BCE to well beyond the first millennium CE, and it is possible that the methods we propose for orienting sacred structures at Nalanda were employed at other sites.9 Since these methods may or may not have originated at Nalanda, we have attempted to determine the orientations of both older and newer temples. For this study, we have selected buildings that satisfy three criteria: they are sacred structures linked to Nalanda through evidence of interactions; they have orientations similar to those of the temples at Nalanda; and they are relatively large and sufficiently intact, with east–west orientations that can be estimated by our technique, described below, using satellite imagery.

For each selected temple, we use satellite imagery to identify a pair of well-defined and near-parallel linear features flanking the temple's center symmetrically to the north and south. We can accurately measure the orientations of such features, and their average provides an estimate of the structure's orientation. Of the temples satisfying the first two criteria, our technique can estimate the orientations of nine, including five of the six at Nalanda. The exception is T3, probably the oldest of temple at Nalanda, a towering brick structure located at the southwestern end of the site. It was constructed in seven successive phases, and its orientation appears to have changed several times over multiple rebuilds (Figure 2).10 We exclude it because we are unable to identify a flanking pair of near-parallel linear features to use in estimating its orientation (Figure 3).11 We do include four other major Buddhist temples: Mahabodhi at Bodhgaya and Vikramasila in India, Somapura in Bangladesh, and Samye in Tibet (Figures 4 and 5). Although they are architecturally diverse, these nine temples were part of a widespread cross-cultural exchange network. We hypothesize that they were deliberately oriented using a common orientation method.12 

Figure 2

T3, Nalanda, Bihar, India, fourth–twelfth centuries CE, north side (photo by Kuili Suganya).

Figure 2

T3, Nalanda, Bihar, India, fourth–twelfth centuries CE, north side (photo by Kuili Suganya).

Figure 3

Nalanda, Bihar, India, fourth–twelfth centuries, synoptic view of T3 and orientations of three linear features (Google, Digital Globe).

Figure 3

Nalanda, Bihar, India, fourth–twelfth centuries, synoptic view of T3 and orientations of three linear features (Google, Digital Globe).

Figure 4

Mahabodhi, Samye, Vikramasila, and Somapura temples, India, fifth–eighth centuries CE, satellite views (Google, Digital Globe; CNES/Airbus).

Figure 4

Mahabodhi, Samye, Vikramasila, and Somapura temples, India, fifth–eighth centuries CE, satellite views (Google, Digital Globe; CNES/Airbus).

Figure 5

Map showing all locations cited in this study (map by authors, QGIS).

Figure 5

Map showing all locations cited in this study (map by authors, QGIS).

Nalanda's Temples and Associated Structures

In January 1812, Francis Buchanan, a Scottish physician, surveyed the ruins at the site that would later be identified as Nalanda.13 “Though he [Buchanan] describes what he saw in considerable detail,” writes the art historian Frederick Asher, “the modern reader would have some difficulty in associating specific monuments at Nalanda with anything he records.”14 Published versions of Buchanan's handwritten diary have omitted his freehand sketches, which add considerable clarity to his text (Figure 6). He referred to the bricks and other debris from collapsed building superstructures as “heaps.” Some of these building materials were recycled at nearby settlements in later centuries, and only portions of the superstructure and the plinth remained intact within each heap.15 These were exposed during subsequent excavations, and large portions of the superstructures we see today were reconstructed using modern bricks of the same dimensions as the originals.16 

Figure 6

Francis Buchanan, sketch of ruins at Nalanda from his journal, January 1812 (MSS EURD87, p. 127, British Library).

Figure 6

Francis Buchanan, sketch of ruins at Nalanda from his journal, January 1812 (MSS EURD87, p. 127, British Library).

Temples T12, T13, and T14 face east and lie nearly equidistant from each other along a north–south axis. The largest of these is T12, with small shrines at each of the four corners of a square plan measuring about 52 meters by 50 meters. This brick building was constructed in two phases and is covered with stucco adornments (Figure 7). Like Mahabodhi at Bodhgaya, T12 has several miniature stupas made of stone and brick, all of which are located on its southern side. Some scholars have suggested that T12 had a superstructure similar to Mahabodhi, but Asher asserts that there is no way to know how T12's superstructure originally looked.17 T13 and T14 are elevated on squarish plinths whose sides measure approximately 52 meters and 50 meters, respectively, and both appear to have been built in two phases (Figure 8). There were huge stucco images, probably of Buddha, at both temples. The Buddha at T14 was seated, and only its lowermost portions and platform remain. T12 likely predates T13 and T14.18 The remaining temples at Nalanda are situated toward the east of the site. T2's plinth, measuring 36 meters by 31 meters, is adorned with about two hundred sculptural panels carved of stone (Figure 9); Sarai Temple, the most recently excavated, is a brick structure that once enshrined a huge standing image of Buddha.

Figure 7

T12, Nalanda, Bihar, India, fourth–twelfth centuries CE, northeast corner (photo by Kuili Suganya).

Figure 7

T12, Nalanda, Bihar, India, fourth–twelfth centuries CE, northeast corner (photo by Kuili Suganya).

Figure 8

T13 (top) and T14 (bottom), Nalanda, Bihar, India, fourth–twelfth centuries CE, east sides (top, photo by Kuili Suganya; bottom, authors' photo).

Figure 8

T13 (top) and T14 (bottom), Nalanda, Bihar, India, fourth–twelfth centuries CE, east sides (top, photo by Kuili Suganya; bottom, authors' photo).

Figure 9

T2, Nalanda, Bihar, India, fourth–twelfth centuries CE, southeast corner (authors' photo).

Figure 9

T2, Nalanda, Bihar, India, fourth–twelfth centuries CE, southeast corner (authors' photo).

The Mahabodhi shrine at Bodhgaya marks the site where Buddha is said to have attained enlightenment. It is therefore the most important of the four main sites connected to his life.19 It has been a major pilgrimage destination for well over two thousand years. The main shrine is made of brick covered with stucco, tapering from a square base and rising to about 55 meters, with four smaller shrines at each corner. The structure seen at Bodhgaya today has been renovated many times, but its orientation is likely unchanged since it was first built in the fifth/sixth century CE.20 The main shrine is surrounded by several smaller stupa-like structures made of brick and stone (Figure 10).

Figure 10

Mahabodhi, Bodhgaya, India, fifth–sixth centuries CE, east side (photo by Kuili Suganya).

Figure 10

Mahabodhi, Bodhgaya, India, fifth–sixth centuries CE, east side (photo by Kuili Suganya).

At Nalanda and Bodhgaya, the dwelling spaces (monasteries) are in buildings distinct from the sacred shrines. In contrast, at both Vikramasila and Somapura the monastic cells form a quadrangle around the main stupa (a brick structure laid in mud mortar). Vikramasila's two-terraced stupa is cruciform in plan (Figure 11). It is raised about 15 meters above ground level and accessed via a flight of steps on the north side. Protruding chambers are located in the four cardinal directions; these once housed colossal stucco images of seated Buddhas. Somapura is similar in organization and form, but it has a slightly smaller ground plan than Vikramasila (see Figure 4), and the superstructure of its central monument is slightly taller. Both Vikramasila and Somapura were constructed by Dharmapala, the second king in eastern India's Pala dynasty, who lived from ca. 770 to 821 CE.21 Pala kings also patronized Nalanda between the eighth and twelfth centuries CE. Judging by its design, Vikramasila was likely built before Somapura.22 

Figure 11

Vikramasila, India, eighth century CE (authors' photos).

Figure 11

Vikramasila, India, eighth century CE (authors' photos).

Odantapuri was the first Pala monastic establishment, but its physical remains have not yet been conclusively identified.23 It played a role in introducing Buddhism into Tibet and influencing the architecture of Samye, Tibet's first Buddhist monastery.24 Samye also has a central shrine surrounded by a monastic quadrangle, with stupas at each corner separated from the quadrangle. Reliable sources date the construction of Samye to around 775 or 779 CE.25 

Measuring Temple Orientations

Measuring the orientation of the east–west axis for any of these nine temples presents difficulties. The first requirement is to identify a straight wall several meters in length. A single brick or a short wall segment may have been restored or recently plastered and may therefore be oriented differently from the overall structure. Vikramasila, Somapura, and the six temples at Nalanda are all restored ruins of partial structures, so it is hard to find intact wall segments of sufficient length to obtain ground-based measurements accurate enough to determine orientation. Mahabodhi and Samye are functioning temples with many ancillary structures built around them, which makes accurate measurements relating to their orientations difficult to obtain.

High-resolution satellite imagery has been used effectively for measuring the orientations of ancient structures in Egypt and China.26 In our study, we used high-resolution satellite images from Google Earth to measure the east–west axis orientations of the nine temples. For accuracy, we identified and measured the orientations of straight lines at least 30 meters long at each temple that align with surviving remnants of an east–west wall or the plinth. Since satellite images can be georeferenced, an added advantage is that geographical north can be established more accurately on these images than at ground level.27 

To minimize measurement error at each site, we examined all available Google Earth images and selected the ones closest to the nadir or direct vertical view; images taken at oblique angles distort the geometry. We made our selections visually, based on the parallax created by tall buildings present in the vicinity of each site. To estimate the orientation of each structure, we identified two near-parallel linear features (walls or plinths) that flank it symmetrically to its north and south and then measured their east–west orientations using AutoCAD. We report the average of these two values as the measured orientation of the central structure for each temple in Table 1.28 An orientation angle of 90° would correspond to an axis perfectly aligned to the cardinal directions east and west.

Table 1
Orientation, Location, and Estimated Date of Construction for the Nine Temples, Based on Available Evidence
SiteLatitudeLongitudeTempleOrientation of East–West Axis (Degrees From True North)Estimated Date of Construction
Nalanda 25.138 85.443 T14 98.1010 Possibly after T13 
T13 95.4630 Possibly after T12 
T12 94.6965  
T2 94.2095  
Sarai T. 96.7300  
Bodhgaya 24.696 84.992 Mahabodhi main temple 95.2070 Fifth century CE (superstructure renovated repeatedly) 
Vikramasila 25.324 87.285 Central chaitya/stupa 98.3925 Between 770 and 821 CE 
Somapura 25.031 88.977 Central chaitya/stupa 96.4845 Between 770 and 821 CE 
Samye 29.327 91.503 Central shrine 98.8215 775 or 779 CE 
SiteLatitudeLongitudeTempleOrientation of East–West Axis (Degrees From True North)Estimated Date of Construction
Nalanda 25.138 85.443 T14 98.1010 Possibly after T13 
T13 95.4630 Possibly after T12 
T12 94.6965  
T2 94.2095  
Sarai T. 96.7300  
Bodhgaya 24.696 84.992 Mahabodhi main temple 95.2070 Fifth century CE (superstructure renovated repeatedly) 
Vikramasila 25.324 87.285 Central chaitya/stupa 98.3925 Between 770 and 821 CE 
Somapura 25.031 88.977 Central chaitya/stupa 96.4845 Between 770 and 821 CE 
Samye 29.327 91.503 Central shrine 98.8215 775 or 779 CE 
Table 2
Date Ranges for Somapura's Construction for Varying Cumulative Error, Based on Assumed Altitudes of Spica and Beta Librae for Temple Orientation All Dates CE)
Altitude of Spica at SomapuraAltitude of Beta Librae at Somapura
Error e (degrees)
0.05 879 to 897 798 to 815 717 to 734 865 to 885 769 to 789 674 to 694 
0.10 871 to 905 790 to 823 709 to 743 855 to 895 759 to 799 664 to 704 
0.15 863 to 913 781 to 831 701 to 751 846 to 905 750 to 809 655 to 713 
0.20 855 to 921 773 to 839 693 to 759 836 to 914 740 to 818 645 to 723 
0.25 847 to 929 765 to 847 685 to 767 826 to 924 730 to 828 635 to 733 
Altitude of Spica at SomapuraAltitude of Beta Librae at Somapura
Error e (degrees)
0.05 879 to 897 798 to 815 717 to 734 865 to 885 769 to 789 674 to 694 
0.10 871 to 905 790 to 823 709 to 743 855 to 895 759 to 799 664 to 704 
0.15 863 to 913 781 to 831 701 to 751 846 to 905 750 to 809 655 to 713 
0.20 855 to 921 773 to 839 693 to 759 836 to 914 740 to 818 645 to 723 
0.25 847 to 929 765 to 847 685 to 767 826 to 924 730 to 828 635 to 733 
Table 3
Linear Models for the Nine Temples
TempleLinear Model z = a + by (z = Azimuth of Spica at 3° Altitude in Year y)Linear Model z = a + by (z = Azimuth of Beta Librae at 4° Altitude in Year y)
Nalanda (all temples) z = 91.513 + (0.006180)y z = 92.455 + (0.00519)y 
Mahabodhi z = 91.485 + (0.006158)y z = 92.417 + (0.00517)y 
Samye z = 91.775 + (0.006424)y z = 92.832 + (0.00539)y 
Vikramasila z = 91.524 + (0.006190)y z = 92.564 + (0.00517)y 
Somapura z = 91.507 + (0.006175)y z = 92.448 + (0.004997)y 
TempleLinear Model z = a + by (z = Azimuth of Spica at 3° Altitude in Year y)Linear Model z = a + by (z = Azimuth of Beta Librae at 4° Altitude in Year y)
Nalanda (all temples) z = 91.513 + (0.006180)y z = 92.455 + (0.00519)y 
Mahabodhi z = 91.485 + (0.006158)y z = 92.417 + (0.00517)y 
Samye z = 91.775 + (0.006424)y z = 92.832 + (0.00539)y 
Vikramasila z = 91.524 + (0.006190)y z = 92.564 + (0.00517)y 
Somapura z = 91.507 + (0.006175)y z = 92.448 + (0.004997)y 

Among the three neighboring temples at Nalanda—T12, T13, and T14—T12 is probably the oldest and T14 the newest. The orientation angles of these three temples increase from T12 (94.697°) to T13 (95.463°) to T14 (98.101°). This pattern—with older temples oriented closer to the cardinal directions than newer temples—holds for several other pairs of temples, including Mahabodhi (fifth/sixth century CE) and Somapura (ca. 770 to 821 CE), but is violated by Vikramasila and Somapura, whose orientations differ by more than 1.9°. We believe that both this pattern and the exceptions to it are significant and explainable.

Celestial Alignments

Several ancient civilizations aligned important structures in specific directions. For instance, Egyptians in the middle of the third millennium BCE may have used the circumpolar stars Kochab (Beta Ursae Minoris) and Mizar (Zeta Ursae Majoris) to align the Great Pyramid at Giza to true north–south.29 The art historian Stella Kramrisch has detailed the Vedic process of selecting and preparing Hindu temple sites prior to construction, which included laying out elaborate altars along the east–west axis. Citing the Rg Veda, one of the four sacred Hindu texts known collectively as the Vedas, Kramrisch states that sunrise and sunset points were used to establish the east–west axis, but she does not discuss the precision achievable by this method.30 Varahamihira (505–87 CE), the renowned astronomer and mathematician, described traditional norms of temple construction in his work Brihat Samhita, stating that temples should face an exact cardinal point rather than an intermediate direction.31 Science historian Michio Yano notes that determining cardinal directions was one of the first steps in constructing temples in ancient India. He divides the orientation methods that were used into two categories: observing fixed stars and observing the shadow of a vertical column, or gnomon.32 

In the first method, the direction of east is determined as a point between rising pairs of nakshatras (lunar mansions).33 The accuracy achieved by this method is unknown because the process of selecting the point between the pair of nakshatras representing east is unclear.34 The second method, named Indian Circle by the eleventh-century Arabic scholar Al-Biruni, was first described before 200 BCE in the Katyayana Sulbasutra, an ancient Indian treatise on mathematics and geometry.35 The mathematician and astronomer Brahmagupta (born in 598 CE) noted that the maximum error using this method of alignment was 0.5°; a correction for this error was first suggested by the astronomer and mathematician Sripati (1039 CE or 1056 CE).36 In 1983, Frits Staal, a Sanskritist who specialized in Vedic rituals, described the twelve-day Agnicayana ritual (as performed in 1975) in Nambudiri Vedic tradition, with a corrected version of Indian Circle as the method for determining the east–west axis prior to preparation of the ritual enclosure.37 

It is unlikely that the nine temples were oriented to the cardinal directions—each is oriented more than 4° south of true east, whereas the well-known and frequently employed Indian Circle method achieved better alignment than that. However, the fact that these temples have very similar orientations despite their being constructed centuries and hundreds of kilometers apart warrants an explanation. We hypothesize that they were intentionally aligned to the easterly rise of a celestial object that was widely considered significant.

The most conspicuous celestial object is the sun, which has been worshipped by many civilizations throughout human history. Architectural historian Pierre Pichard has suggested that the builders of Southeast Asian monuments may have oriented them to the east by marking the shadow of the rising sun at an equinox—one of two days in the year on which day and night are of nearly equal length anywhere on earth.38 This method could have been used to orient the nine temples considered here if shadows were marked a few days before the vernal equinox (around 20 March) or a few days after the autumnal equinox (around 22–23 September), but accurate alignment would have required clear atmospheric conditions on the day and time in question (near the equinox, the sun's shadow moves markedly from day to day, and the angle of the shadow changes quickly in the minutes after sunrise). Further, orientation of the temples to the sun does not provide a consistent explanation for the pattern we have noted. Therefore, we believe that the sun can be ruled out as a target for alignment. The next most prominent celestial object is the moon, but the moon's phases and complex orbit make it difficult to use for precise orientation purposes.39 

Unlike the moon, a prominent star is a point source that can be used for precise orientation. Many ancient structures may have been oriented toward the rising or setting of particular bright stars. For example, the Horus temple on the summit of Djebel Thoth in Western Thebes and the Isis temple at Dendera (both in Egypt) may have been oriented to the rising of Sepdet, or Sirius, while Antares may have been the alignment target for the temple of the Hurlers in Liskeard (England) and the Older Erechtheum in Athens.40 

Terminology

Some explanation of certain astronomical terms and concepts is necessary before we proceed further. Consider an imaginary line joining a star and an observer on earth, and another imaginary line joining the observer and the point on the horizon directly below the star. The angle between these two lines is the altitude of the star, while the angle between the second line and the direction of geographical north from the observer is the azimuth of the star. The altitude of a star just over a clear horizon is nearly 0°, and it increases as the star rises. As the altitude of a star increases, its azimuth increases in the Northern Hemisphere at a rate that depends on the observer's latitude.

The magnitude of a celestial object is a numeric value that is inversely related to the object's brightness. Bright objects have a magnitude of zero (or negative), whereas dimmer objects have positive magnitudes. The apparent magnitude of an object is its brightness as observed from earth (e.g., the apparent magnitudes of the sun and the full moon are –27 and –13, respectively). Celestial objects appear dimmer at lower altitudes—a phenomenon called extinction—because their light must pass through a longer section of atmosphere, where it is absorbed and scattered. For instance, Sirius has an apparent magnitude of –1.45, which falls—or is extincted—to about 0.5 at an altitude of 3°.

The imaginary projection of the earth's equator into outer space defines a disk called the celestial equator. When viewed from earth, the sun appears to move along the rim of another disk called the ecliptic. These two disks are at an angle to each other, because the earth's rotational axis is tilted, and their rims intersect at two points. If the sun is observed from a fixed point on earth over the course of one year, its azimuth at a given altitude (say, 3°) varies between two extreme values—achieved on the solstices—due to this tilt in the earth's rotational axis. Similarly, if a star is observed from a fixed point on earth, its azimuth at a given altitude (again, say, 3°) will vary between two extreme values because the gravitational pull of the sun and moon changes the earth's rotational axis in a slow cycle over a much longer period (about 26,000 years). This phenomenon is called axial precession. One of the ways to specify the position of a star in the sky is by two angles, known as its declination (its north/south angle relative to the celestial equator) and its right ascension (its angle relative to the first point of the constellation Aries, measured eastward along the celestial equator).

Two Significant Stars: Spica and Beta Librae

Spica is the brightest star in the constellation of Virgo and the sixteenth brightest star in the night sky, with an apparent magnitude 0.95, extincted to 2.92 at an altitude of 3°. Spica's declination was 1° north in 210 BCE and 1° south in 145 CE, and it crossed the celestial equator in approximately 31 BCE.41 Thus, in the early centuries of the first millennium CE, Spica was the closest bright star to one of the two intersections of the ecliptic with the celestial equator, being closest in the year 346 CE (Figure 12).42 

Figure 12

Comparison of Spica's locations relative to the intersection of the ecliptic and the celestial equator in 346 CE (top) and 2016 CE (bottom) (Stellarium).

Figure 12

Comparison of Spica's locations relative to the intersection of the ecliptic and the celestial equator in 346 CE (top) and 2016 CE (bottom) (Stellarium).

It is not surprising that a prominent star located at an astronomically prime spot attracted the attention of astronomers from several ancient civilizations. By observing Spica, the Greek astronomer Hipparchus (190–120 BCE) recognized the phenomenon of axial precession in 127 BCE. In his book Almagest, Ptolemy notes that while comparing the longitude of Spica and other bright stars with data recorded earlier by Timocharis (320–260 BCE), Hipparchus discovered that Spica had moved 2° relative to the autumnal equinox.43 David Pingree, a professor of classics, writes:

We can point to evidence indicating that at least four Greek texts expounding Greco-Babylonian astronomy were transmitted to Western India in the second, third, and fourth centuries when the area was ruled from Ujjayini by the Western Kşatrapas, whose territories maintained close commercial ties with the Roman Empire and were hosts to large number of Greek expatriates. Furthermore, it is apparent that some Greek texts (probably two) on planetary theory that were strongly influenced by Peripatetic notions of cosmology and a set of astronomical tables were transmitted to the same area of India shortly before or after 400 AD, when it had come under the domination of the Guptas.44 

Elsewhere, Pingree examines the transmission of the idea of precession to India prior to the twelfth century CE, noting that it appeared in Greek before it appeared in Sanskrit. Consequently, he hypothesizes that this idea was “transmitted to India along with other astronomical theories between the second and fifth centuries A.D.”45 

By the fifth century CE, precession had generated curiosity among Indian astronomers. Varahamihira, who lived in Ujjain, a city in central India that was part of the Gupta Empire, observed a shift in the commencement of the sun's northern and southern course (an observable phenomenon that follows solstices) when compared with what was recorded earlier by the astronomer Lagadha (fifth/fourth century BCE) in his work Jyotisavedanga.46 The celebrated astronomer Aryabhata I (476–550 CE) is known to have worked at Kusumapura, or Pataliputra, capital of the Gupta Empire, now Patna, modern capital of Bihar, 60 kilometers from Nalanda.47 Neither Varahamihira nor Aryabhata I could have proposed our hypothesized practice of orienting temples to the rise of Spica because the orientation of the earliest of our nine temples predates them. It is claimed that Aryabhata I headed the institution or observatory at Nalanda where astronomy was an important field of study.48 In his book Aryabhatiya he notes that the two halves of the ecliptic were divided on one side close to where the Chitra Nakshatra was located.49 In ancient Indian astronomy, Spica (or Chitra in Sanskrit) is one of the twenty-seven lunar mansions—the lone star in the Chitra Nakshatra.50 Spica belongs to both Kanya (or Virgo) and Tula (or Libra) zodiacal constellations.51 Together with Svati (or Arcturus), it forms one of the pairs of stars used in the method of orientation by observing fixed stars noted above.

Thus, it becomes evident that Spica was an important celestial object when the nine temples were commissioned and built. This bright star, possibly the target for orienting Greek temples in Olympia, Athens, Ephesus, and Rhamnous, and the temple of Min in Egypt, may also have been the target for orienting the nine Buddhist temples discussed here.52 Another star that deserves mention in this context is Beta Librae. This star is part of the Vishaka Nakshatra—the birth nakshatra of Buddha—hence its significance is obvious.53 Although it is the brightest star in the constellation Libra with an apparent magnitude 2.60, extincted to 4.20 at an altitude of 4°, it must rise to a slightly higher altitude than Spica to become clearly visible.

Stellar Orientation

We are unaware of any documented ancient method for orienting Indian structures to the rise of stars, but a possible technique using then-available tools would have involved the following steps: After a site was leveled for construction, a gnomon would be planted on the east side of the site. The top of the gnomon would mark the first point, the visibility of which could have been enhanced if necessary by a fire lit at the tip. A person holding a plumb would stand at a point west of the site and then, while facing east, move into a position where the star, the first point, and the thread of the plumb fell into line. This would mark the second point. A straight line could then be drawn between these two points with a rope connecting anchors nailed to them; this would form a baseline for the rest of the plan (Figure 13).54 

Figure 13

A possible method for drawing a baseline aligned with the rise of a star using a gnomon and plumb line: where the horizon is clear and the star is visible close to the horizon (top); where the terrain occludes the star until it rises further (bottom). Dotted arrows in the sky indicate the inclined trajectory of the star as it rises (drawings by authors).

Figure 13

A possible method for drawing a baseline aligned with the rise of a star using a gnomon and plumb line: where the horizon is clear and the star is visible close to the horizon (top); where the terrain occludes the star until it rises further (bottom). Dotted arrows in the sky indicate the inclined trajectory of the star as it rises (drawings by authors).

Those using this technique would need to wait for the star to rise a few degrees above the horizon before they could make accurate alignments. We estimate that a star as bright as Spica would be clearly visible at an altitude of at least 3° above a flat horizon. It would need to reach a higher altitude if there was an occlusion in the direction of star rise.

We can examine the shifting azimuths (at an altitude of 3°) of Spica and Beta Librae (at an altitude of 4°) across a whole precession cycle, spanning about 26,000 years, with measurements made at the coordinates of Nalanda every thousand years, and specifically during the period when the nine temples were built—400–1200 CE (Figures 14 and 15). The orientations of the five temples at Nalanda lie within the azimuth of Spica at an altitude of 3°, which varies from 93.979° in 400 CE to 98.921° in 1200 CE. These orientations also lie within the azimuth of Beta Librae at a slightly higher altitude of 4°, which varies from 94.496° to 98.644° across the same time. Thus, we consider both Spica and Beta Librae as candidate targets for orienting the nine temples.

Figure 14

Graph showing the shifting azimuths of Spica (at 3° altitude) and Beta Librae (at 4° altitude) across a whole precession cycle, with measurements made at the coordinates of Nalanda every one thousand years (graph by authors).

Figure 14

Graph showing the shifting azimuths of Spica (at 3° altitude) and Beta Librae (at 4° altitude) across a whole precession cycle, with measurements made at the coordinates of Nalanda every one thousand years (graph by authors).

Figure 15

Graph showing the shifting azimuths of Spica (at 3° altitude) and Beta Librae (at 4° altitude) from 400 to 1200 CE (the period pertinent to the nine temples) (graph by authors).

Figure 15

Graph showing the shifting azimuths of Spica (at 3° altitude) and Beta Librae (at 4° altitude) from 400 to 1200 CE (the period pertinent to the nine temples) (graph by authors).

Angles and Dates

The variations in Spica's azimuth at 3° altitude and Beta Librae's azimuth at 4° altitude are near linear in the period from 400 CE to 1200 CE (see Figure 15). A similar near-linear relation holds for both stars at every site and altitude under consideration here. We can therefore use a linear model z = a + by to relate the azimuth angle (z) to the year (y), where a and b are constants depending only on the location and altitude of observing the target star. If our hypothesis is correct, a temple oriented at angle z would have been built in year y = (za)/b, assuming there are no errors.55 In fact, there are four primary sources of error: error in measuring the angle of the target star's rise, which depends on the particular method used; error due to differences in the target star's altitude when measurements were made at each temple; error in constructing the temples (i.e., a mismatch between the measured orientations and the actual orientations of the structures); and error in the method we have used to measure the present-day temple orientations.56 

Since it is difficult to estimate the cumulative effect of these possible errors, we draw inferences based on a parameter e representing the cumulative error. The quality of our inferences degrades as e increases. Thus, if the calculated angle of orientation of a temple is z, then the true angle of the target star's azimuth at the time of construction lies in the range z ± e. From the linear model, we can infer that the temple's construction was initiated in a year falling in the range (za)/b ± e/b. If we assume that the cumulative error e is not too large, such an inference may still be useful. For instance, we can compare the linear model for observing the target star at our chosen altitude (3° for Spica, 4° for Beta Librae) with linear models for other altitudes to determine an altitude that fits the known data most accurately. For our comparison, we focus on the temple at Somapura for two reasons: first, among the nine temples under consideration, Somapura is one of three temples whose dates of construction are known, the others being Vikramasila and Samye; and second, unlike Vikramasila and Samye, Somapura has no prominent occlusion to the east.

Table 2 shows the range of years in which the construction of Somapura was initiated using linear models where the altitude of Spica varies from 2° to 4° and the altitude of Beta Librae varies from 3° to 5°.57 Note that the width of the range increases as the error e increases. If we assume that e is not too large, for Spica it is possible to rule out altitudes of 2° or less and 4° or more based on known dates, whereas an altitude of 3° is plausible. Similarly, an altitude of 4° is plausible for Beta Librae.58 Assuming these plausible altitudes, we have constructed linear models at each of the sites as follows. First, we measured the azimuth of Spica at an altitude of 3° and Beta Librae at an altitude of 4° from 400 to 1200 CE, at intervals of one hundred years.59 For each star, using these nine pairs of azimuth (z) and year (y) values and linear regression (with ordinary least squares), we then calculated the coefficients a and b in our linear model. These coefficients are constant for a given geographic location, and the linear models for both stars are summarized in Table 3.

These models cannot be used for two of the nine temples: Vikramasila and Samye (as we explain below). For each of the remaining seven temples, we estimated the year y in which construction was initiated based on the temple's orientation z (see Table 1). The date range for each temple increases as the assumed cumulative error e increases (see Figure 16). Our choice of altitudes for observing Spica and Beta Librae obviously forces the date range for Somapura to be consistent with known records. Having made these choices, however, we note that for both target stars, the date ranges for Mahabodhi are in line with historical estimates, and the date ranges for T12 and T14 are consistent with the temples' relative chronology. The two target stars yield date ranges that differ by a few decades. The most extreme difference—nearly a century—is for T2, but even here there is insufficient evidence to refute either date range.

Figure 16

Estimated year of construction for each temple (vertical axis) based on the assumed cumulative error (horizontal axis) (graphs by authors).

Figure 16

Estimated year of construction for each temple (vertical axis) based on the assumed cumulative error (horizontal axis) (graphs by authors).

As the cumulative error e increases, the relative chronology between temples is progressively blurred. Regardless of which star was chosen as the target, we can propose several novel claims that may be of historical interest, even if they are not yet supported (or refuted) by existing evidence: T12 predates T13 by about a century; Mahabodhi may have been constructed at Bodhgaya in the intervening period; T13 predates Sarai Temple by about two centuries; and Sarai predates T14 by a similar time span (see Figure 16). Confidence in our hypothesis may be strengthened if new evidence is found to support such claims, or it may be eroded if new evidence contradicts them.

Some Exceptions and a Unified Explanation

As noted, the linear models in Table 3 do not apply to Vikramasila and Samye. If the estimated year of construction (y ≈ 800 CE for Vikramasila and Samye) is applied to the linear models for these temples, the estimated orientation z (i.e., Spica's azimuth at 3° altitude or Beta Librae's azimuth at 4° altitude) is always lower than the actual orientation of the temple. Hence, the “error” in our linear models is in only one direction. We have assumed a uniform altitude at which the target star was observed (3° for Spica, 4° for Beta Librae). If there was an occlusion in the direction of the target star's rise, it would be necessary to wait longer for it to rise above the horizon. The azimuth increases for both target stars as they rise, so an explanation for the unexpectedly large angles of orientation of these two temples may be an occlusion toward the east.

Samye lies in a valley north of the Yarlung Tsangpo River, close to several Himalayan mountains. A large hill lies about 6 kilometers away in the approximate direction in which Spica and Beta Librae rise (i.e., a few degrees south of east) (Figure 17). If the monastery had been located nearby north or south, the view in this direction would have been further occluded by hills that are even taller (to the north) or much nearer (to the south). This observation is consistent with our hypothesis that the builders of Samye deliberately tried to observe the rise of the target star with as little occlusion as possible.

Figure 17

Samye Monastery, India, ca. 775–79 CE; note the hills to the east and the Yarlung Tsangpo River streams to the southeast (Google, CNES/Airbus).

Figure 17

Samye Monastery, India, ca. 775–79 CE; note the hills to the east and the Yarlung Tsangpo River streams to the southeast (Google, CNES/Airbus).

At Vikramasila, the river Ganga flows from the west and then bends north before flowing further east/southeast. Kosi, one of the Ganga's largest tributaries, currently joins it just west of Vikramasila. This confluence is believed to have been further east (i.e., north/northeast of the site) less than two centuries ago.60 Even today, Kosi occasionally floods and the flow spreads into a large fan, joining the Ganga at multiple locations lying northwest, north, and northeast of Vikramasila. Therefore, the fluvial deposits and the fluvial geomorphology are highly dynamic in this region. Parts of the Ganga's floodplains have shown alluvial accumulation of approximately 2 to 30 meters.61 At Vikramasila, there are imposing rocky hills to the west, but to the east there is currently a small occluding mound (Figure 18). It is possible that a similar, perhaps larger, fluvial occlusion could have been present when the alignments for constructing this temple were made. Indeed, prior to excavation, only the central monument was visible, appearing as a high mound amid agricultural fields.62 Several meters of alluvial soil had to be cleared to expose the quadrangle of monasteries and other surrounding structures, and today one must descend 6–7 meters down a flight of stairs to reach the level of the excavated ruins.

Figure 18

Digital elevation model (SRTM data of 1 arc-second resolution) showing undulations to the east of Vikramasila in the direction of orientation (top), and view looking east from the central monument at Vikramasila (bottom) (model by authors; photo by Sonia Das).

Figure 18

Digital elevation model (SRTM data of 1 arc-second resolution) showing undulations to the east of Vikramasila in the direction of orientation (top), and view looking east from the central monument at Vikramasila (bottom) (model by authors; photo by Sonia Das).

The evidence for occlusions at these two temples is not conclusive, but a uniform hypothesis is sufficient to explain both apparent discrepancies. At all of the other temples, we find no evidence for permanent occlusions in the direction in which Spica and Beta Librae rise. However, temporary occlusions—caused by human-made structures or trees, for instance—could have similarly required the temples' builders to wait for the target star to rise to a higher altitude for observation. This could explain the unexpectedly high angle for T14.

Conclusion

We have identified the orientations of nine prominent Buddhist temples and found a consistent temporal pattern. We have demonstrated how this pattern can be explained in relation to the rise of a target star, either Spica or Beta Librae. Based on this hypothesis, we argue that a temple's orientation determines when it was oriented prior to its construction. Our calculations require one further consideration: the altitude above the horizon at which the target star was observed. We have shown that the altitudes of 3° for Spica and 4° for Beta Librae result in calculated dates that agree with existing historical records.

Our hypothesis may apply to structures excluded from this study, including T3 at Nalanda, the circular stupas at Sanchi in Madhya Pradesh and Sarnath in Uttar Pradesh, and the mound in Begampur, tentatively identified as a major Buddhist structure, whose orientation is roughly consistent with those of Vikramasila and Somapura.63 It may apply as well not only to individual structures but also to whole layouts such as at Sarnath, where the cruciform structure of the main shrine, its courtyard, and several ancillary structures are all oriented in a manner similar to that found at the temples considered here. If their orientations can be measured accurately using other techniques, including ground-based measurements, our method could be used for estimating their dates of construction.

Notes

Notes
1.
We thank the following scholars: Dr. John R. Marr, Professor Frederick Asher, Professor Jayant Murthy, Dr. R. R. Navalgund, Dr. B. S. Shylaja, Professor James Evans, and Ms. Sonia Das. We thank the Science and Engineering Research Board, Government of India, for funding (through an ongoing project) travel to Nalanda, Vikramasila, and Bodhgaya. Finally, we thank the reviewers at JSAH for their constructive comments.
2.
Fredrick Asher, Nalanda: Situating the Great Monastery (Mumbai: Marg Foundation, 2015), 21–29.
3.
A chaitya is a Buddhist shrine or assembly/prayer hall that houses a stupa.
4.
This skew has been noticed and reported by Asher, Nalanda, 15–49.
5.
The Nalanda complex protected by the Archaeological Survey of India also includes ten monasteries. While the sacred temples may have been carefully oriented, we believe that the orientations of monasteries (dwelling spaces) were dictated by practicality (the majority of these are abutting structures with little variation in their alignments) and do not warrant further explanation in this context. We leave it to future research to determine whether the monasteries reflected the orientations of other structures.
6.
Asher, Nalanda, 43.
7.
Asher, 8.
8.
We believe that the basis of orientation we propose here has far broader applicability, not only to temples in India but also to structures in other parts of the world where orientation was determined in relation to specific stars. We cannot say, however, whether structures distant from the Indian subcontinent used a similar mode of orientation. This would be worth examining in the future.
9.
Pierre-Yves Manguin, A. Mani, and Geoff Wade, eds., Early Interactions between South and Southeast Asia: Reflections on Cross-Cultural Exchange (Singapore: ISEAS, 2011).
10.
There is evidence that some of the remaining temples at Nalanda were also constructed in more than one phase, but there is no indication that their central structures were reoriented. Asher, Nalanda, 53–55.
11.
For the temples we consider, we have found symmetric pairs of flanking linear features whose orientations differ by as little as 0.014° (T14) to at most 0.306° (Mahabodhi). Among the three linear features at T3 (see Figure 3), no pair flanks the central structure symmetrically, and the difference in orientations of any (asymmetric) flanking pair is at least 0.854°.
12.
The method we propose may have been one of several practices for orienting sacred structures. For instance, Ratnagiri and Udayagiri in Orissa state were important Buddhist sites that overlapped temporally with Nalanda. However, their main stupas are oriented almost exactly east–west, unlike the nine temples considered here.
13.
V. H. Jackson, ed., “Journal of Francis Buchanan (Patna and Gaya Districts)” Journal of the Bihar and Orissa Research Society 8, pts. 3–4 (1922), 266–73, 314–16, https://archive.org/details/journalofbiharre08bihauoft (accessed 24 May 2019).
14.
Asher, Nalanda, 39.
15.
Buchanan's sketch of Nalanda marks several more mounds, as does the site plan made by Alexander Cunningham in his Archaeological Survey of India, vol. 1, Four Reports Made during the Years 1862–63–64–65 (Simla: Government Central Press, 1871), 28, plate XVI, https://archive.org/details/in.ernet.dli.2015.94077/page/n127 (accessed 24 May 2019). See also the diagrammatic sketch by Alexander M. Broadly in his Ruins of the Nalanda Monasteries at Burgaon, Subdivision Bihar, Zilla Patna (Calcutta: Bengal Secretariat Press, 1872). Most of these sites are still unexcavated.
16.
Asher, Nalanda, 43.
17.
Asher, 55.
18.
Asher, 55.
19.
The other three sites are Lumbini in Nepal (where he was born); Sarnath, near Varanasi in Uttar Pradesh, India (where he delivered his first sermon); and Kushinagar, also in Uttar Pradesh (where he attained Nirvana).
20.
Janice Leoshko, Sacred Traces: British Explorations of Buddhism in South Asia (Aldershot, England: Ashgate, 2003), 1; “Mahabodhi Temple Complex at Bodh Gaya,” UNESCO World Heritage Centre, http://whc.unesco.org/pg.cfm?cid=31&id_site=1056 (accessed 24 May 2019).
21.
The Tibetan historian Taranatha (whose account was written in 1608 CE and whose sources are unclear) states that Vikramasila was built by Dharmapala and Somapura was built by Devepala; see Tāranātha's History of Buddhism in India, ed. Debiprasad Chattopadhyaya, trans. Lama Chimpa and Alaka Chattopadhyaya (New Delhi: Motilal Banarsidass, 1990), 266, 274. However, inscriptions on clay seals found during Somapura's subsequent excavation suggest that it was built by Dharmapala; see Le Huu Phuoc, Buddhist Architecture (n.p.: Grafikol, 2010), 74. The excavations at Vikramasila have not yielded such inscriptions, but they suggest that Vikramasila was active from the early ninth century CE. See B. S. Verma, Antichak Excavations–2, 1971–1981 (New Delhi: Archaeological Survey of India, 2011), 19–21. Regarding the dates of Dharmapala's reign, Susan Huntington notes that scholars' opinions are divided based on interpretations of various epigraphs and historical records: R. C. Majumdar (1971) has suggested 770–810 CE, A. M. Chowdhury (1967) has suggested 781–821 CE, B. P. Sinha (1977) has suggested 783–820 CE, and D. C. Sircar (1975–76) has suggested 775–812 CE. Susan L. Huntington, The “Påala-Sena” Schools of Sculpture (Leiden: Brill Archive, 1984), 32–37.
22.
Faruque Hasan, The Making and Symbolism of Paharpur Stupa (Morrisville, N.C.: Lulu.com, 2010), 19.
23.
Taranatha notes that this monastery was built during the reign of the first Pala king (Gopala) around the middle of the eighth century CE. Tāranātha's History of Buddhism in India, 262.
24.
Tadeusz Skorupski, “The Religions of Tibet,” in The World's Religions: The Religions of Asia, ed. Friedhelm Hardy (London: Taylor & Francis, 2005), 250.
25.
Lokesh Chandra, ed., The Samye Monastery (New Delhi: International Academy of Indian Culture, 1961), 9; Melvyn C. Goldstein, The Snow Lion and the Dragon: China, Tibet, and the Dalai Lama (Berkeley: University of California Press, 1997), 1.
26.
Mosalam Shaltout, “Studying the Orientations of Luxor Ancient Egyptian Temples Using QuickBird Images,” Journal of Earth Science and Engineering 4 (2014), 194–210; Jaroslav Klokocník and Jan Kostelecký, “Google Earth for the Study of Ancient Civilizations,” in GEOProcessing 2010: The Second International Conference on Advanced Geographic Information Systems, Applications, and Services, ed. Victor Lobo, Bernd Resch, and Bastian Schäffer (Piscataway, N.J.: Institute of Electrical and Electronics Engineers, 2010), 56–61; Jaroslav Klokocník, Jan Kostelecký, and Karel Pavelka, “Google Earth: Inspiration and Instrument for the Study of Ancient Civilizations,” Geoinformatics CTU FCE 6 (2011), 193–211.
27.
Georeferencing is the process of assigning geographic coordinates to each pixel of an image.
28.
All angles reported in this article are measured to the nearest second—1/3600th of a degree—and are therefore reported to three digits of accuracy after the decimal.
29.
Kate Spence, “Ancient Egyptian Chronology and the Astronomical Orientation of Pyramids,” Nature 408 (16 Nov. 2000), 320–24.
30.
Stella Kramrisch, The Hindu Temple (New Delhi: Motilal Banarsidass, 1946), 16–17.
31.
Varahamihira's Brihat Samhita, trans. V. Subahmanya Shastri and M. Ramakrishna Bhat (Bangalore: V. B. Soobbiah, 1946), 491; Ajay Mitra Shastri, Ancient Indian Heritage: Varahamihira's India, vol. 2 (New Delhi: Aryan Books, 1996), 397.
32.
Michio Yano, “Knowledge of Astronomy in Sanskrit Texts of Architecture (Orientation Methods in the Isanasivagurudevapaddhatj),” Indo-Iranian Journal 29 (1986), 17–29.
33.
A lunar mansion is an asterism (a prominent pattern or group of stars that is smaller than a constellation) that is (apparently) transited by the moon as viewed from earth. Many ancient cultures used lunar mansions as part of their calendar systems. Nakshatra is the Sanskrit term for lunar mansion, and it refers to one of twenty-eight (sometimes twenty-seven) sections along the ecliptic (one for each day of the lunar sidereal month, which is about 27.3 days long). Most nakshatras have several stars, but some have only one. Buddha's birth nakshatra (the lunar mansion through which the moon transited on the day Buddha was born) is Vishaka.
34.
Yano, “Knowledge of Astronomy in Sanskrit Texts,” 28n2.
35.
The Sulbasutra of Baudhayana, Apastamba, Katyayana and Manava, trans. S. N. Sen and A. K. Bag (New Delhi: Indian National Science Academy, 1983), 3.
36.
Asger Mollerup, “Orientations of Khmer Temples and the Indian Circle,” in Ancient Khmer Sites in Eastern Thailand (Bangkok: White Lotus, 2012), 147–60.
37.
Frits Staal, Agni: The Vedic Ritual of the Fire Altar, vol. 1 (New Delhi: Motilal Banarsidass, 1983), 244–47.
38.
Pierre Pichard, “Note sur l'orientation des monuments en Asie du Sud-Est,” Aséanie 23 (June 2009), 16.
39.
Studies that suggest lunar orientation of historical buildings have referred to either major lunar standstill or far southerly moonrise: John Cox and Tore Lomsdalen, “Prehistoric Cosmology: Observations of Moonrise and Sunrise from Ancient Temples in Malta and Gozo,” Journal of Cosmology 9 (2010), 2217–31; Anna Sofaer, “The Primary Architecture of the Chacoan Culture: A Cosmological Expression,” in The Architecture of Chaco Canyon, New Mexico, ed. Stephen H. Lekson (Salt Lake City: University of Utah Press, 2007), 225–54; David Furlong, “Egyptian Temple Orientation: Astronomical Alignments in the Temples of Egypt,” May 2007, http://www.davidfurlong.co.uk/pdf/egyptian_temple_orientation.pdf (accessed 24 May 2019). At Nalanda's latitude, the moonrise azimuth during the southern major standstill (also the far southerly moonrise) is 32.273° south of east, the northern major standstill is 31.748° north of east, the southern minor standstill is at 19.938° south of east, and the northern minor standstill is at 19.867° north of east. These azimuth angles are far more divergent from east than are the orientations of the temples analyzed in the present study.
40.
Mosalam Shaltout and Juan Antonio Belmonte, “On the Orientation of Ancient Egyptian Temples: (1) Upper Egypt and Lower Nubia,” Journal for the History of Astronomy 36, no. 3 (July 2005), 273–98; Juan Antonio Belmonte, Magdi Fekri, Yasser A. Abdel-Hadi, Mosalam Shaltout, and A. Cesar González-García, “On the Orientation of Ancient Egyptian Temples: (5) Testing the Theory in Middle Egypt and Sudan,” Journal for the History of Astronomy 41, no. 1 (Feb. 2010), 65–93; Peter Lancaster Brown, Megaliths, Myths and Men: An Introduction to Astro-archaeology (Mineola, N.Y.: Dover, 2000), 75–76; J. Norman Lockyer, The Dawn of Astronomy: A Study of the Temple-Worship and Mythology of the Ancient Egyptians (London, 1894), 419, https://archive.org/details/dawnastronomyas00lockgoog/page/n438 (accessed 24 May 2019). The methods that Lockyer used for data collection and analysis have been questioned by more recent authors; see Maria K. Papathanassiou, “Archaeoastronomy in Greece: Data, Problems and Perspectives,” in Trends in the Historiography of Science, ed. Kostas Gavroglu, Jean Christianidis, and Efthymios Nicolaidis (Dordrecht: Springer, 1994), 433–43; Efrosyni Boutsikas and Clive Ruggles, “Temples, Stars, and Ritual Landscapes: The Potential for Archaeoastronomy in Ancient Greece,” American Journal of Archaeology 115, no. 1 (Jan. 2011), 55–68.
41.
These and all the other details of locations of celestial objects mentioned in this article were measured on Stellarium 0.14.3.
42.
Spica's right ascension in 346 CE was 12h00m0.18s, its declination was 2.118°, and its azimuth was 93.643° at 3° altitude. Today, Spica has shifted its position along the ecliptic (a consequence of precession) and moved away from the latter's intersection with the equator. In 2016 CE, Spica's right ascension was 13h26m4.97s, its declination was –11.248°, and its azimuth was 103.791° at 3° altitude.
43.
Ptolemy's Almagest, trans. G. J. Toomer (Princeton, N.J.: Princeton University Press, 1998), 327.
44.
David Pingree, “The Recovery of Early Greek Astronomy from India,” Journal for the History of Astronomy 7 (1976), 121–22.
45.
David Pingree, “Precession and Trepidation in Indian Astronomy before A.D. 1200,” Journal for the History of Astronomy, 3 (1972), 33.
46.
Pingree, “Recovery of Early Greek Astronomy,” 109–23.
47.
Aryabhatiya of Aryabhata, trans. Krupa Shankar Shukla and K. V. Sarma (New Delhi: Indian National Science Academy, 1976), xviii; Pingree, “Recovery of Early Greek Astronomy,” 109–23.
48.
Aryabhatiya of Aryabhata, xix; S. M. Razaullah Ansari, “Aryabhata I, His Life and His Contributions,” Bulletin of the Astronomical Society of India 5 (Mar. 1977), 10; D. G. Apte, Universities in Ancient India (Vadodara: Maharaja Sayajirao University of Baroda, 1961), 30.
49.
“One half of the ecliptic, running from the beginning of the sign Aries to the end of the sign Virgo, lies obliquely inclined (to the equator) northwards. The remaining half (of the ecliptic) running from the beginning of the sign Libra to the end of the sign Pisces, lies (equally inclined to the equator) southwards.” Since Spica is part of both Kanya and Tula, it would mark the dividing point. Aryabhatiya of Aryabhata, 113. See also Ansari, “Aryabhata I,” 10; Apte, Universities in Ancient India, 30.
50.
Bhaskara I and His Works, pt. 2, Mahabhaskariya, ed. Ram Ballabh (Lucknow: Nav Jyoti Press, 1960), 95–97.
51.
Varahamihira's Brihat Samhita, 762.
52.
William Tyler Olcott, Star Lore: Myths, Legends and Facts (Mineola, N.Y.: Dover, 2004), 387.
53.
Vishaka consists of five, two, or four stars, according to Varahamihira, Brahmagupta, and Lalla, respectively (ι, ϒ, β, and α Librae). Bhaskara I and His Works, 97–98.
54.
The precision in erecting gnomons and the use of plumbs are described in Bhaskara I and His Works, chap. 3, p. 56, sloka 1.
55.
Heinrich Nissen, Norman Lockyer, and Francis Penrose used similar hypotheses to date Greek temples from their orientations, but their methods have been criticized for neglecting several sources of error. See Papathanassiou, “Archaeoastronomy in Greece.”
56.
There may also be additional sources of error. For instance, the astronomical models used by Stellarium are periodically refined based on new data. The cumulative effect of these errors is much smaller, however, than the errors caused by the four primary sources we consider.
57.
The azimuth angles were measured using Stellarium at the given altitude during the heliacal rise of the star—that is, its first visible rising after a period of invisibility due to conjunction with the sun.
58.
We restrict ourselves to integer altitudes for simplicity. The true altitudes at which Spica or Beta Librae were observed need not have been integers.
59.
Stellarium allows the azimuth of a star to be measured at one-second time intervals. We measured the azimuth at the first time point where the altitude rises above 3° (for Spica) or 4° (for Beta Librae). The error in altitude is less than 0.004°.
60.
Tapan Chakraborty, Rimpal Kar, Parthasarathi Ghosh, and Sounak Basu, “Kosi Megafan: Historical Records, Geomorphology and the Recent Avulsion of the Kosi River,” Quaternary International 227, no. 2 (2010), 143–60.
61.
R. Sinha, S. K. Tandon, M. R. Gibling, P. S. Bhattacharjee, and A. S. Dasgupta, “Late Quaternary Geology and Alluvial Stratigraphy of the Ganga Basin,” Himalayan Geology 26, no. 1 (2005), 223–40.
62.
Verma, Antichak Excavations–2, 1–4.
63.
M. B. Rajani, “The Expanse of Archaeological Remains at Nalanda: A Study Using Remote Sensing and GIS,” Archives of Asian Art 66, no. 1 (Spring 2016), 1–23.