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While reading Translation of the Surya Siddhanta and of the Siddhanta Siromani(1861) - Bapu Deva Shastri, I stuck in the follwing.

Chapter I, verse 41 & 42

In a KALPA (4.32 billion years), there are 387 revolutions of the Sun's Apogee (about the earth), 204 of Mars' apogee, 368 of Mercury's apogee, 900 of Jupiter's apogee, 535 of Venus' apogee and 39 of Saturn's apogee.

Now my question is what is meant by 387 revolution of Sun's apogee? It will be helpful if someone can explain this.

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  • I am not exactly sure, But in a Geocentric view (keeping earth at center and the rest of planets and sun revolve) the Sun's Apogee itself (I.e. the point of farthest distance in a orbit) revolves around the earth for 387 times in a kalpa. (Like precession)
    – Proxy
    May 20 at 11:19
  • This happens for moon for every 8.85 years called the Apsidal precession also see moon
    – Proxy
    May 20 at 11:27
  • Maybe you could also add the original sanskrit verses too.
    – peace
    May 20 at 12:51
  • I suggest you to ask this on astronomy stack exchange, there might be few experts on these topics. Maybe they can tell you what's happening exactly. (But most of them might say surya siddhanta is having wrong values)
    – Proxy
    May 22 at 4:40
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We are used to heliocentric view (sun at the center and planets revolves around it). This is the currently accepted model of solar system. (Let me give a fair idea of it, skip it if you dont want to read it)

Things get complicated when we look at geocentric view (earth at center and the rest of planets revolve it). The only 'Graha' that remains invariant in both the views is Moon. Thus we still have its Nodes (पात) and it will be the only example I will show.

Geocentric view

Apogee (मन्दोच्च) is the farthest distance in orbit around the earth. Go anywhere on Internet you will find the Apogee only for Moon. All the other planets have Aprihelion and Perihelion which are farthest point and nearest in orbits around sun. Sun neither has a Apogee nor a Aprihelion in heliocentric view.

Geo vs. Helio

Precession of orbit is calculated by revolution of this apogee. More better is the line connecting Apsides (Apogee and Prigee are collectively called Apsides, however in heliocentric they are Aprihelion and Perihelion). This kind of precession is called apsidal precession, which has very small periods, it literally takes millions of years for the ellipse to orbit once.

Apsides


Now coming to surya siddhanta, it uses both the Heliocentric and Geocentric view. Quoting from "Introduction" of Surya-Siddhanta by Ebenezer Burgess

The ucca is conceived of two classes, the first, mandocca, in the case of sun and the moon, means the apogee where the angular motion is slowest, & in the case of other planets it's the aphelion point of orbit....

Chapter 2 of Surya-Siddhanta deals with the effects of these points on the motion of planets. Now look at the verse 33,

चन्द्रोच्चस्याग्नि शून्याशिववसूसपार्णवा युगे । वामं पातस्य वस्वग्नियमाशिवशिखिदस्त्रकाः॥33॥

Of the moon's apsis, in an age (1 mahayuga), four hundred and eighty-eight thousand, two hundred and three; of its node, in the contrary direction two hundred and thirty-two thousand, two hundred and thirty-eight.

Quoting from the same:

By moon's "apsis" is to be understood her apogee; ucca is literally "hight" I.e. "extreme distance": The commentry explains it by mandocca, "apex of slowest motion": As the same word is used to designate the aphelia of planets, we were obliged to take in translating it the indifferent term apsis which applies equally to both Geocentric and heliocentric motion.

The number of times the Sun's Apogee revolves around the earth is provided for one kalpa for sun (verse 41):

प्राग्गतेः सूर्यमन्दस्य कल्पे सप्ताष्टवह्नयः । कौजस्य वेदखयमा बौधस्याष्टर्तूवह्नयः॥ 41॥

This means that in Geocentric view the Apogee would have revolved for 387 times around the earth in one kalpa. Look at the figure. U is the Apogee of sun or the moon. Which faces the Earth E, if planet is at M its drawn towards P and if at M' its drawn towards P'. By revolving apogee we mean U would move in the Backgroud of Rashi.

Sun and moon

But it's actually a very sensitive calculation! If we look at the length of an kalpa its 4.32 billion years. To observe this in reality we would need a lot of time. For a change of 1 minute sun would need 516.8 years! Again quoting:

...Hindus had no idea of any motion of Apsides and nodes of planets as an actual observable phenomenon; But knowing that the moons apsis and node moved, they fancied that symmtry of universe required that those of the other planets should move also; & constructed their systems accordingly.....the close accordance of different astronomical systems in fixing the position of points which are so difficult of observation and deduction as the nodes and apsides, strongly indicated that either Hindus were remarkably accurate observers or someone of them was followed as authority by others...


Example: Morden calculations show that the period of Apsidal precession of moon is 8.85 years.

Surya-Siddhanta gives this for one mahayuga for moon (verse 33).

The moon's Apogee revolves around for 488203 times. Calculations: 1 Mahayuga = 4,320,000 years. Dividing it by 8.85 years we get 488135.59 which is in an quite excellent agreement with value in Surya-Siddhanta!

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  • Nicely explained. So this planetary Kalpa unit is same as Lord Brahmâ day Kalpa, only when looked at through geocentric perspectives and not heliocentric perspectives?
    – peace
    May 21 at 7:21
  • No no, it's not a "planetry kalpa unit". Its the movement of the point itself in the orbit, where the planet revolves with slowest velocity (mandocch). Which is translated as Apogee. we count how many times does it complete one revolution around earth in 1 kalpa. We could also do it for 1 mahayuga or 1 year of earth but the motion is so slow that its value is negligible. @vivikta
    – Proxy
    May 21 at 7:51
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    Quite a big unit then!
    – peace
    May 21 at 8:04
  • But, according to Einstein's theory in Apsidal precession, for earth a=152.1×10^9m, T=3.156×10^7s, c=3×10^8m/s, e=0.0167 i.e in a year apsidal precession of earth is about 1.92×10^(-7) rad, and so in a KALPA there should be 132 (=1.92×10^(-7)×4.32×10^9×1/2pi) revolutions of sun's apogee (in geocentric view) @Proxy May 21 at 15:48
  • @supriyoHalder that does not make it Geocentric, I am still trying to find a working example for someone other than moon. Also this is the part contributed by relativistic effects. Also if one goes by actual period of pression of 112000 earth years in an kalpa it would be 38571.42.
    – Proxy
    May 21 at 17:53

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