Astronomy Astrology and Vedic Mathematics

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http://www.tharananellur.org


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We explore the eclipse - The ancient Indian astronomers knew the real scientific causes of eclipses even in pre- Aryabhatta period. Aryabhatta I (476 AD) explains the phenomenon briefly. ‘The moon covers the sun and the great shadow of the earth that is Bhu Chaya eclipses the moon’. (Arybhatiya, 4.37.)


Varahamihir of 6th century AD, in his famous Brihat Samhita explains at length the scientific cause of an eclipse and boldly discards traditional myths related to the eclipses. “he tells at the solar eclipse the moon enters (covers) the sun’s Disc”. And he also explains, at the lunar eclipse the moon enters the shadow of the earth. – Brihat Samhita V.8.


In Rig Veda, ‘Oh! Sun when the demon Svarbhanu enveloped you by his shadow, the whole world was seen as if the people have forgotten their position and looked to be stunned. The sage Atri could locate the sun, which was covered with darkness by Svarbhanu. Nobody else could do that’. (RV 5/40)

A late commentary by one of the leading Indian astronomers Lalla in 8th C., Provides a scientific explanation for solar eclipse.“People at different places of earth see different parts of the sun as eclipsed. At some places eclipse is not visible at all. When this is understood who can say Rahu causes eclipse ? – Lalla’s Sishya – dhi – Vriddhida, 20-26


Law of gravity what Veda says? Ancient Indian scriptures mention the existence of gravitational force. We can note several references regarding this, but the modern world waited till Newton to know the existence of gravitational force. A definition to Gravity is discussed in ‘Navya kandali’ as follows:‘Gravity is the cause of falling of liquids and solids. It is invisible and is inferred by the falling motion. Gravity acts not only on the body, but also equally on its finer constituents’

‘If the famous goddess of the earth would not hold on this body by supporting apaana this body would have floated anywhere in the space or fallen down’–( Prshnopanishad–Shaankarabhaashya).This statement is shows clearly that Adi Sankara knew very well about gravitational force of the earth.

It is amazing to know that Indian astronomers have found out the precise numerical values of the planetary motion in such a time when not many sophisticated instruments were available for them. This is possible only because of concentration of power and subtle thinking capacity earned b them from veda. In depth knowledge of Indian astronomers can be guessed by the following sample from AryaBhatta


Work about Planetary Motion.

Distance of Planets
The distance of planets from the sun in terms earth to sun average distance known as
Au. (1.5x108 Km) are:

Planet Aryabhatta’s value Modern value

Mercury 0.375 0.387
Venus 0.725 0.723
Mars 1.538 1.523
Jupiter 5.16 5.20
Saturn 9.41 9.54

Revolution of periods: Sidhanta shiromani of Bhaskaracharys gives earth’s period of revolution as 365.2578756484 days. The periods of other planets are
Planet Aryabhatta’s value Modern value
Moon 27.322 days 27.322 days
Mars 1.881 years 1.881 years
Jupiter 11.861 years 1.862 years
Saturn 29.477 years 29.458 years

‘All the planets whether moving in the orbits or in eccentric circles, move anti clock wise from their apogees and clockwise from their perigees’. Aryabhattiya – chapter 3, verse 17
This law was state in the 5th C.AD, much before Johannes Kepler gave the first law of planetary motion in 1609 AD.

Indian astronomers observe the knowledge of elliptical orbits.
bhapa kramo grahamchcha sisivikshepa apamandalata saadharma
sani-guru-kuja-kha-ka-gargha bhruhu-bhudha kha…..
aaryabhattiya – chapter – 1, verse8

The details about elliptical orbits: The greatest declination of the sun: 24 deg. (modern value 23.deg.30 min)

The greatest celestial latitudes

Planet Aryabhatta’s value Modern value
Moon 4deg.30 min. 5 deg.0.min
Saturn 2deg.0.min 2deg.30min
Jupiter 1deg.0min 1deg.30min
Mars 1deg.30min 1deg.51min
Venus 2deg.0min 3deg.23min
Mercury 2deg.0min 7deg.0min

Circling the square: Baudhayana gives the very interesting construction for a circle whose area is equal to that of a given square approximately. He says if you wish to circle the square, draw half of its diagonal above the center towards the east west line, and then describe a circle together with a third part of that, which lies out side the square

Ancient Indian mathematics at glance

Period Mathematics Notable Mathematicians
3000-1500BC Indus scale, length and weigh
Measurement and standardization

1500-5000BC Vedas, Vedangas and Shulba Sutras,


World of numerals, beginning of astronomy Baudhayana,
Arithmetical operations, Vedic geometry Apastambha
Katyayana
500-200BC Emergence of jain mathematics, Number policy
Permutation and combinations, the Binomial theorem
Pingalas Chandah sutra, Meru prastara


Period Mathematics Notable Mathematicians

200BC–400 AD The Bakshali manuscript, Rules of Mathematical
Operations, first use of zero, simple algebra, unknown
Quantity representation, negative sign concept
400 – 1400AD Best period of Indian Mathematics, imp.Mthcal works Aryabhatta
Written by Aryabhattiya, Panchasidhantika, Bhashya, Parameswara
Mahabhashya,Siddhanta siromani, Venuaroha Nilakantta
Madhava, Bhaskaracharya
Varhamihira, Bhaskara
Brahmagupta, Shridhara etc.

‘In gayatri chandas,one pada has six letters. When this number is made half, it becomes three, remove one from three and make it half to get one. Remove one from it, thus gets the zero’ Pingalachary’s Chanda-Shastra-200BC. Almost 2,600 years ago, Apastamba, the great Indian geometer and author of ‘Apastamba Sulba Sutra’, first time gave remarkably accurate value for squre root of 2, as equal to- =1+1/3 + 1/(34) – 1/(3434). The general linear equation was solved in the Apastamba’s Sulba Sutra