Surya Siddhantha – Brahma Mana

Finally, the grandest of all timescale – the Brahma Mana:

Here is the Surya Siddhantha definitions of Kalpa and Para:

Fourteen such Manus with their Sandhis (as mentioned before), constitute a Kalpa, at the beginning of which is the fifteenth Sandhi which contains as many years as a Krita does. – Chapter 1, Verse 19

Thus a thousand of the great Yugas make a Kalpa, a period which destroys the whole world. It is a day of the God Brahma, and his night is equal to his day. – Chapter 1, Verse 20

And the age of Brahma consists of a hundred years – according to the enumeration of day and night (mentioned in the preceding verse). – Chapter 1, Verse 21

This timescale moves beyond millions with the Kalpa being 4.32 Billion solar years and a Para being 311.04 Trillion solar years! These are clearly astronomical timescale – compare with the age of the Earth estimated by modern science at 4.54 Billion years and the age of the Universe estimated at 13.75 Billion years since the Big Bang.

That completes my series on the Surya Siddhantha.

Surya Siddhantha – Prajapatya Mana

I have already written about the time scales covered in the Prajapatya Mana in an earlier post, without using the nomenclature explicitly.

The Prajapatya Mana leverages the Divya Mana to build a grand timescale spanning millions of solar years as follows:

This model is best read from right to left:

• The basic building block of these long-count timescales is a Pada which is made up of 1200 Divya Varshas.
• Using the Padas four Yugas are constituted – Satya Yuga (4 Padas), Trita Yuga (3 Padas), Dwapara Yuga (2 Padas) and Kali Yuga (1 Pada)
• Each Yuga includes within itself a dawn and a twilight totaling a duration one sixth of the Yuga.
• These four Yugas are combined in order to form a Maha Yuga.
• Seventy one Maha Yugas are then combined to form a Manvantara.
• A Manvatara is followed by a period called a Sandhi which is as long as a Satya Yuga in duration.

A quick calculation reveals that the duration of a Maha Yuga is 4.32 Million solar years and that of a Manvantara is 306.72 Million solar years!

The Surya Siddhantha definitions are as follows:

Surya Siddhantha – Divya Mana

After the 60 years cycle of Jupiter (Guror Mana) comes the 360 year timescale of the Gods.

The Divya Mana is modeled as follows:

The Surya Siddhantha defines the timescale of the Gods as follows:

…A solar year consists of twelve solar months and this is called a day of the Gods. – Chapter 1, Verse 14

An Ahoratra (day and night) of the Gods and that of the Demons are mutually the reverse of each other. Sixty Ahoratras multiplied by six make a year of the Gods and Demons. – Chapter 1, Verse 14

Surya Siddhantha – Guror Mana

Now let us move into the longer timeframes, sarting with the Guror Mana (aka Bruhaspatya Mana).

The Surya Siddhantha defines Guror Mana as a timescale based on Jupiter’s orbital period around the earth multiplied five times:

…by the Māna of Jupiter is to be determined the year of the cycle of sixty years… – Chapter 14, Verse 2

Multiply the number of elapsed revolutions of Jupiter (in a Maha Yuga) by 12; to the product add the number of the signs from Mesha to that occupied by Jupiter; divide the mount by 60, and reckoning the remainder from Vijaya, you will find the present Samvatsara. – Chapter 1, Verse 55

Surya Siddhantha – Pitruvya Mana

The Surya Siddhantha places the lunar month in a separate timescale called Pitruvya Mana (the timescale of the ancestors) and even defines a day and night time for the Pitrus (ancestors), as follows:

A lunar month which consists of 30 lunar days is, as mentioned before, a day and night of the Pitrus [पित्रु]. The end of a (lunar) month and that of the light half of that month take place in the middle of them (the day and night of the Pitrus) respectively. – Chapter 14, Verse 14

For all practical purposes, the lunar month meanigfully belongs in the Chandra Mana, and this classification of Pirtuvya Mana has only religious importance to the Hindus.

Surya Siddhantha – Correlating Saura Mana and Chandra Mana

The Surya Siddhantha correlates the lunar months and the solar months in somewhat indirect and rather complicated fashion, which is modeled below:

The correlation is defined in an innocuous fashion as follows:

Again Brahma, of subdued passions, divided a circle (the ecliptic), invented by himself, into 12 parts, naming it thr Rashi Vritta, and the same circle into 27 parts, naming it the Nakshatra Vritta. – Chapter 12, Verse 25

…The lunar months are named from the Nakshatras [नक्षत्र] (or asterisms) which take place (or in which the moon is) on the 15^th day of these months. – Chapter 14, Verse 15

On the 15^th day of (each of the lunar months) Kārtika and others, (either of every) couple of Nakshatras reckoned from Krittika takes place successively. (But on the 15^th day of each of) the three months such as the last (i.e. Ashvina) and that coming before the last (i.e. Bhādrapada) and the fifth (i.e. Phālguna) one of three Nakshatras takes place. – Chapter 14, Verse 16

Surya Siddhantha – Chandra Mana

Now we proceed to the second important element of the Hindu Luni-Solar calendar – the lunar part.

The Chandra Mana time scales are modeled below:

The key to understanding this model is to start with the lunar month:

• The Chandra Masa (lunar month) is the time taken by the Moon to move from one conjunction with the Sun (i.e. New Moon day) to the next, as observed from the Earth.
• A Chandra Masa is divided into two fortnights (Paksha), one corresponding to the waxing Moon (Shukla Paksha) and  the other corresponding to the waning Moon (Krishna Paksha); the Shukla Paksha cuminates with the Full Moon day and the Krishna Paksha culminates with the New Moon day.
• A Tithi (lunar day) is defined as the time taken by the Moon to move successive 12 degrees from the Earth-Sun axis, i.e. a Thithi in mathematical terms is a thirtieth of a lunar month.  Each half of a Tithi is called a Karana.

Surya Siddhantha – Saura Mana

Now we come to one of the two core components of the Indian Luni-Solar calendar – the solar time scales.

Surya Siddhantha’s definitions of Saura Mana is quite comprehensive:

 

This is best understood by starting with the solar year:

• A Saura Varsha (solar year) is the time taken by the Sun to traverse the 360 degrees of  the ecliptic. This is nothing but the modern sidereal year.
• The ecliptic is divided into 12 segments, each called a Rashi.
• A Saura Varsha  is divided into two parts – Uttarayana (northward movement of the Sun) and Dashinayana (Southward movement of the Sun), each consisting of six Saura Masas (solar months).
• A Saura Masa (solar month) starts at the moment when the Sun  enters a Rashi (this moment in time is called a Sankranthi / Sankramana). The solar month inherits its name from the name of the Rashi. The duration of a solar month is the time take by the Sun to traverse a Rashi. Mesha is the first month of the solar year, i.e. a solar year starts with a Mesha Sankranthi.
• There is no definition for a Saura Day (if there was one, it should be in terms of the Sun’s motion around the ecliptic; there is none). Instead, in practice, Hindu calenders use a Savana day (defined in the previous post)
• There are six seasons defined, each being the time taken by the Sun to traverse two Rashis (i.e. two Saura Masas)

This does not complete the solar model. There are additional definitions that are relevant to modern astronomy – those of the solstices and equinoxes:

Surya Siddhantha – Savana Mana

From sidereal defintions let us now move to solar definitions.

The Savana Mana is defined by Surya Siddhantha as follows:

The Surya Siddhantha explains this as follows:

The time from one rising of the sun to the next is called a Savana day… – Chapter 14, Verse 18

…Thirty Savana days make a Savana month. – Chapter 1, Verse 12

Very simple time scale, but this definition of a day is very much in use in Indian as all Indian calendars reckon a day this way.

Surya Siddhantha – Nakshatra Mana

The Nakshatra Mana defines the smallest timescale in Surya Siddhantha.

I will allow the Surya Siddhantha to explain  the above class diagram:

The time called Murta begins with Prana and the time called Amurta begins with Truti. The time which contains six Pranas is called a Vinadi and that which contains sixty Vinadi is called a Nadi. – Chapter 1, Verse 11

The time which contains sixty Nadis is called Nakshatra Ahoratra and a Nakshatra Masa consists of  thirty Nakshatra Ahoratras… – Chapter 1, Verse 12

As for the correctness of the astronomy, the fact that the term Nakshatra Ahoratra is indeed meant to represent a sidereal revolution is attested to in Chapter 14:

A daily revolution of the starry sphere is called a Nakshatra day… – Chapter 14, Verse 15

The above verse says the celestial sphere is rotating since the earth is considered to be stationary at the center of the celestial sphere.

We know that a sidereal day is 24 Hours. Once the value of Nakshatra Ahoratra is thus related to a modern measure of time, a quick calculation will reveal that a Nadi is 24 minutes, a Vinadi is 24 seconds and a Prana is 4 modern Seconds (which is a reasonable time frame for one Prana which is nothing but an inhalation of breath).

The Surya Siddhantha not bother to define a Nakshatra Year. Even the definition of a Nakshatra Month as above is not used anywhere in practice.