Brief: We all know about two motions of the Earth, Rotation and Revolution. There are many other motions of the Earth and one of them is the Precession of Equinox. This 3^rd motion of the Earth resembles Earth’s movement like a Top where the axis of the Earth keeps moving in a Circular shape.

The objective of this paper is to-

1. Understand the concept of Precession of Equinox as defined in Surya Siddhanta (referred to as SS hereafter) which is the most respected book in the field of Astronomy and give credit to it (SS) for originating this concept and bringing it to the world’s notice.
2. Derive the correct value of the number of years in one cycle of Precession of Equinox.
3. Be a plinth to apply the concept to the software used in Astronomy and Calendar management along with any other place where this concept is applicable.

The concept of Precession of Equinox is a common concept in the world of Astronomy (Jyotisha/Khagolshastra in the Bharatiya culture). Let us understand the concept.

Any point on the equator (specifically the intersection of Prime Meridian at the time of day of Spring (20/21-March in current time 2024 CE) or Autumn (21/22-September in current time 2024 CE) Equinox when projected on the celestial equator coinciding with the Ecliptic (plane of earth’s revolution), is called the point of Equinox. On the day of Equinox, day and night are of equal length on the Equator.

It is believed that this point keeps on moving on the ecliptic in an westward direction with a very slow motion due to the forces applied by the Sun, Moon and Jupiter on the Earth, giving birth to the concept of Precession of Equinox. The proof and origin of this concept as defined in SS, as a Theorem will be covered in detail in this paper.

We all know that the Earth’s axis which is an imaginary line between the Earth’s North and South Pole is tilted by an angle of 23.44° in current time (2024 CE) with respect to the perpendicular line to the ecliptic (plane of Earth’s revolution).

The axis points to the North Celestial Pole (Pole Star above the North Pole) in the Northern direction and towards the South Celestial Pole in the Southern direction.

Due to the continuous movement of the point of Equinox over the years slowly westwards, the axis also rotates and makes a circle and returns to the point of origin of the circle after a certain number of years. The circular path made by the axis is called the Circle of Precession.

While the axis traverses on the Circle of Precession, it keeps on pointing to the new Pole Star as years pass by and comes back to the one pointing where it started from.
The axis points to the Pole Star named Polaris in the current time (2024 CE). The axis pointed to a pole star called Vega thousands of years back which is considered approximately halfway on the Circle of Precession.

This phenomenon of movement of the point of Equinox across the ecliptic in an westward direction thereby making the axis also follow a circular path along the Circle of Presession is called Precession of Equinox.

Background- Effect of Precession of Equinox on the Earth:

One might think of 2 questions-

1. How much time does the circle of Equinox movement take to complete?
2. What is the effect on daily life and other unknowns?

As we understood that the axis moves in a counterclockwise movement due to the movement of the point of Equinox, the backdrop stars for the Equinox point also keep on changing as it moves along the circle of precession.
These backdrop stars are 27 Nakshatras which are equally spaced across the ecliptic at 13.33 degrees apart as stated in the formula [360 degrees / 27 = 13.33 degrees].

As the point of Equinox covers 13.33°, the full moon in that lunar month points to a Nakshatra next and westwards the earlier one. 12 out of 27 Nakshatras are used for marking the lunar months.

As the point of Equinox traverses 26.67° i.e. [2 x 13.33 degrees = 26.67 degrees (2 Nakshatra Stars)], this changes the lunar month coinciding with the month of the Gregorian calendar. For example, if Equinox at one point in time falls on the lunar month of Chaitra and the Gregorian month of March in year X, then after a couple of years, in year Y, the lunar month of Chaitra will fall in the Gregorian month of April.

The effect of the Precession of Equinox also impacts Seasons coinciding with Bharatiya (Indian) Lunar and Gregorian months.

There are 6 seasons in Bhartiya tradition, separated with each one covering ~2.25 Lunar or Gregorian months.
For example, if the point of Vernal Equinox  (referred to as VE hereafter) shifts 26.67 i.e. 2 Nakshatras, then it’s called a shift of 1 lunar month, but the season still remains the same. But if VE shifts by 53.33 i.e. 4 Nakshatras it then marks a shift of ~2.25 lunar months and 1 season. This implies that the  Lunar month of Chaitra falls in the Vasant/Spring season then it will start falling in the Greeshma (Summer) season after the VE shifts by 53.33westwards.

Note: The primary intention of this paper is to explain the number of years lapsed in shifting of point of Equinox by 1°. This will be revealed in the later part.

The Source of Truth for the Research:

Amongst many ancient texts that originated in Bharat, Surya Siddhanta (SS) is a marvel in the field of Astronomy.

SS is a pocketbook of astronomical concepts like Theorems defined in the form of Shlokas. Many Sholkas talk about mathematical formulas to derive the intent of the concept.

SS is the most respected text in Astronomy and covers fundamental concepts about the complete Solar System and constellations visible to the naked eye (stars that surround the ecliptic), Earth’s motions, etc.

Contributions of SS are not just limited to Astronomy but also to Geography, Mathematics and Languages like Sanskrit.

 Poorva Paksha– Throwing light on the research that happened in the past:

Before we delve into the content research paper, we need to understand the problem with many theories which are claimed to be correct in the past but unfortunately, they lack corroboration with other astronomical phenomena.

Many researchers have tried to understand and locate the concept of the Precession of Equinox in Surya Siddhanta and other Bhartiya texts. They have concluded the years of the cycle with different numbers. Unfortunately, the numbers derived by them do not match with the numbers indicated by Bharatiya Panchang and Astronomical software.

Incorrect interpretation of the concept impacts in understanding the dates of our historical texts and scriptures. This creates a negative image of Bharat despite its stupendous contributions in the fields of Astronomy, Geography, Geology, Mathematics, Physics and Language.

The concept of Precession of Equinox has been researched by many researchers including E Burgess (Online Version English translation of SS by Mr. E. Burgess) and Dr. Jayasree Saranathan (Siddhantic Concept of Precession of Equinoxes -New Revelations by Jayasree Sarananthan), but none were able to get through the exact interpretation of Sholkas of SS in 3^rd chapter Triprashnadhikar.

The most common interpretation of the concept as understood from Shlokas of SS is a Pendulum movement which is an eastward and westward movement of Equinox with a cycle of 7200 years (Siddhantic Concept of Precession of Equinoxes -New Revelations by Jayasree Sarananthan) and movement of VE 54 arcsec per year.

After understanding the shlokas, this theory didn’t fit the bill. It is important to note that the figure of 7200 years doesn’t corroborate the fact that the pole stars keep changing every couple of thousands of years and come back to one where the precession of the circle begins. We will not see pole stars like Thuban and Vega if the 7200-year cycle holds true.

Some researchers have also derived the following figures (in years), to complete one cycle of VE across the ecliptic.
28800 (How ancient are Vedas, Vedanga Jyotisha and Surya Siddhantha? by Pidaparty Purna Satya Hariprasad),
27400 (How ancient are Vedas, Vedanga Jyotisha and Surya Siddhantha? by Pidaparty Purna Satya Hariprasad),
26000 (Vishuvat Chalana (Procession of Equinoxes):  A brief and authentic journey from Vedic times to the present by Pidaparty Purna Satya Hariprasad),
24000 (Journal: Bulletin of the Astronomical Society of India, vol. 26, p.33 with title Samanta Chandra Sekhar: The great naked eye astronomer by Naik, P. C. & Satpathy, L),
25868 (PRECESSION OF THE EQUINOXES),
25800 (Precession of Earth’s Axis by Shri Arbind Kumar Mallik from Department of Physics, Tribhuwan Multiple Campus, Palpa),
25772 (Orbital Spin: A New Hypothesis to Explain Precession of Equinox―The Third Motion of Earth by Shri Rama Chandra Murthy Mothe)

I am a new researcher and have much respect for everyone who has done and is doing the research on this concept and also thank them. It is entirely by Dev Krupa (god’s grace) that I got this opportunity to solve this problem.

My intention is to understand the concept given in SS and bring it to light so that the world can-

1. Give credit to the original text of discovering this concept of a unique motion of the Earth
2. Course-correct the software and calendar applications to re-align the lunar months and seasons.

All Bharatiya (Indians) are fortunate to have researchers like Shree Nilesh Nilkanth Oak Ji and Sushree Rupa Bhaty Ji to perform fundamental research on Bhartiya Itihaas and enlighten and encourage others to join hands in this noble cause.

Uttara Paksha: Research on Precession of Equinox as defined and documented in Surya Siddhanta

The concept of Precession of Equinox is well defined in Surya Siddhanta’s 3^rd chapter called Triprashnadhikar

Triprashnadhikar covers Sholkas which address concepts on three things-

1. Direction
2. Place
3. Time/Duration

We need to indulge with problems related to either or all these 3 things.
SS being a far superior text, basics of scientific principles and structures are assumed to have been followed. SS addresses concepts of these three basic things differently to help build the fundamentals of Astronomy and Mathematics.

Before we delve into the concept of Precession of Equinox, we first need to understand the concept of Time in a focused manner wherein we will just look at shlokas which define time in the form of Yugas and is conceptualised in the 1^st chapter called Madhyamadhikar.

Concept of Yugas from Chapter Madhyamadhikar of SS:

The shlokas which define the concept are:

Shloka १.१४ points to 1 Solar year (~360 days) on the Earth is 1 Divya Day for Sur-Asur (a metaphor for Dev and Rakshasas living in the Northern and Southern hemispheres respectively) and 360 Solar years is 1 Divya year for Sur-Asur.
Note: 360 is the number inherited from 360° of a circle as all astral bodies are circular (spherical).

We will now talk about the limited stuff required to decipher the concept of the precession of Equinox (as referred to in chapter Triprashnadhikar), from shlokas १.१५, १.१६, १.१७ of chapter Madhyamadhikar only, else we might get caught into many other concepts which aren’t required at this juncture to delve deeper.

The Shlokas refer to 4 yugas covering a total period of 12000 Divya years 360 x 12000 = 4320000 solar years. These 4 yugas are placed in a ratio of 4:3:2:1- Kruta:Treta:Dwapar: Kali yugas respectively
As per this ratio, Kruta (Sat Yuga) is of duration 4800 Divya years 360 x 4800 = 1728000 solar years

Note: Before we move on further, we need to understand that the Solar and Divya years are a scale apart i.e. Divya year is just a multiple of the Solar year. Hence it doesn’t matter what we refer to, just that whichever is chosen as a reference, it must be consistent across the calculations.

Concept of Precession of Equinox from chapter Triprashnadhikar of SS:

Let us choose a point amongst 2 Equinoxes we have, Spring and Autumn for discussion further, say Spring Equinox, which is technically referred to as Vernal Equinox in Astronomy.

We will refer to 3 Shlokas, 2 from head अयनांशसाधनम्‌ and 1 from head अयनचलनस्य ट्क्‍्प्रतीति.
The point where VE coincides with the ecliptic is called Ayanansh. The first head talks about the movement and speed of VE (which we are interested in) and 2^nd one talks about the direction of movement and its visual appearance.

The shlokas are as follows:

 

Before we delve deeper into the calculations and concept in Shloka ३.९, ३.१०, let us understand the words of the Sholkas to formulate the calculation.

त्रिंशत॒कृत्यो युगे – In 30 Kruta (Sat) Yuga
भानां चक्र प्राक् परिलम्बते – slow movement of circle of Nakshatras in eastward direction
तदगुणाद्धूदिनै घ्यु – multiply it by double the number of hours in a day on the Earth
र्भक्तादू गणाद्यदवाप्यते - resembles and supports the movement across group of Nakshatras
तद्दोस्त्रिघ्न दशाप्तांशा – further divide by 27 and 10
विज्ञेया अयनाभिधा: – is known as the movement of the point of Equinox
तत्सस्कृतांदग्रहात्‌ क्रान्तिच्छायाचरदलादिकम्‌ - revolution of VE across the ecliptic

Note: It is very interesting to note that SS uses such a cryptic and scientific way using Sanskrit in this Shloka to depict the number 27 in the form of word स्त्रिघ्न which refers to divine ladies which are nothing but the Nakshatras or Asterisms which are also referred as wives of Moon in Puranas. The thought process of our ancestors was truly commendable.

When we put these terms in chronological order we get one revolution of movement of VE across the ecliptic, we get output as 25,600 years.

Calculation
[(30 x 4800 x 24 x 2) / (27 x 10) = 25600 years] 
[Thirty multiplied by Four Thousand and Eight Hundred further multiplied by Twenty Four further multiplied by 2 further divided by Twenty Seven further divided by Ten]

To reinstate, it takes 25,600 years for VE to complete one iteration of the circle of precession going in the westward direction and 360 (1 Divya year is 360 Solar years) such iterations are done in 30 Kruta (Sat) Yugas.

This also infers to:

1. It takes VE to move [25600 / 360 = 71.111 years]  to move 1 across the ecliptic in the westward direction
2. VE moves 50.625 arc-seconds every year on the ecliptic in the westward direction.

Next, we delve deeper into the meaning of Shloka ३.११, by understanding the words of the Sholka.

स्फुटं – It is clear
दृकतुल्यतां – visual appearance
गच्छेदयने विषुवद्धये – Point of Equinox (VE) which is on the equator keeps shifting

प्राक् चक्रं चलितं हीने छायाकात्‌ करणागते – a visual appearance of Circle of Nakshatra is seen moving eastwards which is the cause of feeling of cinematography where point of VE moving westwards
अन्तरांशैरथावृत्य पश्चाच्छेषेस्तथाधि – at a defined interval across the circle called ecliptic in westward direction

Another inference can also be derived that the Circle of Asterism/Nakshatras is seen moving eastwards as VE moves westwards along the Ecliptic.

Re-instating the Claim

Fig 1. Depicts the concept and effect of the Precession of the Equinox

As per SS, the VE moves westwards on the ecliptic at a steady and slow pace with a cycle of 25,600 years to complete one revolution of the ecliptic which translates to a movement of 1 in every 71.111 years or 50.625 arc-seconds [60 x 60 x 1 / 71.111 = 50.625 arc-seconds] every year, in the westward direction along the ecliptic and this phenomenon is called Precession of Equinox or Vishuvat Sampaat Chalan.

Glossary

Prime Meridian – A longitude or vertical line running from North pole to South pole at 0° whose parallels are other longitudes separated by a couple of degrees, progressing eastwards
Equator – Horizontal line covering the circumference of the Earth at the intersection of the Northern and Southern hemisphere
Celestial Equator – Projection of Equator parallelly in the sky
Equinox – Point on the Equator or Celestial Equator coinciding with the Ecliptic
Vernal Equinox (VE) – Point of Spring Equinox (21^st March) which intersects with the celestial equator
Ecliptic – Elliptical path of Earth’s revolution around the Sun
Nakshatras – Constellation of Stars across the Ecliptic separated by 13.33°. They are also called Asterisms or Lunar mansions
Pole Star/North Celestial Pole – The Star which is seen most bright amongst the points above the North/South Pole. This star lies on the same tilted axis (Obliquity)
Yuga – A time period used for astronomical calculations
Arc-Seconds – A movement of a point which is 1/3600 of a minute. This unit is generally used to calculate extremely slow movements to make accurate measurements

 

References

List of some references from past researchers who have concluded the concept of Precession of Equinox in their own way

1. Online Version Hindi translation of SS by Shri Prof Ram Chandra Pandey
2. Online version English translation of SS by Mr. E. Burgess
3. Siddhantic Concept of Precession of Equinoxes -New Revelations by Jayasree Sarananthan
4. Orbital Spin: A New Hypothesis to Explain Precession of Equinox―The Third Motion of Earth by Shri Rama Chandra Murthy Mother
5. Precession of Earth’s Axis by Shri Arbind Kumar Mallik from Department of Physics, Tribhuwan Multiple Campus, Palpa
6. The Alleged Babylonian Discovery of the Precession of the Equinoxes by Mr. O. Neugebauer
7. Ptolemy’s Precession by Mr. A Kannekoek
8. Equatorial insolation: from precession harmonics to eccentricity frequencies by A. Berger, M. F. Loutre and J. L. Melice
9. PRECESSION OF THE EQUINOXES
10. How ancient are Vedas, Vedanga Jyotisha and Surya Siddhantha? by Pidaparty Purna Satya Hariprasad
11. Vishuvat Chalana (Procession of Equinoxes):  A brief and authentic journey from Vedic times to the present by Pidaparty Purna Satya Hariprasad
12. Journal: Bulletin of the Astronomical Society of India, vol. 26, p.33 with title Samanta Chandra Sekhar: The great naked eye astronomer by Naik, P. C. & Satpathy, L