[Advaita-l] Velocity of the planets as told by Aryabhata

[P R]

Namaste Raghav ji ,
First of all, sorry for the late response and  thank you very much for
having shown interest and doing the calculations,
You have asked whether the heliocentrical model of the earth is mentioned
anywhere in the texts, The Aryabhatiya talks about the Heliocentric model ,
whereas the texts like brahmanda purana and Bhagavatha Purana talk about
the Geocentric model of the universe

This does not mean that Bhagavatha was wrong or something like that , but
research still needs to be done on this.
And regarding Rahu and ketu , puranas tell us all sorts of stories, but
astronomically speaking , just like how a circle has one centre, an ellipse
has two foci , for all astronomical calculations regarding rahu ,ketu and
eclipses , these two points are considered and based on these two points.
You can find citations for the same in many astronomical texts like
aryabhatiya or bruhatsamhita and commentaries on the same.

My next article in this series would be about Lagrange's theorem for
solving a numerical of type " Nx^2 + y^2 = C " as mentioned in indian texts
of Bhaskaracharya and other mathematicians, hope you would like that too :)

Thanks and Regards

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On Sat, Sep 19, 2020 at 9:43 PM Raghav Kumar Dwivedula via Advaita-l <
advaita-l at lists.advaita-vedanta.org> wrote:

> On Sat, 19 Sep, 2020, 4:08 PM P R via Advaita-l, <
> advaita-l at lists.advaita-vedanta.org> wrote:
>
> > *Velocity of the planets in a yuga from Aryabhatiya*
> >
> >
> >
> > The velocity of the planets, that is the number of revolutions in a yuga
> (
> > 432 * 10^ 4) are mentioned in the aryabhatiya gitika shloka 3 and 4
> >
> > The planets are arranged in the increasing order if their velocity, along
> > with explanations
> >
> > The rule *अङ्कानाम् वामतोगतिः* is used invariably here
> >
> >
> > 1.  Saturn ( Shani) दुङ्विध्व
> >
> > ढ् (उ) + ङ् (इ) + व् (इ) + घ् (अ) +व् (अ)
> >
> > 14( 10^4) + 5 (10^2) + 6(10^3) +4(1) +6(10)
> >
> > = 1,46,564
>
>
> Namaste Sri PR ji
> I have not seen the Aryabhatiya.
>
> Thanks for sharing your interesting explanation of the chaturyuga cycle
> measured in terms of number of planetary orbits.
>
> If we wish to check with modern figures, I  observed that 146564*29 yrs
> (orbital period of Saturn from modern observation) gives 4,250,356 which is
> a close fit for one chaturyuga cycle. That is neat. This tally with modern
> observation is a testimony to a fairly reasonable precision in ancient
> Indian observational astronomy.
>
> >
> > 2. Guru ( Jupiter) ख्इच्युभ
> > ख(इ) + र् (इ) + च् (उ) + य्(उ) + भ् (अ)
> >
> > 2(10^2)+ 4(10^3) + 6 (10^4) + 3(10^ 5) +24(1)
> >
> > = 3,64, 224
> >
>
> This gives us 4,297,843 yrs agsin a decent fit for a 11.9 yr orbit of
> Jupiter.
>
>
> > 3 Mangala ( Mars) भद्लिझुनुखृ
> >
> > भ(उ) +द्(इ) +ल् (इ) + झ् (उ) + न् (उ) + ख(ऋ)
> >
> > 24(10^0) + 18(10^2) + 5(10^3)+ 9(10^4)+20(10^4) +2(10^6)
> > = 22,96,824
> >
>
> Multiplying by 687 days martian orbit/365 we get 4323063 years which is
> also close to the chaturyoga time.
>
>
> > 4. Ravi (sun) ख्युघृ
> >
> >  ख् (उ) +य् (उ)+घ्(ऋ)
> > 2(10^4) + 3(10^3)+ 4(10^6)
> >
> > = 4320000
> >
> > 5. Soma (moon) चयगियिङुशुछृलृ
> >
> > च्(अ) +य्(अ) +ग्(इ) +य्(इ) +ङ्(उ) + श्(उ) + छ् (ऋ) +ल् (ऋ)
> >
> > 6(1)+3(10)+3(10^2)+3(10^3)+5(10^4)+7(10^5)+7(10^6)+5(10^7).
>
>
> This gives 5,77,53,336 lunar revolutions times 27.3 days per lunar orbit
> gives 43,19,633 years - again a good match.
>
> *अङ्कानाम्
> > वामतोगतिः* rule is used here
> >
> > Just a small observation and calculation done while reading the
> aryabhatiya
> > with the commentary bhaTTa deepikA by paramadievara
> >
>
> I wish to ask you a question.
> Do you happen to know if any of the ancient astronomical treatises mention
> a heliocentric model?
>
> We did know for example, that the lunar nodes created by the inclination of
> the lunar orbit with the ecliptic plane gives rise to the Rahu and Ketu
> nodal points which themselves move due to precession of the lunar orbital
> plane w.r.t. the ecliptic plane . Thus we were able to accurately predict
> solar and lunar eclipses. Many modern Indians don't know that the ancient
> astronomers of India clearly knew the cause of eclipses as the shadow of
> the moon and Sun. The popular folktale of Rahu and ketu being monsters
> swallowing the sun and moon was treated as just a folktale. At least by
> Aryabhata and Varahamihira's time in c.500 AD, the cause and occurrences of
> eclipses was clearly understood.
>
> My request is about a different issue -  if you could share with us
> whether, a heliocentric theory was in vogue in any of these ancient texts
> like AryabhaTIya or brihatsamhitA etc . ( I have only heard of these texts
> , never studied them.)
>
> I do appreciate that a driggaNita based observational astronomical model is
> sufficient and even quite convenient for say, astrological uses. But that
> (the chart looks geocentric) need not imply that they (Aryabhata etc)
> actually believed in a geocentric theory in recording their ephemeris - it
> may have been only for practical convenience.
>
> So, is there any mention of heliocentrism anywhere?
>
> Thank you
> Raghav
>
>
>
>
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