The polestar (Dhruvaloka) is the central pivot of the universal planetary system

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Srimad-Bhagavatam

SB Canto 4

The polestar, called Dhruvaloka, is the pivot of this universe, and all planets move around this polestar.
SB 4.29.42-44, Purport:

All the great sages mentioned in this verse have their planets near Brahmaloka, the planet where Lord Brahmā resides along with four great sages—Sanaka, Sanātana, Sanandana and Sanat-kumāra. These sages reside in different stars known as the southern stars, which circle the polestar. The polestar, called Dhruvaloka, is the pivot of this universe, and all planets move around this polestar. All the stars are planets, as far as we can see, within this one universe. According to Western theory, all the stars are different suns, but according to Vedic information, there is only one sun within this universe. All the so-called stars are but different planets. Besides this universe, there are many millions of other universes, and each of them contains similar innumerable stars and planets.

SB Canto 5

Like bulls yoked to a central pivot, all the planetary systems revolve around Dhruvaloka, impelled by eternal time.
SB 5.23 Summary:

This chapter describes how all the planetary systems take shelter of the polestar, Dhruvaloka. It also describes the totality of these planetary systems to be Śiśumāra, another expansion of the external body of the Supreme Personality of Godhead. Dhruvaloka, the abode of Lord Viṣṇu within this universe, is situated 1,300,000 yojanas from the seven stars. In the planetary system of Dhruvaloka are the planets of the fire-god, Indra, Prajāpati, Kaśyapa and Dharma, all of whom are very respectful to the great devotee Dhruva, who lives on the polestar. Like bulls yoked to a central pivot, all the planetary systems revolve around Dhruvaloka, impelled by eternal time. Those who worship the virāṭ-puruṣa, the universal form of the Lord, conceive of this entire rotating system of planets as an animal known as śiśumāra. This imaginary śiśumāra is another form of the Lord. The head of the śiśumāra form is downward, and its body appears like that of a coiled snake. On the end of its tail is Dhruvaloka, on the body of the tail are Prajāpati, Agni, Indra and Dharma, and on the root of the tail are Dhātā and Vidhātā. On its waist are the seven great sages. The entire body of the śiśumāra faces toward its right and appears like a coil of stars. On the right side of this coil are the fourteen prominent stars from Abhijit to Punarvasu, and on the left side are the fourteen prominent stars from Puṣyā to Uttarāṣāḍhā. The stars known as Punarvasu and Puṣyā are on the right and left hips of the śiśumāra, and the stars known as Ārdrā and Aśleṣā are on the right and left feet of the śiśumāra. Other stars are also fixed on different sides of the Śiśumāra planetary system according to the calculations of Vedic astronomers. To concentrate their minds, yogīs worship the Śiśumāra planetary system, which is technically known as the kuṇḍalini-cakra.

SB 5.23.2, Translation:

Established by the supreme will of the Supreme Personality of Godhead, the polestar, which is the planet of Mahārāja Dhruva, constantly shines as the central pivot for all the stars and planets. The unsleeping, invisible, most powerful time factor causes these luminaries to revolve around the polestar without cessation.

SB 5.23.3, Translation:

When bulls are yoked together and tied to a central post to thresh rice, they tread around that pivot without deviating from their proper positions—one bull being closest to the post, another in the middle, and a third on the outside. Similarly, all the planets and all the hundreds and thousands of stars revolve around the polestar, the planet of Mahārāja Dhruva, in their respective orbits, some higher and some lower. Fastened by the Supreme Personality of Godhead to the machine of material nature according to the results of their fruitive acts, they are driven around the polestar by the wind and will continue to be so until the end of creation. These planets float in the air within the vast sky, just as clouds with hundreds of tons of water float in the air or as the great śyena eagles, due to the results of past activities, fly high in the sky and have no chance of falling to the ground.

Lectures

Sri Caitanya-caritamrta Lectures

From Bhāgavatam we understand sun is not fixed up in one place but it is going round. And the whole universal planetary system, they are also moving, making the polestar, making the polestar as the pivot.
Lecture on CC Madhya-lila 20.110-111 -- Bombay, November 17, 1975:

So the example is given: just like fire is localized in a place but the heat and light is expanded. The vivid example we can see, the sun. The sun globe is situated in one place—every one of us, we can see—and the heat and light is distributed throughout the whole universe. According to our Vedic conception, the sun is moving round, not the sun is the center. It is in the center of the universe, but it is going round. Kala-cakra. It is called kala-cakra. In Brahma-saṁhitā it is said,

yac-cakṣur eṣa savitā sakala-grahāṇāṁ
rājā samasta-sura-mūrtir aśeṣa-tejāḥ
yasyājñayā bhramati sambhṛta-kāla-cakro
govindam ādi-puruṣaṁ tam ahaṁ bhajāmi

From Bhāgavatam we understand sun is not fixed up in one place but it is going round. And the whole universal planetary system, they are also moving, making the polestar, making the polestar as the pivot.

Conversations and Morning Walks

1975 Conversations and Morning Walks

The pivot is the polestar. Fixing, the pole-star, they are moving like this. And there is sun's movemen.
Morning Walk -- October 25, 1975, Mauritius:

Indian man: In the moon too there is fire? But it is cold, as the, our sages say.

Prabhupāda: It is surrounded by cooling atmosphere.

Indian man: It rotates?

Prabhupāda: In a different way, not as they explain.

Indian man: They rotate.

Prabhupāda: Just like my hands is moving... (break) ...like that.

Indian man: And it does not go all around other planets?

Prabhupāda: No.

Cyavana: They all move together?

Prabhupāda: Yes.

Cyavana: They move together?

Prabhupāda: Yes. The pivot is the polestar. Fixing, the pole-star, they are moving like this. And there is sun's movement.

1976 Conversations and Morning Walks

That is the polestar. That is the up side of the universe. And that we have described in the Bhāgavatam. That is the pivot, and the whole planetary system is moving twenty-four hours.
Room Conversation -- June 15, 1976, Detroit:

Prabhupāda: So all of you now make a complete idea how to make Vedic planetary, planetarium. Another question. Why in every map the northern side is accepted up? (laughter) Can anyone answer this? North, south. South is considered down. East, west. Why not other ways? I can make east on that side. Why it is north only up side? Can anyone answer?

Ambarīṣa: It might have something to do with the magnetic poles. The magnetic force is always pulling to the north.

Prabhupāda: That is the polestar. Yes. That is the up side of the universe. And that we have described in the Bhāgavatam. That is the pivot, and the whole planetary system is moving twenty-four hours.

Puṣṭa Kṛṣṇa: That's factual also. Because they see that all of these stars and constellations are going around the North Star.

Prabhupāda: But the modern astronomy, they do not say like that.

Jayādvaita: No. They don't say it is moving around. They don't say that it's moving around the polestar. They have some other explanation.

Prabhupāda: That means they're imperfect.

Mādhavānanda: They say that it's fixed. They say the polestar is fixed, but it doesn't revolve around. They say everything moves, but the polestar is...

Prabhupāda: Polestar is fixed, that is fact. And all.... It is like pivot. Everyone round, round. Ūrdhva-mūlam adhah-śākham (BG 15.1). This tree is spread downwards. The root is upward.

Puṣṭa Kṛṣṇa: The scientists also say all of the stars are moving around. But they don't see the earth as moving around.

Prabhupāda: Why not? What is this nonsense? If all the stars can move, what is the earth? That is their nonsense.

Correspondence

1975 Correspondence

The universe is pivoting around the pole star. That is one movement. The second movement is that the sun is revolving around the universe, or as if it were going around the tree.
Letter to Svarupa Damodara -- Bombay 21 November, 1975:

From the Srimad-Bhagavatam we learn that the universe is like a tree with the roots being upwards. The pole star which is situated within the Asking question starts 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, or as if it were going around the tree. That is the second movement. The sun is not fixed. If this is proved, then their whole scientific theory collapses. According to them, the stars are all suns. The stars may have the same composition as the sun but they are not suns. The Brahma-samhita says that the sun is the king with unlimited light and temperature. The Srimad-Bhagavatam sublime literature describes all these things and it was written five thousand years ago. And they say that five thousand years ago there was no civilization. That Srimad-Bhagavatam has this information proves that Indian civilization is the oldest civilization.

1976 Correspondence

Just as a tree has branches and leaves so the universe is also composed of planets which are fixed up in the tree like the leaves, flowers, fruits, etc. of the tree. The pivot is the pole star, and the whole tree is rotating on this pivot.
Letter to Svarupa Damodara -- Auckland 27 April, 1976:

Now our Ph.D's must collaborate and study the 5th Canto to make a model for building the Vedic Planetarium. My final decision is that the universe is just like a tree, with root upwards. Just as a tree has branches and leaves so the universe is also composed of planets which are fixed up in the tree like the leaves, flowers, fruits, etc. of the tree. The pivot is the pole star, and the whole tree is rotating on this pivot. Mount Sumeru is the center, trunk, and is like a steep hill, like the alps mountains which also have very high peaks. I have seen in Switzerland one mountain peak which was so high that is penetrated through the clouds. The tree is turning and therefore, all the branches and leaves turn with the tree. The planets have their fixed orbits, but still they are turning with the turning of the great tree. There are pathways leading from one planet to another made of gold, copper, etc., and these are like the branches. Distances are also described in the 5th Canto just how far one planet is from another.

We can see that at night, how the whole planetary system is turning around, the pole star being the pivot. Each planet has its orbit fixed but the sun is moving up and down, north and south. It is not that we shall accept the theory that the sun is fixed up and the others are all going around the sun.
Letter to Svarupa Damodara -- Auckland 27 April, 1976:

We can see that at night, how the whole planetary system is turning around, the pole star being the pivot. Each planet has its orbit fixed but the sun is moving up and down, north and south. It is not that we shall accept the theory that the sun is fixed up and the others are all going around the sun. That is not correct. Even the 7th star is rotating once around the pole star in each 24 hours. The whole universe is just like a big tree, that is a fact. I do not think that the modern astronomers have any such idea that the whole universe is like a big tree. The planets which are full of living entities are one after another, one above the other. The relative positions of the planets is fixed up but the whole thing is turning. The sun is going north and south, it has its own orbit below the moon. So now you all Ph.D.'s must carefully study the details of the 5th Canto and make a working model of the universe. If we can explain the passing seasons, eclipses, phases of the moon, passing of day and night, etc. then it will be very powerful propaganda.