Summary of the book
The 5th Canto of Srimad Bhagavatam provides us arc measurements. On earth, latitude is measured in an arc on maps.
For example, the arc of the sun on earth is measured like this: 1,652 miles ( arc or latitude ) ÷ 23.6 ( degree of the sun at southernmost or northernmost Ayana )= 69.172 ( degrees of a circle ) X 360 ( every circle has 360 degrees ) = 24,902
24,902 is our base of operations.
Similarly, the Bhagavatam provides arcs and if we know the base of operations we can find the necessary declinations. This is the secret.
With declination every astronomer and astrologer knows and has always known from antiquity we can find Sun, Moon, Constellations, Venus, Mercury, Mars, Jupiter, Saturn.
These declinations are respectively 23.6, 28.7, 9, 27.8, 25.6, 27.2, 23.5, 22.8.
After finding orbits for Mars, Jupiter and Saturn we must multiply by 2.
The arc for the sun is approx. 51,899,110.64
51,899,110.64 ÷ 23.6 X 360 = 791,681,348.7. This is the orbit of the sun at the time it passes across the celestial equator. Thus Bhagavatam is describing a geocentric model.
To derive the moon we add 800,000 miles to arc, etc.
The second axle of the sun is actually provided for us to derive the equant. Equant means the position of the earth ( Visvanatha Cakravarti’s commentary states that earth lies above the saltwater Ocean. )
Math for this I have provided. The equant is important as it helps prove 7 sages and Dhruvaloka. The math is found in the book.
For the higher planetary bodies, we are not given declination. Because of this reason ( and many others ), I am sure many have attempted the arc method without meeting a success.
However, the base of operations for the higher planets up to the Vaikunthalioka planet ( yes there is a Vaikuntha planet in this universe ) is Lokaloka at 2,065,911,329 and universe circumference 12,566,370,610 respectively.
Moving down the universe we first encounter Rahu. It is calculated according to time instead of declination. The time is 27.32 or the days it takes for Moon to make one full revolution.
The next verse explains how to calculate the eclipses ( Sizes means eclipses according to Madvacarya and Visvanatha Cakravarti commentaries ) I give this method of calculating in the book.
That Rahu can also be a planet is explained in the book.
Siddhaloka, Vidyadharaloka and Caranaloka use the same base of operations as the constellations. This is apparently Orion’s Belt.
Antariksa is calculated from trapezoidal math.
Earth has already been determined so earth in Srimad Bhagavatam ( 800 miles below Rahu ) is the Bhumandala. Its base of operations is 1,274,229,800 miles.
The 7 lower planetary divisions are equal in size ( stated in SB. And confirmed by acharyas commentaries ) to Bhumandala.
The Hellish planets and the Garbodaka ocean are calculated with trapezoidal math. Where Hell ends Garbodaka begins. That is what the math indicates.
The method of calculating by the arc is brilliant. It allows those who memorize the arcs to pass on the science in its entirety.
This book is offered free of charge to the Bhaktivedanta book trust and the TOVP.