Introduction
Astronomical dating of Ramayana when compared to Mahabharata suffers from two main issues. First issue is that the proposed dates for Ramayana go back thousands of years. The commonly used astronomy/astrology tools lack the accuracy to validate the astronomical events. The second issue is that the key astronomical evidences in Ramayana is more ambiguous and subject to multiple interpretation.
1. The JPL DE441 data
The first problem has been solved by Jet Propulsion Lab (JPL). The JPL released planetary and lunar ephemeris DE431 in 2013. It spans the years -13200 to 17191. The data was updated to DE441 and released in 2020.
While using the DE441 for dating Indian text, the two most important coordinate systems, are the Ecliptic and the EclipticJ2000 coordinates. The Ecliptic coordinates place its 0 Degree longitude at the vernal equinox point of the year. Since the 0 Degree point moves with the precession of earth, the ecliptic coordinate system is very useful for defining tropical events like Ritu. The EclipticJ2000 coordinates place its 0 Degree longitude at the vernal equinox of the year 2000AD. The 0 Degree point does not change with the precession of Earth. Hence the Ecliptic J2000 is very useful in defining the Sidereal coordinates of the planets, the sun and the moon.
Definition of the tropical terms
To use the data in JPL's DE441 we must agree upon the definitions of the astronomical terms in the Indian text. First let us define the tropical terms as shown in the Table 1.
Table 1 shows the Indian seasons or Ritu. There are six seasons in the Indian calendar year. The starting and the ending ecliptic coordinates defining the seasons are provided in the table.
In the ecliptic coordinate system 0 Degree longitude is the vernal equinox, 90 Degrees is the summer solstice, 180 Degrees is the autumnal equinox and finally 270 Degrees is the winter solstice.
Definition of the sidereal terms
The Indian sidereal coordinates are the Rashi/zodiac. These can be further broken down into Nakshatras and their Padas. The Table 2 provides the definition of Rashi, Nakshatras, Padas and their respective boundaries in the eclipticJ2000 coordinates. The definition uses the Chitra Paksha Ayanamsha.
Table 2: Sidereal definitions
Couple of other important sidereal term are the Masa and Tithi. The Masa spans between two Amavasyas. The Masa names are shown in the table 1. These Masa given in the Table 1 succeeds the Amavasya (sun and moon) whose ecliptic J2000 coordinates falls within the range of the first two columns. When two lunar month in a year falls in the same row in the Table, the first month is called an Adhika masa (Intercalary month) and the second one is called the Nija Masa.
Tithi is the phase angle between the moon and the sun. Every Tithi spans 12 Degrees. The phase angle from 0 to 180 Degrees have 15 Tithis starting with the Prathama and ending in the Purnima. These are the Shukla Paksha Tithis. The phase angles from 180 Degrees to 360 Degrees have 15 Tithis starting again with the Prathama and ending with the Amavasya. These are the Krishna Paksha Tithis.
2. Sri Rama's Birth chart
A birth chart has very low probability of repeating itself over a tens of thousands of years. The probability of a Graha such as Saturn, Jupiter, Mars, Sun and Moon at any house is an independent event. So the probability of two birth charts with same Graha position in different years is 1/(12x12x12x12x12) =0.0004%.
Unfortunately the multiple interpretation and controversies surrounding the key astronomical evidences, particularly the birth chart of Lord Rama, presents a problem.
The original Verse and its multiple interpretation
The verse in figure 1 is used to derive Lord Rama's birth chart.
Figure 1: Birth chart of Sri Rama
Let us look at all the Grahas and try to address the controversies and ambiguities around it.
Jupiter: Jupiter's position is the least controversial. There is a general agreement that Jupiter is placed in the Karka/Cancer sign.
Moon: It is generally accepted that Sri Rama was born in the Punarvasu nakshatra in the Cancer zodiac. This would then be Punarvasu's 4th Pada as per the Table 1. But some researchers argue that Sri Rama was born in the Pushya nakshatra [1]. In fact the author says that all his brothers were born in the same star of Pushya since all of their naming ceremony happened on 11th day from Sri Rama's birth. This is not a generally accepted opinion. We can safely assume that on Sri Rama's birthday, moon was at Punarvasu 4th Pada.
Sun: Most astrologers place Sun in Aries in Sri Rama's birth chart. But it has been proved by some astrologers like K.N.Rao that Sun has to be in Pisces. The Sun and the Moon must be at least 12x8=96Degrees apart on the Navami Tithi. Even if the Moon was at the border of Gemini and Cancer, the Sun must be no more than 90 Degrees behind the Moon to be in the Aries. Hence Sun must be in the Pisces.
Saturn/Mars/Venus: The Saturn is usually placed in Libra. The Mars is placed in Capricorn. The Venus is placed in Pisces. This is based on the verse claiming 5 planets to be in either own house or in exaltation. The other two being the Jupiter in exaltation and the Moon in the own house of Cancer. Though this is generally accepted, it is possible that the Saturn, the Mars and the Venus are in their own house instead of exaltation. Then the Saturn can be in Capricorn or Aquarius. The Mars can be in Aries or Scorpio. The Venus can be in Taurus or Libra. This open up many combinations. But for now let us assume that the three planets are in exaltation.
Mercury/Rahu/Ketu: The above verse does not give any position for Mercury or Rahu or Ketu. Though the verse is ambiguous about which 5 planets are in exaltation or own house, it is clear it cannot be the Mercury, the Rahu or the Ketu. The Sun being in Pisces, Mercury will be close to the Sun. Hence the Mercury is far from its own house (Gemini) or exaltation (Virgo). The Rahu and The Ketu cannot be simultaneously be in its own house. Even though the verse do not give any indication of the position, several astrological traditions have placed the Mercury in Aries, the Rahu in Sagittarius and the Ketu in Gemini. But there is no evidence from Valmiki Ramayana to back it up.
The possible dates for Sri Rama's birth
Assuming the Chaitra Shukla Navami Punarvasu Nakshatra and Jupiter, Saturn, Mars and Venus in exaltation there are only two candidate years in the entire DE441 ephemeris data.
The first candidate is the year 4498 BCE Jan 06 12PM UTC (Gregorian Calendar) (Figure 2).
Figure 2: Birth chart for Chaitra Navami in 4498BCE
The second candidate is the year 6267 BCE Dec 11 12PM UTC (Gregorian Calendar) (Figure 3).
Figure 3: Birth chart for Chaitra Navami in 6267BCE
The 6267 BCE coincidentally places Rahu in Sagittarius and Ketu in Gemini. This aligns with certain astrological traditions.
3. Lower limit 6225 B.C
To pick the right candidate among 4498BCE and 6267 BCE we need a few more evidences to establish the lower limit for dating Ramayana.
Pausha masa Hemant Ritu
The verses in figure 4 and 5 are from Sarga 16 in Aranya Kanda in Valmiki Ramayana. The Sarga starts by mentioning the arrival of Hemant Ritu. Sri Lakshmana in the Sarga describes the start of Pausha masa in the Hemant ritu .
Figure 4: Arrival of Hemant Ritu in the Aranya kanda Sarga 16
Figure 5: Arrival of Pausha masa with the arrival of Hemant Ritu in Aranya Kanda Sarga 16
With the Precession of equinox there is a lower limit beyond which the Hemant Ritu cannot happen in the Pausha masa. This is shown in the figure 6 from the DE441 data. Any year below 6187 BCE cannot have even the last day of Pausha masa (Amavasya) in the Hemant Ritu.
Figure 6: 6187 BCE is the last year to have Hemant Ritu in the Pausha masa
Karthika masa and Sharad Ritu
The verses in figure 7 and 8 are from Sarga 26 in the Kishkinda Kanda in Valmiki Ramayana. The Sarga quotes Sri Rama advising Sugriva to go back to his capital since the rainy season is starting in the month of Shravana. He advises the monkeys to start the preparation for finding Sita and killing Ravana in the Kartika masa after the rainy season ends.
Figure 7: Rainy season begin in Shravana. Kishkinda Kanda Sarga 26
Figure 8: No Rainy season in the Karthika masa. Kishkinda Kanda Sarga 26
Figure 9: 6225 BCE is the last year to have the Sharad Ritu in the Karthika masa
With Precession of equinox there is a lower limit beyond which the Sharad Ritu cannot occur in the Kartika masa. This is shown in the figure 9 from the DE441 data. Any year below 6225 BCE will not have even the last day of Kartika masa (Amavasya) in the Sharad Ritu.
Based on the lower limit of 6225 BCE and 6187 BCE, we can safely eliminate the 6267BCE as the candidate for Sri Rama's birth. The only possible year left will be 4498BCE
4. Chaitra Masa & Vasant Ritu?
Figure 10: Possible lower limit of 3816 BCE based on the Vasant Ritu in the Chaitra masa
Alternate birth chart for Sri Rama
As we have seen in the section 2, there is no other alternative position of sun, moon and Jupiter from the verse. Those are clearly fixed. The only option is to looks at the alternate positions of Saturn, Mars and Venus. Rather than placing them in exaltation we must explore the option of placing them in their own house. Based on all possible combination of Saturn, Mars and Venus, Table 3 presents possible candidate years for Sri Rama's birth.
With a lower limit of 3816 BCE, the only viable candidate will be 2280BCE. Other historical and textual evidences will eliminate the possibility of 904 BCE, 394 BCE and 335 BCE which is outside the scope of this article.
The possible birth chart for the year 2280BCE is given in the figure 11.
Figure 11: Birth chart for Sri Rama for the year 2280 BCE
5. Conclusion and Future work:
Based on the JPL's DE441 Ephemeris and the accepted traditional birth chart of Sri Rama the most likely candidate for Sri Rama's birth year is 4498BCE. But the choice of the year needs to be scrutinized with other evidences in Ramayana to be conclusive. Another candidate for Sri Rama's birth is 2280BCE. But 2280BCE will face resistance from the Indian astrological community.
6. Reference
[1] Absolute dating of Ramayana, Sri Harsha Indrasena. Devpura publications. 2020
[2] Refutation of Nilesh Oak's Astronomical Dating of Ramayana to 12209BCE, Raja Ram Mohan Roy, 2021.
