All the 3K dates of Mahabharata (3067BCE, 3163BCE, 3140BCE, 3136 BCE) place Magha Shukla Ashtami in the Uttarayana. It is astronomically impossible for the Magha Shukla Ashtami day to be in the Uttarayana for the years prior to 3000BCE. But the months after Magha such as Phalguna etc. can be in the Uttarayana. By falsely claiming the Phalguna month to be the Magha month, the 3K dates get away with the deception.
The key to the deception of the 3K dates is to introduce an Adhika masa where none exists. By inserting an Adhika masa, the subsequent month (Phalguna) can be referred by the previous month's name (Magha). For the 3067BCE, 3163BCE and 3140BCE, it has been shown how an Adhika masa was cleverly inserted. The deception was exposed by studying the full moons of the months succeeding the Adhika masa.
In this article we will go into detail why the claim of Adhika masa in 3067BCE is wrong. The arguments made here will apply for any 3K dates.
Maximum length of Adhika masa breached in 3067BCE
To understand the maximum length we must look into the definition of the Adhika masa.
What is an Adhika masa?
In a sidereal solar year, as observed from earth, sun traverses 360 Degrees. If the sidereal solar year is broken into 12 sidereal solar months, for each solar month the sun would traverse 30 Degrees. In a 12 lunar month sidereal year, each solar month will have one new moon. But every 19 years, there are 7 years when a sidereal year has 13 new moons. The 13 new moons when distributed among the 12 solar months causes one of the solar month to have 2 new moons/Amavasya. The lunar month between the two Amavasya in one solar month is the Adhika masa.
What is the maximum length of Adhika masa?
Let us define the length of a lunar month as the angle traversed by the sun from a new moon to the following new moon. By the definition of the Adhika masa, the two new moons/Amavasya fall within a sidereal solar month. Since sun travels only 30 Degrees in a sidereal solar month, an Adhika masa cannot exceed 30 Degrees.
An Adhika masa containing solar month must also contain the Amavasya Thithi from the previous month. Hence during the Adhika masa sun traverses not more than 29 Degrees. This can be confirmed by measuring the length of all the 7 Adhika masa in a 19 year cycle as shown in the table 1.
Length of all the 7 Adhika masa in a 19 year cycle
The table 1 lists all the Adhika masa and the succeeding month in a 19 year period of 2002 to 2021. The table also shows the absolute angle of the sun (and the moon) during the new moon in the ecliptic J2000 coordinates. The last column of the table shows the length of the Adhika masa by subtracting the sun's absolute position during the two new moons.
The Adhika masa listed in the table 1 never exceeds 29 Degrees.
Table 1: Seven Adhika masa in a 19 year cycle (2002-2021)
3067 BCE Adhika masa deception
Let us look at the length of the month which the author of the 3067 BCE date claims is an Adhika masa.
Table 2 lists all the new moons in the 3067 BCE and 3066BCE period of interest. The absolute position of the sun (and the moon) as recorded by planetary software are given in the second column. The third column lists the length of the lunar month succeeding the new moon. The length is obtained by taking the difference between the absolute position of sun in a new moon with the previous absolute position. The fourth columns provides the correct names of the lunar months succeeding the new moon. While the last column gives the names as per the author of the 3067 BCE date.
From table 2 we can see the length of the month named Adhika Magha by the author of 3067 BCE as 30.07 Degrees. This clearly breaches the maximum length of an Adhika masa. Hence there is no Adhika Magha possible in 3067 BCE.
The succeeding month is a Phalguna masa and not the Magha masa as claimed by the author. The Phalguna masa in 3067BCE time frame has a Uttarayana. The author uses this Phalguna masa Uttarayana deceptively as the Magha Shukla Ashtami Uttarayana.
Table 2: The list of new moons in the year 3067-3066BCE
Deriving the correct lunar month names in 3067BCE
The fourth column in the Table 2 lists the correct names for the lunar month succeeding the dates mentioned in first column. These can be derived from the absolute angle of the sun in the new moon listed in the second column as described below.
12 solar month in a Hindu calendar
First let us study the 12 solar months in a Hindu calendar. These 12 month are : Mesha, Vrishaba, Mithuna, Karka, Simha, Kanya, Tula, Vrichika, Dhanu, Makara, Kumbha and Meena. These are listed in the third column in table 3. The table 3 also lists the date and time when the sun enters these 12 months from a Hindu calendar for the year 2021. The final column gives the angle of the sun in the Ecliptic J2000 Degree. Clearly each sidereal solar month is 30 Degrees in length.
Table 3: Position of sun at the start of a solar month
How to name the lunar month from a solar month?
A lunar month's name is derived from the solar month in which the preceding new moon falls
The table 4 first column lists all the solar month. The second and the third column gives the absolute angle of the sun in ecliptic J2000 coordinates for the start and the end of the solar month. The start and the end angles are from the table 3
The fourth column gives the name of the lunar month that succeeds a new moon which falls in the range given in second and third column. The fifth column lists the angle of all the new moons in a 19 year cycle (2002 - 2021) for the lunar month mentioned in the fourth column. The fifth column confirms that the new moon falls within the range given in the second and the third column.
Table 4: Deriving the name of the lunar month from a solar month
Adhika masa and the solar month
Let us compare the table 4 with the Adhika masa table 1. All the absolute angle of sun in a new moon given in the third column of the table 1 falls in the range given by the second and third column in Table 4 for the corresponding lunar months.
Interestingly, the Adhika masa new moon falls very close to the starting values of the range given in the table 4. For example, the new moon preceding the Adhika Ashwina is at 174.46 Deg while the definition of the Ashwina masa from the table 4 starts from 173.52. This ensures that the new moon at the end of the Adhika Ashwina falls within the Kanya solar month. Hence the succeeding month will also be Ashwina as per the definition of the Adhika masa.
The correct name of months in 3067 BCE
Now let us look at table 2 of all the new moons in the 3067 BCE to derive their correct name. If we match the second column absolute angle of the sun in new moon with the ranges given in the table 4, we can derive the correct names for the lunar months. These names are listed in the fourth column of the table 2.
The angle of the new moon sun on December 12 3067 BCE as given in table 2 is 307.47 Deg. From table 4, this angle falls in the middle of the the Makara solar month (293.52 - 323.52). The 307.47 Deg angle of the new moon is not even close to the starting angle of the solar month (293.52 Deg). Clearly the lunar month succeeding the Dec 12 3067 BCE is the Magha month. It cannot be a Adhika Magha.
The angle of the new moon sun on January 11 3066 BCE as given in table 2 is 337.18 Deg. From table 4, this angle falls in the middle of the the Kumbha solar month (323.52-353.52). Clearly the lunar month succeeding the January 11 3066 BCE is the Phalguna masa. It cannot be a Magha masa as claimed by the author.
Conclusion
The deception of Adhika masa in the 3k dates of Mahabharata is exposed in this article. The length of the so called Adhika masa breaches the maximum limit. The correct names of the lunar months derived from the position of the preceding new moon does not match the names claimed by the author of the 3K dates.
