Sidereal Zero Point – A Mathematical Solution

K. Chandra Hari

Abstract

Present paper is an attempt to decipher the sidereal zero point of Suryasiddhanta, which had

a fixed anomaly in view of the stationery aphelion/perihelion. It is shown by modern

astronomical computation that the vernal equinox coincided with the fixed anomaly zero

point of Suryasiddhanta roughly during AD233-AD238.On examining the luni-solar

configuration of the nearby equinoxes it was found that the original epoch of Siddhantic

astronomy where-in the Caitra sukla prathama coincided with vernal equinox and the

nirayana zero point is the Vernal Equinox of AD 231. This result provides substantiation to

the fact that Mula had played a fiducial role in the Indian/Babylonian astronomy in the period

prior to the extant version of Suryasiddhanta.

Key Words:

Zero Point, Suryasiddhanta, aphelion, vernal equinox

I. Introduction

The sidereal zero point of Indian astronomy has remained an intriguing problem to modern

researchers since the eighteenth century. The Calendar Reform Committee (1) headed by Dr.

M. N. Saha(1) did try to answer the problem based on the polar longitudes of stars available

in Suryasiddhanta, but the deciphered zero points viz., the vernal equinox of AD285 and

AD576 i.e. Citrapaksa and Revatipaksa, are not in conformity with the solar year length of

365.25875 days(2). For the reasons mentioned elsewhere (3) these longitudes were not at all

suitable for the above purpose and hence the inferences drawn contradicted the

mathematical framework of Suryasiddhanta itself.

Another intricacy of Siddhantic astronomy is that even though the treatises like

Aryabhatiya(Kalakriyapada-verse 11)ϕ declares Caitra-suklapratipada as the beginning of

the year and the greater divisions of time such as Yuga, Kalpa etc., neither of the Siddhantic

epochs, say of Suryasiddhanta or Aryabhatiya satisfied this stipulation. As such we are not

aware of the original epoch of Siddhantic astronomy itself. It must be remembered here that

even Vedanga-jyotisha had a computational epoch beginning from Sukla-pratipada that

coincided with the winter solstice. Obviously when the year beginning had a shift to the

Vernal equinox it must have taken place at a coincidence of the Vernal equinox with the

Caitra-suklapratipada. In the absence of such a tradition there was no reason for the

Siddhantic astronomers to ascribe a beginning for Year with the Caitra-suklapratipada.

The present paper is an attempt to set the record right by providing a mathematical solution

to the above problem of the sidereal zero point.

ϕ Yugavarsamasadivasah samampravarttastu caitrasukladeh

II. Important Theoretical Considerations

(1) According to Suryasiddhanta a synodic super conjunction and Sun marked the

zero point at the beginning of Kaliyuga on UT-3101 February 17, 18:30:00

(JD=588435.2708). We shall refer to this epoch as K0 in the following discussion.

(2) Sun corresponding to the expiry of the respective Kali year, has remained the

zero point ever since K0 and the planetary mean longitudes as per

Suryasiddhanta were all simply elongations with reference to the sun.(4)

(3) Solar aphelion/perihelion had been almost stationery (7'12''only in 3600 years)(5)

and obviously the zero point had a constant mean anomaly since K0.

(4) Mean anomaly at Ko as per modern astronomical computation is 105o 16' for Sun

that marked the fixed zero point.

III. Vernal Equinox That Coincided With The Sidereal Zero Point

As the sidereal fixed zero point had a constant mean anomaly of 105016' since K0, the vernal

equinox that fell over the zero point also must have the same mean anomaly as the fixed

anomaly of the zero point. According to modern astronomical computations the spring

equinox had a mean anomaly of 105o 16’ in AD238 and the respective Kalidinam

(Aharganam) contained precisely 3339 anomalistic years.

IV. Mula’s (λ-Scorpii) fiducial role

As described elsewhere (6) if Mūla is taken as the fiducial star it must have a fixed sidereal

longitude of 2400. As can be seen in Indian Astronomical Ephemeris the proper motion of

Mūla can be taken as zero and accordingly Mula had it’s sidereal and tropical longitude

equal to 2400 at the vernal equinox of AD 233 (UT: 21 March 233, o3:23; JD = 1806240.641)

This latter epoch had a difference of 1217775.37 days from K0 and this constituted roughly

3334 anomalistic years (3334 x 365.2595591) – the vernal equinox had the same anomaly

as the anomaly of the Sun/zero point at K0.

The difference of 5 years between the computations based on fixed mean anomaly of the

zero point and the fiducial star Mūla, is quite negligible in view of the large period involved. It

is quite possible that more precisely computed anomaly might lead us to the epoch of AD233

rather than AD238. Accordingly the ayanamsa of J2000 will be 24035' 8''.79.

V. Original Epoch of Indian Siddhāntic Astronomy

On examining the luni-solar configuration of the vernal equinoxes around AD 233, the

following astronomical data strikes our attention. The vernal equinox of AD 231 precisely

satisfied all the aforementioned astronomical factors that would have truly characterized the

original siddhantic epoch and year beginning with Caitra suklapratipada.

Epoch: 21 march 231AD, Monday 17 33 UT (22 36 Ujjain LMT), Vernal Equinox coincided

with Caitra sukla pratipada.

JD: 1805510.231

Mūla (λ-Scorpii) precisely had a longitude of 239058' = 2400 from the vernal equinox.

New moon took place on Monday at 1046UT or 1549(Ujjain LMT) for JD=1805509.866 -

midnight of 21/22 March. Monday coinciding with the Sukla-1 marked the beginning of Caitra

at Ujjain. The epochs K0 and K3332 were as shown below at Ujjain:

K0 K3332

JD: 588465.2104 1805510.2104

UT:17/18 Feb.3102BC Thursday Midnight 21/22 March 231 AD Monday Midnight

Mean Sun 301°36' 358°05’

Solar anomaly 105°38' 105°26'

Mean Moon 297°11' 07°26'

True Sun 303°34’ 00°03' 47''

True Moon 315°37 ' 03°17'

True sidereal sun at K0 = 3030 34’+ 450 55’ = 3490 29’ *

K3332 - Ko =1217045 days = 3332 X 365.2596038i.e. 3332 anomalistic years separated the

two epochs

Discussion

Aryabhata's choice of Wednesday sunrise as Yugādi is untenable as the mean new moon

was on Thursday night. This wrong choice was a consequence of the modification of the

epoch from AD 231 to AD 522 during which the Vernal equinox got shifted by four degrees.

To account for this shift Aryabhata reduced the year length by 9.232 X 10E-04 days (which

accumulated to 3.345 days in 3623 years) and shifted the Yugādi by (-0.75 days from

Thursday midnight to Wednesday Sun rise.

b) Varāhamihira chose the expiry of Kali 3606 which corresponds to JD=1905588.263 as his

epoch and this very nearly marked the mean equinox of AD 505. 3606 years of 365.25875

days on counting back took him to the midnight of Thursday rather than Wednesday sunrise

of Aryabhata at Yugadi. According to modern computation the new Moon corresponded to

21 March 505 AD 1955 (Ujjain LMT) (JD=1905589.12) with the Sun having a true longitude

of 2032'. True equinox was on 19 march 505 AD at 05 47(Ujjain LMT) with

JD=1905586.528.True Moon was 3290 08'

* Note: The length of the sidereal year in 231AD was 365.2563586 days. The anomalistic

year of 365.2596038 therefore meant an eastward regression of 11''.5 for the initial point and this accumulates to 10039' in 3332 years. This in fact is the 'deviation' of Sun relative to the "zero point with Mula as fiducial" at K0 This explains the choice of Ko as Yugadi and the concept undoubtedly belongs to the Pre -Aryabhata period.

It is apparent from the above that the astronomical phenomenon of AD231 only is

compatible with the assumption of a mean new Moon at Yugadi on Thursday midnight.

Varahamihira stuck to the tradition as far as Yugadi is concerned but his epoch of AD 505 is

only computational i.e. the mean equinox coinciding with a mean new moon and hence the

epoch cannot be taken as observational as in AD231 where the spring equinox and Sukla-1

coincided almost perfectly.

The spring equinox of AD 231 having the same anomaly as the sun of K0 and coinciding with

Caitra sukla-1 precisely over the point 1200 east of Mūla renders irrefutable evidence

towards a pre-Aryabhatan or pre-siddhantic existence for the Indian sidereal astronomy and

Mūlādhāra Rāhu-Sikhi Cakra (Sidereal Zodiac as the 'Wheel of Nodes or Serpent, with λ –

Scorpii as Reference Star).

VI. Conclusions

The sidereal fixed zero point of Suryasiddhanta and the fixed mean anomaly/stationery

aphelion lead us only to the vernal equinox of AD238/AD233 as coincident with the Zero

point. The vernal equinox of AD285/499/576, as deciphered by the Calendar Reform

Committee are contradictory to the theoretical foundations out of which Suryasiddhanta

evolved. The solar year length of 365.25875 days and that of Aryabhatiya etc. are not in

conformity with the fixed zero point and aphelion postulated by these treatises. The sources

of this discrepancy can be traced only to the modifications (7) that the original treatise must

have undergone since the 3rd century AD.

The Vernal equinox of AD231 coincident with Caitra-suklapratipada and the fixed anomaly

zero point of Siddhantic astronomy provide substantiation for the fact that the star Mūla

(Lambda Scorpii) had played a fiducial role in the sidereal astronomy of India and Babylon (6).

VII. References

(1) Dr. M. N. Saha & N.C. Lahiri, Indian Calendar; Pub:CSIR, New Delhi.

(2) K. Chandra Hari, True Rationale of Suryasiddhanta IJHS 32(3), INSA, New Delhi-2.

(3) Ibid.,

(4) K. Chandra Hari, On The Origin Of ‘Kaliyugadi’ Synodic Superconjunction P.194,

IJHS 33 (3), INSA, New Delhi-2.

(5) S. B. Dikshit, Bharatiya Jyotish Sastra Part II PP 67-68, Pub:The Controller Of

Publications, Civil Lines, New Delhi-54.

(6) K. Chandra Hari, On The Origin Of Sidereal Zodiac and Astronomy IJHS 33(4),

INSA, New Delhi-2.

(7) Prof. P. C. Sengupta, In his Introduction to the English translation of Suryasiddhanta

by Rev. E. Burgess p. xxix