Compiled by Mayesa dasa, edited by Gauragopala dasa
On April 27, 1976, Srila Prabhupada wrote Bhakti Svarupa Damodara Maharaja, "So now all you must carefully study the details of the Fifth 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."
At first glance, the 5th Canto of the Srimad Bhagavatam deals only with a picturesque vision of the universe. While working with Danavir Gosvami Maharaja and his team in India on deciphering this valuable text, I became convinced that there had to be a mathematical formula to unlock the 5th Canto's mystery. If you will take a few minutes to read this article you will begin to understand the thrill of discovering what is contained in these cryptic verses.
Sun, Moon and Rahu
Part One - Rahu
At the official website for NASA you may scroll down and find a section labeled Orbital Parameters. Scroll down to Inclination to the Equator (deg). http://nssdc.gsfc.nasa.gov/pla.....nfact.html
You will find here 18.28-28.58. This is called declination. If you have a globe and you draw a line around its circumference, that is 0 degrees.
Either side of that line, any point you make will be on some degree of the ball. On this website NASA says that the degree of the Moon's travel is from 18.28 degrees to 28.58 degrees. And sometimes he goes as much as 28.58 degrees. The Sun goes only to approx. 23.5 degrees.
The meaning of this is that as the Moon travels back and forth across the equator it never goes to less than 18.28 degrees. In the Srimad Bhagavatam 5th Canto, Chapter 24, text 2 we find the following:
The sun globe, which is a source of heat, extends for 10,000 yojanas [80,000 miles]. The moon extends for 20,000 yojanas [160,000 miles], and Rahu extends for 30,000 yojanas [240,000 miles]...
Before we proceed to show the incredible accuracy of the Srimad Bhagavatam we must know something about the size of the Earth. The modern calculation of the Earth is 24,902 miles in circumference. Divide this number by 360 to know what each degree would be separately.
24,902 divided by 360 = 69.172222 We must also know that there are 60 minutes in an hour and 60 seconds in a minute and 24 hours in a day.
The Bhagavatam verse gives the timing of the eclipses down to the second. The Vedas also divide the day into 86,400 seconds, into minutes of sixty seconds.
It all works out the same whether you use minutes or muhutas (forty-eight minutes is a muhuta) or hour. The seconds are exactly identical because the unit of 86,400 seconds a day is the same.
These particular calculations are for measuring three different things which science (modern) agrees with. 86,400 divided by 60 divided by 60 equals 24. 24 hours of sixty minutes containing sixty seconds.
And we must know similarly that degrees on a circle also can be measured in this way. We shall begin with Rahu. This means in this case the lowest degree to the equator. (The moon travels from zero to 18.28 at its lowest and 0 to 28.58 at its highest.)
The figure of the size of Dhruvaloka is 512,157,669. Dhruvaloka is said to be a planet at the extreme north of the universe. How we derive the figure for Dhruvaloka we shall show later. The 5th Canto is a precise mathematical puzzle with interlocking parts.
The last number mentioned in the Bhagavatam in a previous chapter was for Dhruvaloka. So we utilize Dhruvaloka for our next mathematical problem.
512,157,669 divided by 240,000 =2,133.990288. Square this (multiply number by itself) = 4,553,914.547. Now divide by 60, divide by 60 again. And divide by a single degree of the earth 69.172=18.28734458.
What did the NASA website say? It said 18.28 Moon Fact Sheet http://nssdc.gsfc.nasa.gov/pla.....nfact.html
Part Two - Length of Sun's eclipse
Utilizing again data which can be found by googling eclipse or googling length of eclipses, we learn that there are two main eclipses. There is a lunar eclipse, and there is a solar eclipse. Both of these eclipses have been timed by modern science. Would you be surprised to learn that their exact times are found in the 5th Canto of Srimad Bhagavatam?
Again we begin with the number of miles around Dhruvaloka. (We shall show how to get this number later.) And we follow the instructions found in Canto 5, Ch. 24, text 2 of Srimad Bhagavatam.
512,157,669 divide by 80,000 = 6,401.970863. Square this number (multiply it by itself) = 40,985,230.92. Now divide by the minutes of an eclipse of the sun which if you google it, you will find is 25,214.
25,214 is 7 minutes and 14 seconds or 7 times 60 times 60 plus 14. So again we divide 40,985,230.92 by 25,214=1,625.495. Now divide that by a single degree of the earth 1,625.495, divide by 69.172=23.499.
The length of the longest possible solar eclipse then is approx. 7 minutes 14 seconds. At least the Srimad Bhagavatam and modern science think so.
Part Three - The length of a lunar eclipse
We are showing that ancient astronomers were far from ignorant about the most modern calculations of the Sun and Moon.
The longest lunar eclipse is estimated on various sites you can google. Here is how we derive this figure from Srimad Bhagavatam 5th Canto, Ch. 24, text 2:
First we take the number of miles circumference of the planet Dhruvaloka and begin – 512,157,669 divide by 160,000 = 3,200.985431. Now we square that number (multiply the number by itself) = 10,246,307.73. Now divide this number by the minutes in a lunar eclipse, which is 359,496.
This number 359,496 is 99.86 minutes. Or 98.86 times 60 times 60 = 359,496. So we divide 10246307.73 by 359496 = 28.5.
Of course my number for Dhruva could be off a fraction or my number for the circumference of the earth, but we see how so very accurate the Srimad Bhagavatam is. We have an accurate measurement of the Moon's lowest declination.
We have an accurate time of solar eclipse. And we have an accurate time of lunar eclipse. At first, it may escape us how much has been revealed in this one verse.
We have learned the movement of the Moon without spending a moment surveying the stars. We have learned the size and shape of the earth without experiment. We have learned the length of lunar and solar eclipses without timing them. And how did the ancients time these things without watches?
It appears such revelations as these put a hole in the theory that mankind is descended from primitive men. Modern Science has not improved a fraction on these conclusions. One wonders what other amazing information is to be found in the 5th Canto of Srimad Bhagavatam.
The Path of Rahu - Part four
The Srimad Bhagavatam 5th Canto, Chapter 24, text 6 says, 'Below the abodes of the Yaksas and Raksas by a distance of 100 yojanas (800 miles) is the planet earth'.
To understand the mathematical construct found in the 5th Canto we shall begin with the earth. The earth according to modern calculation is 24,902 miles around. How many degrees does a round object have? 360.
24,902 times 360 = 8,964,720. Divide this number by the circumference of the constellations that is 2,031,946,146 (we shall show how to derive this number later). Then multiply by (31,500,000-(80,000+80,000+800)) = then multiply by 360 = 49,775,421.11. This is the orbit of the planets called Siddhaloka, Caranaloka and Vidyadhara loka.
Srimad Bhagavatam Canto 5, Ch. 24, text 4 says, 'Below Rahu by 10,000 yojanas [80,000 miles] are the planets known as Siddhaloka, Caranaloka and Vidyadhara-loka.'
Although these planets are located above Dhruvaloka. Below is meant for the mathematician, however I am working backwards, which is more difficult mathematics. Let us begin with Dhruvaloka (we shall explain how to get Dhruvaloka later) and move thru Rahu to Siddhaloka etc. and to Earth. In this way we are following the texts as they appear in the Bhagavatam.
Dhruvaloka's orbit is 512,157,669. Divide by 360, divide by (31,500,000-80,000)) times 2,031,946,146 (constellations) divided by 18.19 degree of Rahu's declination) = 5,057,949.548 times 360 = 1,820,861,837 This is Rahu's orbit through the universe.
The Path of Rahu - Part five
In our mathematical formula, which found the orbit of Rahu, we begin from that very same number to discover the path of Siddhaloka, Caranaloka and Vidyadhara-loka. (Of course we do not know if they revolve or are stationary, or what is their exact configuration or if they are above or below Dhruvaloka.)
1,820,861,837 divide by 360 divide by ((31,500,000-(80,000+80,000)) times 2,031,946,146 divide by 6.588,290,665 = 49,775,421.111 Siddhaloka
49,775,421.111 divide by 360 divide by ((31,500,000-(80,000+80,000+800)) times 2,031,946,146 = 8,964,720 divide by 360 = 24,902 Earth
The Path of Rahu - Part six
The formula we are using will not be thoroughly understood until all the pieces are in place. But it uses the circumference of a planet and divides by 360 degrees to get the numbers for one single degree of that circumference.
Then it follows the formula of Bhagavatam using the 31,500,000 figure of the sun's second axle to subtract or add as the texts indicate. Then we multiply by the constellations. That gives us what is called declination.
We must already know what the declination is for a certain planet and divide by that number. That gives us one single degree of the new planet's circumference. So when we multiply by 360 we have the planet's circumference (orbit).
There is a little more in understanding the movement of the planets north and south, but we shall learn that as we go. The formula that I have described only works after it has been introduced in the text.
As we proceed, and each and every planet's orbit is found, including its north and south circumferences, things will become clearer. At last we shall draw each planetary orbit and see how they actually move.
Part seven. The Constellations, The Big Dipper (Seven Sages) and Dhruva:
Discovering the number 56,400,000 and how to use it, it has occurred to me that the mathematical system of the 5th Canto of Srimad Bhagavatam could be fashioned on such a system (see Sun's Chariot diagram).
It was finding the mention of such numbers in an Ancient Astronomy book attributed to Hipparchus that I thought I must be on the right track. It was through thousands of wrong calculations that the Lord was kind enough to let me crack the mathematics for one other planet. Then it was a matter of filling in the others. (Not a trivial task.)
I am indebted to Danavir Gosvami. I should also thank Dr. Nick Lomb, the Curator of Astronomy at the Powerhouse Museum for kindly supplying me the greatest declinations to the main planets.
We have shown how the circumference of the moon is derived. In the Srimad Bhagavatam the next text after discussing the moon is Canto 5, Ch. 22, text 11:
There are many stars located 2,000,000 yojanas [1,600,000] above the moon, they are fixed on the wheel of time, and there are twenty-eight important stars, headed by Abhijit. (Abhijit is a star in the constellations.)
Here is the math to derive the constellations:
Moon 709,558,416.2 divide by 360 divide by (31,500,000 + 800,000 + 1,600,000) =.058,141,463 times 864,000,000 divide by 8.9 times 360 = 2,031,946,146
The axle of the Sun is 31,500,000 and we are to add 1,600,000 miles to it. We have already added 800,000 to it for the moon. We divide by 8.9 because if you are standing on the equator of Earth, the constellations extend to the north approx 8.9 degrees and to the south approx 8.9 degrees.
Later we shall address Venus, Mercury, Mars, Jupiter, Saturn and the Seven Sages. For now we shall begin with the circumference of the Seven Sages (later we shall show the math on how to derive this number) and show how to derive Dhruvaloka.
Circumference of the Seven Sages is 1,386,038,221 divide by 360 divide by (31,500,000+800,000+1,600,000+(5 X 1,600,000) + 8,800,000 + 10,400,000 =.063,013,194 times 2,031,946,146 = 128,039,417.2 divide by 90 =1,422,660.192 times 360 = 512,157,669 the circumference of Dhruvaloka.
The number 90 is used as declination for Dhruva, as Dhruva is located in the center northern topward position of the universe. He is in line with Meru at the south.
Earth is out to the side from middle, so modern astronomers, not thinking that the universe has a "design", calculates from Earth. In this way they calculate the North Star or pole star as 89.1 degrees or something like that. Bhagavatam apparently calculates from the center of the universe, which is Dhruva, even though Dhruva may or may not be visible to us.
Because this was once the prevailing view of the universe, in the course of my studies I found many statements alluding to Earth being near or in the center of the universe.
In fact, a great amount of information has been handed down through time in various scriptures explaining the constellations as being the home of demigods and angels and of the existence of a second earthly dimension below this one.
Gradually over time the factual history of that ancient information slipped away with the advancement of Kali-yuga and the introduction of modern atheistic science and technologies however, it was once held as true by the most erudite philosophers, astronomers and great sages. As late as Descarte we find him discussing the constellations as an area of divine beings
Part eight - Calculating the distance to Venus and Mercury
In Srimad Bhagavatam 5th Canto we have seen how to calculate the distance of the Sun. In this way the sages have devised a method of calculating other planetary bodies also. Let us review.
We take the sun's circumference (circular path) as it travels around the equator, which is 756,000,000 divide by 360 divide by 31,500,000, and multiply by sun's lowest circumference 864,000,000 to get 57,600,000. Both figures 57,600,000 and 756,000,000 are found in Linga and Visnu and Vayu Puranas (Danavir Gosvami has published the cosmological sections of these books).
So that looks like this: 756,000,000 divided by 360 divided by 31,500,000 times 864,000,000 equals 57,600,000. 57,600,000 in this case appear to be an approximation. The sun travels 23.7 or 23.8 degrees. 57,600,000 divide by 24 equals 2,400,000 times 360 equals 864,000,000.
Of course this is easy when we already know what is the circumference of a planet. The Srimad Bhagavatam 5th Canto gives us a system for finding the planets. Now the Sun is the first planet and the second mentioned is the Moon. But how do we understand this?
We must start out the same way: 756,000,000 divide by 360. But now the formula says to add 800,000 miles so the formula looks like this: 756,000,000 divide by 360 divide by (31,500,000 + 800,000) times 864,000,000 equals 56,173,374.61.
This is the declination in miles of the Moon. To get the circumference or circular orbit around the equator of Earth divide that number by 28.5, now multiply by 360. The circumference of the orbit of the Moon is 709,558,416.2, its declination is 28.5 degrees or 56,173,374.61 miles.
The next planetary body is the constellations. Now we use the last number found to begin our calculation. The math looks like this 709,558,416.2 divide by 360 divide by (31,500,000 + 800,000 + 1,600,000) multiply by 864,000,000 divide by 8.9 multiply by 360.
The constellation belts circumference around us at the equator is 2,031,946,146 its declination is 8.9 degrees or 50,234,224.17 miles. Now that the figure for the constellations has been introduced we will use it in the formula rather than the Sun's circumference of 864,000,000.
Note, we can find the declination of a planetary body if we know its circumference around the equator. If its orbit is 105,000,000 miles around us in a circle then divide the circle by 360 degrees and multiply by the declination. So if the declination was 5 the math is as follows: 100,000,000 divide by 360 times 5 = 1,388,888.88
That does not mean the planet is on that declination now. This means that 5 degrees is where it travels sometime in the future
Part nine - Calculating the distance to Venus and Mercury
The last "planet's" distance we found was the Moon, so we begin with the Moon. The math looks like this: 709,558,416.2 divide by 360 divide by (31,500,000 + 800,000 + 1,600,000 + 1,600,000) times (2,031,946,146 divided by 2) = 56,407,843.86 divide by 8.9 =6,337,959.985 divide by 27.8 times 360 = 1,459,772,842 Now divide that number by 2.
The circumference of Venus as that planet orbits around Earth at the equator is 729,886,420.9.
Unlike the Moon, whose lower and higher declinations bend back towards the Earth like a backwards 'C', Venus follows alongside of and in front of and behind the Sun. Srimad Bhagavatam 5th Canto, Chapter 22, Text 12 says in part - "Sometimes Venus moves behind the sun, sometimes in front of the sun and sometimes along with it."
To calculate the lowest circumference of Venus we divide by cos (27.8) = 825,121,092.8 to get its highest circumference multiply 729,886,420.9 by cos (27.8) =645,643,642.
The circumference of the Sun at the equator is 756,000,000 so if Venus is 729,886,420.9, Venus would be in front of the Sun. However, if Venus is at 729,886,420.9 while the Sun is at 648,000,000, the Sun is technically closer.
These two planets never occupy the same space and therefore never collide, although their paths are similar. We can also note that the Moon is closer, then Venus and then the Sun.
Part ten - Calculating the distance to Venus and Mercury
The last planetary distance we found was for Venus. So we begin with that number to find the next planet, Mercury. The math looks like this: 729,886,420.9 divide by 360 divide by (31,500,000 + 800,000 + 1,600,000 + 1,600,000 +1,600,000) multiply by (2,031,946,146 divided by 2) = 55,521,484.72 divide by 25.6 times 360 = 780,770,878.9.
Now you will notice that the orbit of Mercury is beyond the 756,000,000 of the Sun. If we do the math we can subtract these distances from each other and find that Venus is further away from the Sun and Mercury is closer. Whether or not these planets "circle" the Sun I do not know. But we could program the Fifth Canto math into a computer and find out. Again, as with Venus, Mercury is sometimes behind, sometimes with and sometimes in front of the Sun.
In Srimad Bhagavatam 5th Canto, Ch 22, text 12, Mercury is described to be similar to Venus, in that it moves sometimes behind the Sun, sometimes in front of the Sun and sometimes along with it.
Again we can find the higher and lower declinations by dividing the circumference by cos (25.6) or by multiplying the circumference by cos (25.6) We can also note that Venus is further from the Sun than Mercury, possibly placing Venus's orbit around Mercury. But it is by plugging the numbers into a computer we shall learn
Part eleven - The Chariot of the Sun is 28,800,000 miles long
You can begin the calculation in the following way. Fifth Canto Srimad Bhagavatam explains the "chariot of the sun" is 28,800,000 miles long. By several other verses, which give different figures, we can understand that the "chariot of the sun" has to be multiplied by 30.
This figure 30 is the number of muhurtas. (There are 30 muhurtas in a 24-hour period). 30 x 28,800,000 is 864,000,000, now this is the Sun at 23.5 degrees south. Similarly a figure is there in Bhagavatam 756,000,000, that is the Sun at 0 degrees celestial. Then the Sun goes to the north to 648,000,000.
All this means is that you can demonstrate this to yourself on a ball. Take only one-half of the ball and wrap something around it so that it gradually moves away from the center towards the top so that at every moment the Sun is moving up and closer to the Earth. This means that the Sun is further away when it goes to the south 23.5 degrees and closer as he moves northward.
This is also confirmed in Matsya Purana, that the Sun is gathering water from the entire universe up to Dhruvaloka. Therefore the Sun changes sizes as he moves up and down. In the spring and summer he is gathering water, then he releases the water. We do not notice any change in size because he changes distance.
The modern scientist speculates that the Sun is only a ball of gases, however, the Srimad Bhagavatam explains that a civilization lives there. What we see with telescopes and space probes is only a limited view of all the cosmos.
The fact is, our gross material senses and their material technological extensions that magnify the material universe around us are not seeing the universe in its full potential.
That includes other higher and lower dimensional realities such as the Yamadutas when they come to detain an embodied soul encased in a subtle material body on the death of their gross biological body.
Modern material science therefore has not the eyes to see the Demigods' realities, that include the Sun Planet and his chariot as explained in the 5th Canto of the Srimad Bhagavatam, nor can they see the clouds surrounding the Sun composed of water that the Sun has drawn there, as explained in the Matsya Puranas.
Part twelve - Drawing the 'Chariot of the sun' diagram based on the descriptions found in 5th Canto of the Srimad Bhagavatam
How to draw a diagram of the Sun from the side explained in this way:
First take a square. (It will be helpful if you make it three or four inches on each side because we will be writing numbers under or on top of those lines later on) Then inside the square draw a circle. Where the circle touches the top and sides, draw lines. That divides the circle into four quadrants. It looks something like a gun site. (A square with a circle inside with a cross inside that.)
For this circle we will borrow the image of a clock to help us label its "points". I have already written how to draw it but let us go over it again. (I will also draw this out as I describe it where I am sitting typing this, so I do not make an error.) We shall label points where lines intersect as A, B, C, etc., then we can give the numbers of miles for these lines.
Where the two lines intersect in the middle of our circle will be point A. Where the horizontal middle line intersects the circle on the right will be B. (This is where the circle touches the square on the right.) At two 'o'clock we will make a point C.
Between two o'clock and three o'clock (on the clock face - the circle, exactly midway between C and B) make point D.
Draw a horizontal line from C to center vertical line. That point is E. Draw a horizontal line from point D to center vertical line. That is point F. We now have all our points. They should be on three parallel lines in the upper right quadrant of our circle.
We need two more lines.
Draw a line from point C to point F.
Draw a line from point F to point B.
We now have our points and lines. This is how to draw the diagram of the Sun from Srimad Bhagavatam. (It should look like two flags or pennants, one upside down and one right side up, the lower one larger and the upper one smaller.)
In the second step we will now insert numbers that are miles of distance.
Part thirteen - Constructing diagram of Chariot of the Sun
Now we shall write on top of or under our lines the numbers of the distances between all the points above.
Line AB is 137,509,870.8
Line BD is 56,400,000 (Although this line is circular it is called a line)
Line CD is 56,400,000 (Although this line is circular it is called a line)
Line FB is 149,946,415.4
Line FD is 120,321,137
Line AF is 59,790,993.67
Line FC is 112,459,811.5
Line EC is 103,132,403.1
Line EF is 44,843,245.13
NOTE:
The chariot of the sun in 5th Canto Bhagavatam is said to be 28,800,000. The meaning is that this is the Sun's greatest distance of movement in a muhurta. (There are 30 muhurtas in a 24-hour period.) He travels different distances every day. In fact, he loses 39,425 miles every muhurta, so that we can know the distance the next day. 864,000,000 minus (39,425 times 30) which is 862,817,250.
This will become obvious after you understand the math of the Sun's chariot diagram.
Part fourteen - Circumference of the Sun
If the circumference of the Sun is 28,800,000 times 30 = 864,000,000 we divided by 2 and by 3.141592654=137,509,870.8. That is line AB (The formula is circumference divided by 2 and by PI - Pi is 3.141592654. Pi is a number that has no end because there is always (theoretically) a measurement smaller on a circle). 137,509,870.8 divide by cos (23.5) is 149,946,415.3, that is line FB.
The formula we used is the formula for finding the hypotenuse of a right triangle if we know the bottom side. (Mathematicians have several different names for the bottom of a right triangle. I like to refer to it as the "floor" or "bottom". Hypotenuse I call the "roof" because it slants. Or I just call it hypotenuse. The smallest side I call the "wall." The hypotenuse squared minus the floor squared equals the wall. That gives us line AF. Line FD is 756,000,000 divide by 2 and divide by PI (We get the figure 756,000,000 from Vayu and Linga Puranas)
These math formulas can be used to get line EC and EF. In order to get the arc or circular lines on our diagram we divide 864,000,000 by 360.
(There are 360 degrees in a circle) Then we multiply that number by the degrees we wish to know. 864,000,000 divided by 360 times 23.5 = 56,400,000.
NOTE:
If we came from the outside of the universe at its top we would look down and see the Sun circling Meru (which would be the unmoving center of a circle) in a clockwise fashion.
We would see Meru in the center, then Earth out to its side (maybe stationary), then the moon circling Meru and the Earth in a clockwise fashion, then the Sun circling Meru and the moon and the Earth in a clockwise fashion etc.
That is not the diagram of the Sun.
The diagram of the Sun is what you would see if you came from outside of this universe from the side of the universe. The diagram is like a snapshot of the Sun's movement. But it is on a piece of paper or on a screen, which is flat (one dimensional) and does not show that the Sun is moving in three dimensions.
The Sun starts at point B and moves towards the viewer (leaving the page) and then to the left side of our square and then backs behind it; in this way it has a circular movement (three-dimensional).
This is described in the Bhagavatam as just like an axle that is fixed to the top of Meru. The Sun's circle is getting smaller everyday and he is moving northward at the same time. He continues like this until he reaches his highest height and begins to descend in the same matter. As he descends he begins to add 30 times 39,425 miles every 24 hours.
For those keeping track of this site, I have found a small mathematical error in my computations. It does not however appear to affect the entire formula. The method I have employed for finding a circumference is mentioned below. So here is the proper method for finding a circumference so that we can get perfect results. It affects four of the planets so now this revised formula will prove more perfect.
Formerly I have written that to get the highest circumference of a planet from its middle you multiply by the cos of the declination, however, this is the proper way to change circumference and make this mathematics final and clearer:
"If I want to know the Sun's 864,000,000 circumference at 23.5 degrees south I use this formula: 864,000,000 / 360 = 2,400,000 x (360- (23.5 X 1.913553055) = 756,000,000. The number 1.913553055 can always be used even when the declinations or circumferences are different. We shall present a paper summarizing all mathematical formulas at the end of these articles".
The chariots of the other planets and their distances can be derived from Bhagavatam also, as I have explained. The universe has an edge in every direction where the universe ends and the spiritual world begins.
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