Advanced Astronomy In the Shrimad-Bhagavatam
This ancient Vedic text gives an accurate map of the planetary orbits known to modern astronomy.
By Sadaputa Dasa
TODAY WE TAKE for granted that the earth is a sphere, but the early Greeks tended to think it was flat. For example, in the fifth century B.C. the philosopher Thales thought of the earth as a disk floating on water like a log.**1 About a century later, Anaxagoras taught that it is flat like a lid and stays suspended in air.**2 A few decades later, the famous atomist Democritus argued that the earth is shaped like a tambourine and is tilted downwards toward the south.**3 Although some say that Pythagoras, in the sixth century B.C., was the first to view the earth as a sphere, this idea did not catch on quickly among the Greeks, and the first attempt to measure the earth’s diameter is generally attributed to Eratosthenes in the second century B.C.
Scholars widely believe that prior to the philosophical and scientific achievements of the Greeks, people in ancient civilized societies regarded the earth as a flat disk. So to find that the Bhagavata Purana of India appears to describe a flat earth comes as no surprise. The Bhagavata Purana, or Shrimad-Bhagavatam, is dated by scholars to A.D. 500–1000, although it is acknowledged to contain much older material and its traditional date is the beginning of the third millennium B.C.
In the Bhagavatam, Bhumandala—the “earth mandala”—is a disk 500 million yojanas in diameter. The yojana is a unit of distance about 8 miles long, and so the diameter of Bhumandala is about 4 billion miles.** Bhumandala is marked by circular features designated as islands and oceans. These features are listed in Table 1, along with their dimensions, as given in the Bhagavatam.
N Inner Radius Outer Radius Thickness Feature
1 0 50 50 Jambudvipa
2 50 150 100 Lavanoda
3 150 350 200 Plakshadvipa
4 350 550 200 Ikshura
5 550 950 400 Shalmalidvipa
6 950 1,350 400 Suroda
7 1,350 2,150 800 Kushadvipa
8 2,150 2,950 800 Ghritoda
9 2,950 4,550 1,600 Krauncadvipa
10 4,550 6,150 1,600 Kshiroda
11 6,150 9,350 3,200 Shakadvipa
12 9,350 12,550 3,200 Dadhyoda
13 12,550 15,750 3,200 Inner Pushkaradvipa
14 15,750 18,950 3,200 Outer Pushkaradvipa
15 18,950 25,350 6,400 Svadudaka
16 25,350 41,100 15,750 Kancanibhumi
17 41,100 125,000 83,900 Adarshatalopama
18 125,000 250,000 125,000 Aloka-varsha
Table 1. The radii in thousands of yojanas of the islands and oceans of Bhumandala, as given in the Bhagavata Purana.
There are seven islands, called dvipas, ranging from Jambudvipa to Pushkaradvipa. Jambudvipa, the innermost, is a disk, and the other six are successively larger rings. The islands alternate with ring-shaped oceans, beginning with Lavanoda, the Salt Water Ocean surrounding Jambudvipa, and ending with Svadudaka, the Sweet Water Ocean. Beyond Svadudaka is another ring, called Kancanibhumi, or the Golden Land, and then yet another, called Adarshatalopama, the Mirrorlike Land.**5
There are also three circular mountains we should note. The first is Mount Meru, situated in the center of Bhumandala and shaped like an inverted cone, with a radius ranging from 8,000 yojanas at the bottom to 16,000 yojanas at the top. The other two mountains can be thought of as very thin rings or circles. The first, called Manasottara, has a radius of 15,750 thousand yojanas and divides the island of Pushkaradvipa into two rings of equal thickness. (In Table 1 these are referred to as inner and outer Pushkaradvipa.) The second mountain, called Lokaloka, has a radius of 125,000 thousand yojanas and separates the inner, illuminated region of Bhumandala (ending with the Mirrorlike Land) from the outer region of darkness, Aloka-varsha.
At first glance, Bhumandala appears to be a highly artificial portrayal of the earth as an enormous flat disk, with continents and oceans that do not tally with geographical experience. But careful consideration shows that Bhumandala does not really represent the earth at all. To see why, we have to consider the motion of the sun.
In the Bhagavatam the sun is said to travel on a chariot (Figure 2). The wheel of this chariot is made of parts of the year, such as months and seasons. So it might be argued that the chariot is meant to be taken metaphorically, rather than literally. But here we are concerned more with the chariot’s dimensions than with its composition. The chariot has an axle that rests at one end on Mount Meru, in the center of Jambudvipa. On the other end, the axle connects to a wheel that “continuously rotates on Manasottara Mountain like the wheel of an oil-pressing machine.”**6 The wheel rolls on top of Mount Manasottara, which is like a circular race track.
The sun rides on a platform joined to the axle at an elevation of 100,000 thousand yojanas from the surface of Bhumandala. Since the axle extends from Mount Meru to Mount Manasottara, its length must be 15,750 thousand yojanas, or 157.5 times as long as the height of the sun above Bhumandala. Since the sun’s platform is somewhere on the axle between Meru (in the center) and the wheel (running on the circular track of Manasottara), it follows that to an observer at the center the sun always seems very close to the surface of Bhumandala.
To see this, imagine building a scale model of the sun’s chariot on a level field, with 1 foot representing 100,000 thousand yojanas. In this model, the sun is a ball riding 1 foot above the field on an axle 157.5 feet long. One end of the axle pivots around Mount Meru, which is about 1 foot high (or a little less), and the other end goes through a wheel about 1 foot in diameter which follows a circular track. If the sun is a good part of the way out from the center (say, 50 feet or more), it will seem close to the field from the point of view of an observer lying down with his eye close to the base of Mount Meru. The same is true if the model is scaled up to actual size.
Suppose that Bhumandala represents our local horizon extended out into a huge flat disk—the so-called flat earth. Then an observer standing in Jambudvipa, near the center, must see the sun continuously skim around the horizon in a big circle, without either rising into the sky or setting. This is actually what one can see at the north or south pole at certain times in the year, but it is not what one sees in India. The conclusion, therefore, is that Bhumandala does not represent an extension of our local horizon. Since the sun is always close to Bhumandala, and since the sun rises, goes high into the sky, and then sets, it follows that the disk of Bhumandala is tilted at a steep angle to an observer standing in India.
In brief, Bhumandala is where the sun goes. It extends high into the sky overhead and also far beneath the observer’s feet. Furthermore, it must be regarded as invisible, for if it were opaque it would block our view of a good part of the sky.
Bhumandala is not the “flat earth,” but what is it? One possibility is the solar system. In modern astronomy, each planet orbits the sun in a plane. The planes of these orbits lie at small angles to one another, and thus all the orbits are close to one plane. Astronomers call the plane of the earth’s orbit the ecliptic, and this is also the plane of the sun’s orbit, from the point of view of an observer stationed on the earth. To an observer on the earth, the solar system is a more-or-less flat arrangement of planetary orbits that stay close to the path of the sun.
Bhumandala is far too big to be the earth, but in size it turns out quite a reasonable match for the solar system. Bhumandala has a radius of 250 million yojanas, and at the traditional figure of 8 miles per yojana this comes to 2 billion miles. For comparison, the orbit of Uranus has a radius of about 1.8 billion miles.
If we move in from the outer edge of Bhumandala we meet the Lokaloka mountain, with a radius of 125 million yojanas, or about 1 billion miles. From Uranus the next planet inward is Saturn, with an orbital radius of about 0.9 billion miles. Thus we find a rough agreement between certain planetary orbits and some circular features of Bhumandala.
Of course, Bhumandala is earth centered. Its innermost island, Jambudvipa, contains Bharata-varsha, which Shrila Prabhupada has repeatedly identified as the planet earth.7 In contrast, the orbits of the planets are centered on the sun. How, then, can they be compared to earth-centered features of Bhumandala?
The solution is to express the orbits of the planets in geocentric (earth-centered) form. Although the calculations of modern astronomy treat these orbits as heliocentric (sun-centered), the orbits can be expressed in relation to any desired center of observation, including the earth. In fact, since we live on the earth, it is reasonable for us to look at planetary orbits from a geocentric point of view.
The geocentric orbit of a planet is a product of two heliocentric motions, the motion of the earth around the sun and the motion of the planet around the sun. To draw it, we shift to the earth as center, and show the planet orbiting the sun, which in turn orbits the earth. This is shown in Figure 1 for the planet Mercury. The looping curve of the planet’s geocentric orbit lies between two boundary curves, in the figure marked A and B. If we continue plotting the orbit for a long enough time, the orbital paths completely fill the donut-shaped area between these two curves.
If we superimpose the orbits of Mercury, Venus, Mars, Jupiter, and Saturn on a map of Bhumandala, we find that the boundary curves of each planet’s orbit tend to line up with circular features of Bhumandala. Thus the inner boundary of Mercury’s orbit swings in and nearly grazes feature 10 in Table 1, and its outer boundary swings out and nearly grazes feature 13. We can sum this up by saying that Mercury’s boundary curves are tangent to features 10 and 13. The boundary curves of the orbit of Venus are likewise tangent to features 8 and 14 as shown in Figure 4, and those of the orbit of Mars are tangent to features 9 and 15. Figure 5 shows the alignments between features of Bhumandala and the boundary curves of Mercury, Venus, and Mars. The inner boundary of Jupiter’s orbit is tangent to feature 16, and the outer boundary of Saturn’s orbit is tangent to feature 17. These alignments are shown graphically in Figure 6. If we include Uranus, we find that its outer boundary lines up with feature 18, the outer edge of Bhumandala. The orbital alignments make use of over half the circular features of Bhumandala. Each of the features from 8 to 18, with the exception of 11 and 12, aligns with one orbital boundary curve. But it turns out that features 11 and 12 also fit into the orbital picture. Unlike the planetary orbits, the geocentric orbit of the sun is nearly circular, since it is simply the earth’s heliocentric orbit as seen from the earth. The sun’s orbit lies almost exactly halfway between the circular features 11 and 12, and this is shown in Figure 5.
To compare geocentric orbits measured in miles with Bhumandala features measured in yojanas, we have to know how many miles there are in a yojana. I began by using 8 miles per yojana, in accordance with Prabhupada’s statement “One yojana equals approximately eight miles.”**8 But there is a simple way to refine this estimate. We have seen that the boundary curves of the planets tend to line up with the circular features of Bhumandala. The trick, then, is to find the number of miles per yojana at which the curves and features line up the best.
A boundary curve can touch a circular feature at either its apogee (point furthest from the earth) or its perigee (point closest to the earth). This gives us 4 points (apogee and perigee of curves A and B) that I call turning points. This is illustrated in Figure 7.
In note 9 I use turning points to define a measure of “goodness of fit” that tells us how good an alignment of features and orbits is. Figure 3 is a plot of goodness of fit against the length of the yojana, for lengths ranging from 5 to 10 miles. The curve has a pronounced peak at 8.575 miles per yojana. This value—reasonably close to the traditional figure of 8 miles—gives the best fit between features of Bhumandala and planetary orbits.
To compute the geocentric orbits of the planets, I used a modern ephemeris program.**10 Such calculations must be done for a particular date. I used the traditional date for the beginning of Kali-yuga: February 18, 3102 B.C. But it turns out that the results are nearly the same for a wide range of dates. So the orbital calculations do not tell us when the Bhagavatam was written, but they are consistent with the traditional date of about 3100 B.C.
Table 2 lists the correlations between planetary boundary curves and features of Bhumandala, using 8.575 miles per yojana. The error percentages tell how far the radius of each feature differs from the radius of its corresponding turning point, and they show that there is a close agreement between planetary orbits and various features of Bhumandala.**11 Besides the planets Mercury, Venus, Mars, Jupiter, and Saturn, I have included the sun, the planet Uranus, and Ceres, the principal asteroid, since these are also part of the total pattern.
N Planet Turning
Point Turning
Point Radius Feature
Radius Error
Percentage
1 Mercury A perigee 5,976.0 6,150 2.9
2 Mercury B apogee 15,701.1 15,750 0.3
3 Venus A perigee 2,851.0 2,950 3.5
4 Venus B apogee 18,813.0 18,950 0.7
5 Mars A perigee 4,090.0 4,550 11.2
6 Mars B perigee 25,736.5 25,350 -1.5
7 Jupiter A perigee 43.422.8 41,100 -5.3
8 Saturn B apogee 121,599.6 125,000 2.8
9 Sun mean 10840.4 10,950 1.0
10 Ceres B apogee 42,683.2 41,100 -3.7
11 Uranus B apogee 229,811.0 250,000 8.9
Table 2. Correlation between radii of features of Bhumandala and orbital turning points. The feature radii are from Table 1 and are in thousands of yojanas. Error percentage is the error in the feature radius relative to the corresponding orbital turning point. The orbital turning points are calculated for the beginning of Kali-yuga, using a modern ephemeris program. They are expressed in thousands of yojanas using 8.575 miles per yojana.
The sun’s mean orbital radius falls within 1% of the center of Dadhyoda (the Yogurt Ocean), which is bounded by features 11 and 12 in Table 1. This puts the sun about halfway between Mounts Meru and Manasottara along the axle of its chariot.
Although Uranus is not mentioned in the Bhagavatam, its orbit lies near the outer boundary of Bhumandala, in the region of darkness called Aloka-varsha. It is noteworthy that the inner boundary of Aloka-varsha is the circular Lokaloka Mountain, said to serve as the outer boundary for all luminaries.12 This is consistent with the fact that the five planets visible to the naked eye are Mercury through Saturn (Saturn’s orbit lies just within the boundary of Lokaloka Mountain).
Asteroids orbit mainly in the region between Mars and Jupiter where astronomers, on the basis of orbital regularities (the so-called Bode-Titius law), predicted the existence of a planet. Asteroids are generally thought to be raw materials for a planet that never formed, though some astronomers have speculated that asteroids may be debris from a planet that disintegrated. Ceres is the largest body in the asteroid belt, and its geocentric orbit lines up well with the outer boundary of Kancanibhumi (feature 16). The hundreds of orbits of smaller main-belt asteroids are scattered fairly evenly around the orbit of Ceres.
As already mentioned, and as shown in Figure 3, the correlation between Bhumandala and the planetary orbits is best at 8.575 miles per yojana. This length for the yojana was calculated entirely on the basis of the Bhagavatam and the planetary orbits. Yet it is confirmed by a completely different line of investigation. As I explained in the previous issue of BTG, the yojana has close ties to the dimensions of the earth globe and to units of measurement used in ancient Western civilizations. My investigations about this led independently to a length of 8.59 miles for one standard of the yojana, a figure that agrees well with the length of 8.575 miles obtained from the orbital study. This agreement underscores the point that Bhumandala does not represent the planet earth, since the 8.59 mile figure reflects accurate knowledge of the size and shape of the earth globe (including the slight polar flattening).
We should note that the Bhagavatam lists heights of the planets above Bhumandala. These heights are sometimes interpreted as the distances in a straight line from the planets to the earth globe, but they are far too small for this. Table 3 compares the heights listed in the Bhagavatam with the mean distances of the planets from the earth, which are many times larger.
Planet Height
(Bhagavatam) Height
(Modern) Mean Distance
Sun 100 100 10,840
Venus 600 555 10,840
Mercury 800 572 10,840
Mars 1,000 690 14,480
Jupiter 1,200 1,733 56,381
Saturn 1,400 5,205 103,474
Table 3. Heights of the planets above Bhumandala in thousands of yojanas, as given in the Bhagavata Purana and as calculated using modern astronomy. The modern heights denote the maximum distances the planets move perpendicular to the plane of the solar system, the plane I have suggested that Bhumandala represents. For comparison, the mean distances of the planets from the earth are listed.** (The mean distance is the halfway point between the minimum and maximum distance of the planet from the earth, as computed using modern astronomy.)
The arguments presented here suggest that the planetary heights actually represent distances perpendicular to the plane of Bhumandala. Since Bhumandala represents the plane of the solar system, the heights listed in the Bhagavatam should be compared to the furthest distances the planets move perpendicular to the ecliptic plane. (Since the sun in the ecliptic plane lies 100 thousand yojanas from Bhumandala, the figures should be offset by that amount.) Table 3 makes this comparison and this is also indicated in Figure 8. We see that for the sun, Venus, Mercury, Mars, and Jupiter, the height listed in the Bhagavatam roughly agrees with the modern height. For Saturn the modern height is about 4 times too large, but it is still much closer to the Bhagavatam height than the mean distance, which is about 74 times too large.
I suggest that the heights listed in the Bhagavatam give a simple estimate of the maximum movement of the planets away from the ecliptic plane. This supports the interpretation of Bhumandala as a simple but realistic map of the planetary orbits in the solar system. The flatness of the solar system is also indicated by the small magnitude of the Bhagavatam heights in comparison with the large radial distances listed in Tables 1, 2, and 3.
In conclusion, the circular features of Bhumandala from 8 through 18 correlate strikingly with the orbits of the planets from Mercury through Uranus (with the sun standing in for the earth because of the geocentric perspective). It would seem that Bhumandala can be interpreted as a realistic map of the solar system, showing how the planets move relative to the earth. Statistical studies (not documented here) support this conclusion by bearing out that when you choose sets of concentric circles at random, they do not tend to match planetary orbits closely and systematically like the features of Bhumandala.
The small percentages of error in Table 2 imply that the author of the Bhagavatam was able to take advantage of advanced astronomy. Since he made use of a unit of distance (the yojana) defined accurately in terms of the dimensions of the earth, he must also have had access to advanced geographical knowledge. Such knowledge of astronomy and geography was not developed in recent times until the late eighteenth and early nineteenth centuries. It was not available to the most advanced of the ancient Greek astronomers, Claudius Ptolemy, in the second century A.D., and it was certainly unknown to the pre-Socratic Greek philosophers of the fifth century B.C.
It would appear that advanced astronomical knowledge was developed by some earlier civilization and then lost until recent times. The so-called flat earth of classical antiquity may represent a later misunderstanding of a realistic astronomical concept that dates back to an earlier time and is still preserved within the text of the Shrimad-Bhagavatam.
Notes
1. Kirk, G. S. and Raven, J. E., 1963, The Presocratic Philosophers, Cambridge: Cambridge Univ. Press., p. 87.
2. Kirk and Raven, 1963, p. 391.
3. Kirk and Raven, 1963, p. 412.
4. British readers, please note: The billions in this article are American; the British billion has three zeros more.
5. The translation of Shrimad-Bhagavatam 5.20.35 says that beyond the ocean of sweet water is a tract of land as wide as the distance from Mount Meru to Manasottara Mountain (15,750 thousand yojanas), and beyond it is a land of gold with a mirrorlike surface. But examination of the Sanskrit text shows that the first tract of land is made of gold, and beyond it is a land with a mirrorlike surface. We have listed this as Adarshatalopama, based on the text.
6. Shrimad-Bhagavatam 5.21.13.
7. In several places Shrila Prabhupada has written that the planet earth was named Bharata-varsha after Maharaja Bharata, the son of Rishabhadeva.
8. Shrimad-Bhagavatam Fifth Canto, Chapter 16, Chapter Summary.
9. “Goodness of fit” can be defined as follows: For each planetary orbit, we can find the shortest distance from a turning point to a circular feature of Bhumandala. The reciprocal of the root mean square of these distances for Mercury through Saturn is the measure of goodness of fit. This measure becomes large when the average distance from turning points to Bhumandala features becomes small.
10. All orbital calculations were performed using the ephemeris programs of Duffett-Smith, Peter, 1985, Astronomy with Your Personal Computer, Cambridge: Cambridge University Press.
11. The 11.2% error of Mars stands out as larger than the others, since Mars partially crosses over feature 9, the outer boundary of Krauncadvipa. The Bhagavatam may refer to this indirectly, since it states in verse 5.20.19 that Mount Kraunca in Krauncadvipa was attacked by Kartikeya, who is the regent of Mars.
12. Shrimad-Bhagavatam 5.20.37.
13. The mean distances of the sun, Venus, and Mercury are the same because Venus and Mercury are inner planets that orbit the sun as the sun orbits the earth (when seen from a geocentric point of view).
Sadaputa Dasa (Richard L. Thompson) earned his Ph.D. in mathematics from Cornell University. He is the author of several books, of which the most recent is Alien Identities: Ancient Insights into Modern UFO Phenomena.
Published in Back to Godhead, 1997, Nov-Dec