The Orbit of the Sun

“The universe is like a tree with the roots being upwards. The polestar which is situated within the Asking question star constellation is the root. The universe is pivoting around the pole star. That is one movement. The second movement is that the sun is revolving around the universe, as if it were going around the tree” (letter from Śrīla Prabhupāda to Svarūpa Dāmodara dāsa, November 21, 1975).

In this section we will discuss what the Bhāgavatam has to say about the movement of the sun, and then we will use this information to develop the two hypotheses about the projection of Bhū-maṇḍala on the sky that we mentioned in Section 3.b.2. As Śrīla Prabhupāda indicates in the above quote, the sun moves with respect to the reference frame of this earth in two different ways. The most noticeable motion is the daily rotation of the sun from east to west around the earth, which produces the phenomena of day and night. The stars and planets also participate in this motion, and they all appear to revolve once per day around a fixed axis passing through the polestar.

The second motion is the slow movement of the sun from west to east with respect to the stars. This movement takes place along the celestial great circle known as the ecliptic. To visualize this, consider that stars are present during the day, but we cannot see them due to the brilliant sunlight. If we could see them, we would see that on a particular day the sun is surrounded by certain stars. A day later, the sun will have shifted eastward relative to these stars by about one degree. Day by day the sun continues to shift until it completes one revolution around the ecliptic in one year. In the course of this revolution it passes by the various star constellations of the zodiac, which are laid out along the ecliptic (see Figs. 10 and 15).

The ecliptic is tilted at a 23.5 degrees angle to the celestial equator, which is perpendicular to the polar axis. Thus, as the sun moves along the ecliptic, it moves toward the celestial north pole (the polestar) for half the year, and it moves toward the celestial south pole for the other half. When it is north of the celestial equator, days are longer than nights in the Northern Hemisphere, and the opposite is true in the Southern Hemisphere. This situation is reversed when the sun is south of the celestial equator.

3.d.1. The Ecliptic as the Projection of
Bhū-maṇḍala on the Celestial Sphere
Our first hypothesis is that the projection of Bhū-maṇḍala on the celestial sphere coincides closely with the ecliptic. The basic argument for this goes as follows: In the Fifth Canto we read that the sun orbits Mount Meru, moving above a ring-shaped mountain in Bhū-maṇḍala called Mānasottara. This ring is centered on Mount Meru, and it has a circumference of 95,100,000 yojanas (SB 5.21.7). The radius of this ring is about 15,750,000 yojanas, and the height of the sun above Bhū-maṇḍala is 100,000 yojanas (SB 5.23.9p). (Here the Bhāgavatam is using 3 as an approximation for pi.) This means that the distance from the sun to an observer on the earth is much greater (by a factor of 157.5) than the distance from the sun to the plane of Bhū-maṇḍala.

Therefore, the part of Bhū-maṇḍala that lies directly underneath the sun at any given time must seem to be very close to the sun from the point of view of an observer on the earth. In other words, that part of Bhū-maṇḍala must project to a point on the celestial sphere that is very close to the location of the sun. We know where the sun is on the celestial sphere at any given time. So, if we can find out where the sun is in Bhū-maṇḍala at successive moments in time, then we can see where Bhū-maṇḍala falls on the celestial sphere.

The following statements from the Bhāgavatam indicate that the sun makes one circuit around Mānasottara Mountain per year, and that the sun is due north of Mount Meru when it moves farthest to the north on the celestial sphere. (This is called the summer solstice, and it occurs in June.)

[1] Encircling Sumeru Hill on his chariot, the sun-god illuminates all the surrounding planetary systems. However, when the sun is on the northern side of the hill, the south receives less light, and when the sun is in the south, the north receives less [SB 5.1.30]. [Śrīla Prabhupāda comments,] According to Jyotir Veda, the science of astronomy in the Vedic literature, the sun moves for six months on the northern side of Sumeru Hill and for six months on the southern side. We have practical experience on this planet that when there is summer in the north there is winter in the south and vice versa.

[2] In the chariot of the sun-god, the sun travels on the top of the [Mānasottara] mountain in an orbit called Saṁvatsara, encircling Mount Meru. The sun’s path on the northern side is called Uttarāyaṇa, and its path on the southern side is called Dakṣiṇāyana. One side represents a day for the demigods, and the other represents their night [SB 5.20.30].

[3] Śukadeva Gosvāmī continued: My dear King, as stated before, the learned say that the sun travels over all sides of Mānasottara Mountain in a circle whose length is 95,100,000 yojanas [760,800,000 miles]. On Mānasottara Mountain, due east of Mount Sumeru, is a place known as Devadhānī, possessed by King Indra. Similarly, in the south is a place known as Saṁyamanī, possessed by Yamarāja, in the west is a place known as Nimlocanī, possessed by Varuṇa, and in the north is a place named Vibhāvarī, possessed by the moon-god. Sunrise, midday, sunset, and midnight occur in all those places according to specific times, thus engaging all living entities in their various occupational duties and also making them cease such duties [SB 5.21.7].

Passages (1) and (2) indicate that the sun takes one year to make a complete circuit around Mānasottara Mountain. From passage (3) we see that on the plane of Bhū-maṇḍala, the directions north, south, east, and west are laid out in the same way as on a flat Mercator projection of the earth’s surface. In Jambūdvīpa, Bhārata-varṣa is to the south of Mount Meru, and Uttarakuru-varṣa is to the north. Saṁyamanī is much further to the south, on the ring-shaped dvīpa of Puṣkaradvīpa, and Vibhāvarī is located on this dvīpa equally far to the north of Mount Meru. It would seem that the sun spends half the year in the part of its orbit lying to the north of Mount Meru, and half the year in the part lying to the south. This yearly circuit of the sun through Bhū-maṇḍala provides a simple explanation for the many statements in the Bhāgavatam indicating that the demigods’ day (24 hours) lasts for one earthly year.

The motion of the sun through Bhū-maṇḍala is described as follows in the Bhāgavatam:
The chariot of the sun-god has only one wheel, which is known as Saṁvatsara. The twelve months are calculated to be its twelve spokes, the six seasons are the sections of its rim, and the three cātur-māsya periods are its three-sectioned hub. One side of the axle carrying the wheel rests upon the summit of Mount Sumeru, and the other rests upon Mānasottara Mountain. Affixed to the outer end of the axle, the wheel continuously rotates on Mānasottara Mountain like the wheel of an oil-pressing machine [SB 5.21.13].

According to this description, we can imagine the sun moving in a circle around Bhū-maṇḍala in much the same way as a horse-drawn chariot moves around a race track. In discussing this verse, we should comment on the use of metaphor in the Bhāgavatam. One example of metaphorical description is the story of the city of nine gates entered by King Purañjana. There the different gates of the city symbolize different bodily senses. In the verse we have just quoted, the different parts of the wheel of the sun-god’s chariot similarly symbolize different divisions of the year. Thus one might take this verse as a metaphorical description of the movement of the sun during the year. As a general rule, since the purpose of metaphor is to increase understanding and not to obscure it, such indirect interpretation is justified only if the intended metaphorical meaning is transparently clear. One should not devise a metaphorical interpretation simply to replace a clear direct meaning.

Whether the Saṁvatsara wheel should be taken metaphorically or not, the verse clearly states that the sun is moving only a short distance above Bhū-maṇḍala. The comparison with an oil-pressing machine indicates that the chariot of the sun is always directly in contact with the upper surface of the ring-shaped Mānasottara Mountain. The identification of the wheel with the year is also consistent with the view that the sun takes one year to make a complete circuit of Bhū-maṇḍala.

When the path of the sun is projected onto the sky from our vantage point, it lies in the zodiac. According to SB 5.22.5, “Passing through twelve months on the wheel of time, the sun comes in touch with twelve different signs of the zodiac and assumes twelve different names according to those signs. The aggregate of those twelve months is called a saṁvatsara, or an entire year.” If the circuit of the sun through Bhū-maṇḍala (called “Saṁvatsara” in (2) above) takes one year, then the successive parts of Bhū-maṇḍala visited by the sun must correspond to the successive parts of the zodiac lying along the ecliptic. From this we conclude that when Bhū-maṇḍala is projected in the sky, it must lie on the ecliptic, with the northernmost part of Mānasottara Mountain corresponding to the summer solstice.

This means that Bhū-maṇḍala remains stationary with respect to the stars, with the signs Gemini and Cancer (Mithuna and Karkaṭa) in the direction of Vibhāvarī to the north of Mount Meru, and the signs Capricorn and Sagittarius (Makara and Dhanur) in the direction of Saṁyamanī to the south of Mount Meru (see SB 5.21cs). Since the stars rotate once per day around the polar axis, it must be that Bhū-maṇḍala also rotates once per day around this axis. This in turn implies that there is a relative rotation between Bhū-maṇḍala and the earth of our experience.

It is not correct to assume naively that this earth and the rest of Bhū-maṇḍala form a single rigid plate.
Now, this conclusion might be regarded as a drawback to the hypothesis that Bhū-maṇḍala corresponds to the ecliptic. It could be argued that the “earth,” or Bhū, is motionless according to the Vedic literature. If Bhū-maṇḍala rotates daily with the stars and planets, then its system of directions-north, south, east, and west-also rotates and therefore does not correspond to our earthly system of directions. It could also be argued that in the statement that the sun spends half the year to the north of Mount Meru, “north” should be interpreted as meaning the north of the celestial sphere, and “Mount Meru” should be taken as the equator of this sphere.

In response to these arguments, one can reply that if Bhū-maṇḍala is indeed a system of spherical planets floating in space, then why shouldn’t it rotate daily around the celestial pole along with the other stars and planets? We can see how the yearly circling of the sun through this system would produce a day of one year for the higher beings on each of these planets, if they do not rotate about their own axes. In any event, whether Bhū-maṇḍala rotates or not, its system of directions cannot correspond to the earthly system: The earthly north, south, east, and west point in different directions at different points on the spherical earth, while a set of directions on a plane have the same orientation at every point. (For example, at the North Pole every direction is south, but at Mount Meru the four directions are clearly defined.)

3.d.2. The Celestial Equator as the Projection of
Bhu-maṇḍala on the Celestial Sphere
These objections to our first hypothesis suggest a second hypothesis about the projection of Bhū-maṇḍala. This is that the projection of Bhū-maṇḍala on the sky coincides with the celestial equator. This implies that the plane of Bhū-maṇḍala is parallel to the earth’s surface at the poles. At the North Pole, the sun is visible in the sky for half the year. It rises above the horizon at the time of the vernal equinox and spirals slowly up into the sky, making one turn per day. At the time of the summer solstice it reaches a high point of 23.5 degrees above the horizon, and then slowly spirals down, reaching the horizon again at the autumnal equinox. According to this hypothesis, this is how the behavior of the sun would appear to a hypothetical observer standing on one of the dvīpas of Bhū-maṇḍala.

To back up this hypothesis, we first note the following verses, which seem to contradict the idea that the sun makes one circuit through Bhū-maṇḍala per year:
When the sun travels from Devadhānī, the residence of Indra, to Saṁyamanī, the residence of Yamarāja, it travels 23,775,000 yojanas [190,200,000 miles] in fifteen ghaṭikās [six hours].
From the residence of Yamarāja the sun travels to Nimlocanī, the residence of Varuṇa, from there to Vibhāvarī, the residence of the moon-god, and from there again to the residence of Indra. In a similar way, the moon, along with the other stars and planets, becomes visible in the celestial sphere and then sets and again becomes invisible.
Thus the chariot of the sun-god, which is trayīmaya, or worshiped by the words oṁ bhūr bhuvaḥ svaḥ, travels through the four residences mentioned above at a speed of 3,400,800 yojanas [27,206,400 miles] in a muhūrta” [SB 5.21.10-12].

Here we should note some technical details. First, 15 ghaṭikās equals one fourth of a day, and 23,775,000 yojanas is indeed one fourth of the 95,100,000-yojana circumference of Mount Mānasottara. The figure of 3,400,800 yojanas per muhūrta is more difficult to interpret. Normally, there are 30 muhūrtas in a day. However, SB 3.11.8 implies that standards of 24 or 28 muhūrtas per day were also used. If we use 28, we see that 28 times 3,400,000 is 95,200,000. Also, in SB 5.21.19 the sun is said to move 2,000.5 yojanas per moment, or kṣaṇa. This is consistent with 3,400,800 yojanas per muhūrta if we use 1,700 moments per 20 muhūrta. (SB 3.11.7-8 indicates 2,250 kṣaṇas per muhūrta.)

All of these verses say that the sun makes one circuit through Bhū-maṇḍala in a day. If we take this to be the case, then on each day there will be a time when the sun is located above Vibhāvarī, the residence of the moon-god on Mount Mānasottara. At this time on successive days, the sun will occupy a succession of different positions along the ecliptic. The ecliptic itself makes one rotation per sidereal day around the polar axis, and in one solar day it makes slightly more than one rotation. (A sidereal day is measured from star-rise to star-rise, and a solar day is measured from sunrise to sunrise.) If we argue, as before, that Vibhāvarī must be close to the sun on the celestial sphere when the sun passes over it, then it follows that the projection of Vibhāvarī on the celestial sphere must make one orbit per year through the ecliptic.

Combining this motion with the motion of the ecliptic on successive days, and assuming that the sun rotates around Mānasottara Mountain once per solar day, we find that the position of Vibhāvarī on successive days moves slowly up and down between the uppermost and lowermost limits of the ecliptic. By applying this reasoning to a number of other locations in Bhū-maṇḍala, we arrive at the following picture: Bhū-maṇḍala itself moves up and down parallel to the celestial equator in a cyclic motion taking one year to complete.

This is a very strange motion, and it contradicts the assumption that the earth is located in the plane of Bhū-maṇḍala. Clearly something has to give here. One possibility is to relax the requirement that the sun is always close to Bhū-maṇḍala (relative to its distance from us). This allows us to place Bhū-maṇḍala in the plane of the celestial equator. We now suppose that the sun moves up and down with respect to Bhū-maṇḍala in a yearly cycle while also circling Bhū-maṇḍala once per day. This gives the pattern of solar motion that is seen at the North Pole.
This is our second hypothesis. Although it conforms with SB 5.21.10-12, it does have the drawback that it allows the sun to move quite far from the plane of Bhū-maṇḍala.

According to the Bhāgavatam, the distance from Jambūdvīpa to Mānasottara Mountain is 126 million miles. Thus at the summer solstice, when the sun is 23.5Ṭ above the celestial equator, our second hypothesis implies that the sun is about 54,786,000 miles above Bhū-maṇḍala. At the vernal and autumnal equinoxes it is in the plane of Bhū-maṇḍala, and at the winter solstice it is 54,786,000 miles below this plane. This does not agree very well with the descriptions of the sun’s motion around Mount Meru on a chariot comparable to an oil-pressing machine. It also does not agree with the story of Mahārāja Priyavrata, who followed the sun in a chariot that moved over the plane of Bhū-maṇḍala and created the seven oceans by making ruts with its wheels.

The point can also be made that the daily clockwise (or east-to-west) motion of the sun is due to the dakṣiṇāvarta wind, according to SB 5.21.8-9. In general, the movement of the planets around the polar axis is attributed to a wind (SB 5.23.3). If the daily motion of the sun is also due to this wind, then one can suggest that the sun’s yearly counter-clockwise motion could be due to the movement of the sun’s chariot through Bhū-maṇḍala. This interpretation supports our first hypothesis, and it is confirmed by the following remark by Śrīdhara Svāmī in his commentary on SB 5.21.8-9:

Although leftward movement, facing the constellations, is their own motion [svagatya], the luminaries [sun, moon, etc.] move around Meru to the right daily, being blown by the pravaha wind, due to the power of the [kāla] cakra.
Here the svagatya, or “own motion,” of the sun must be its yearly motion around the ecliptic, since this movement is to the left (if one faces the constellations of the zodiac) and the daily motion due to the wind is to the right. Thus the sun’s chariot should be moving counter-clockwise around Mount Meru. (This assumes that the observer is, say, in northern India, where the constellations of the zodiac are to the south. In the southern hemisphere, south of the tropic of Capricorn, everything would be reversed, but the same conclusion about the movement of the sun would hold.)

We suggest that further research will be necessary for us to give a final conclusion regarding the celestial orientation of Bhū-maṇḍala in Vedic cosmology. Here we tentatively propose that the Fifth Canto of the Bhāgavatam is presenting a combined description of the two types of solar motion. Bhū-maṇḍala is being used as the underlying framework in each description, and thus a contradictory picture of its position seems to emerge. We note that a combined description of the two forms of solar motion is explicitly made in SB 5.21.8-9 and SB 5.22.1-2, and the idea of relative motion is introduced. These verses speak of the sun-god circling Mount Meru with the mountain on his left and on his right. Unfortunately, however, they do not specify which motion is actually taking place, relative to the plane of Bhū-maṇḍala.

In spite of these ambiguities, it does appear that the intent of the Bhāgavatam is to present Bhū-maṇḍala as an actually-existing, disc-shaped domain. We have suggested that its location in space must be related to the geocentric orbit of the sun. In Section 4.b we will also argue that its location can be related to the orbits of the moon and other planets. This argument will provide further evidence in support of the hypothesis connecting Bhū-maṇḍala with the ecliptic.

We would finally like to draw attention to the statement in SB 5.21.11 that “in a similar way, the moon, along with the other stars and planets, becomes visible in the celestial sphere and then sets and again becomes invisible.” This statement seems to be another indirect reference to the spherical shape of the earth planet: Since the luminaries are rotating once per day around this sphere, they seem to rise and set daily at any given place (between the Arctic and Antarctic circles).