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Advanced Astronomy In the Srimad-Bhagavatam
This ancient Vedic text gives an accurate map of the planetary orbits
known to modern astronomy.
By Sadaputa Dasa (Richard Thompson, Ph.D)
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. About a century later, Anaxagoras taught that it is
flat like a lid and stays suspended in air.
A few decades later, the famous atomist Democritus argued that the
earth is shaped like a tambourine and is tilted downwards toward the
south. 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
earths 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 Srimad-Bhagavatam, is dated by scholars to
A.D. 5001000, 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, Bhumandalathe earth mandalais 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.
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 AdarSatalopama, the Mirrorlike Land.
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 chariots 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 suns 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 suns 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 diskthe 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 observers 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 earths orbit the ecliptic, and this
is also the plane of the suns 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 Srila Prabhupada has
repeatedly identified as the planet earth. 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 planets 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 planets orbit tend to line up with circular features of
Bhumandala.
Thus the inner boundary of Mercurys 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 Mercurys
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
Jupiters orbit is tangent to feature 16, and the outer boundary of
Saturns 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 earths heliocentric orbit
as seen from the earth. The suns 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.
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 valuereasonably close
to the traditional figure of 8 milesgives the best fit between
features of Bhumandala and planetary orbits.
To compute the geocentric orbits of the planets, I used a modern
ephemeris program. 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. 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.
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 suns 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.
This is consistent with the fact that the five planets visible to the
naked eye are Mercury through Saturn (Saturns 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.
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
Srimad-Bhagavatam.
4. British readers, please note: The billions in this article are
American; the British billion has three zeros more.
5. The translation of Srimad-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 - AdarSatalopama, based on the text.
6. Srimad-Bhagavatam 5.21.13.
7. In several places Srila Prabhupada has written that the planet
earth was named Bharata-varsha after Maharaja Bharata, the son of
Rishabhadeva.
8. Srimad-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. Srimad-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.