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Consider the following excerpt from the Mahabharatha, which discuss possible implications of the astrological phenomenon

"Beholding these signs that indicated the perverse course of Time, and seeing that the day of the new moon coincided with the thirteenth (and the fourteenth) lunation, Hrishikesa, summoning the Yadavas, said unto them these words: ‘The fourteenth lunation has been made the fifteenth by Rahu once more. Such a day had happened at the time of the great battle of the Bharatas. It has once more appeared, it seems, for our destruction.’ "The slayer of Keshi, Janardana, thinking upon the omens that Time showed, understood that the thirty-sixth year had come, and that what Gandhari, burning with grief on account of the death of her sons, and deprived of all her kinsmen, had said was about to transpire.

[2, Mausala Parva, The Mahabharata]

Thirteen lunation is Trayodasi and fourteen is Chaturdasi. Although Krishna knows about Gandhari's curse, he explicitly mentioned the day of Amavasya along with Chaturdasi as an astrological cause for destruction. It is mentioned in the chapter that such a combination (Chaturdasi + Amavasya) happened after 36 years.

I want to know whether such a combination happens every 36 years, if not, then what is the general frequency of such occurrence?

If such a combination happens, then is it true that there are more chances of destruction? Does scriptures of astrology mention about destruction aspect of this combination?

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 It is mentioned in the chapter that such a combination (Chaturdasi + Amavasya) happened after 36 years.

Nope, Amavasya falling on Chaturdashi is quite normal. It atleast happens once a year (at minimal)
You misunderstood the lines, let me explain.

Beholding these signs that indicated the perverse course of Time, and seeing that the day of the new moon coincided with the thirteenth lunation,

If you read this once again you will understand that Amavasya fell on Trayodashi (and not chaturdashi).

Hrishikesa, summoning the Yadavas, said unto them these words: The fourteenth lunation has been made the fifteenth by Rahu once more.

It means that Chaturdashi was made into Amavasya by Grahan(by Rahu). Thus, Amavasya coincided on Tryodashi (which is next to impossible. But happened only in Mahabharata)

It can be expalined as,

Krishn returned from Hastinaapura after his unsuccessful peace mission on Uttara Palghuna day. Starting from that day, the seventh day is New-moon day (amaavaasya) with Saturn on Rohini Nakshatra as discussed by Vyaasa. Rahu was approaching the Sun(to cast Surya Grahan), and the Moon was turning towards Amaavaasya (New-Moon day).

Well, 36 years after the Mahabharat war, the same constelations were once again formed and thus the Yaadava kula was destroyed. This was predicted by Krishn by astrological happening - "Rahu has compressed Amavasya on Chaturdasi.(Thus falling on Tryodashi directly). This happened once before the Mahabharata war and again will be happening soon and this will lead to our destruction". He remembered Gandhari's curse on the Yadava kula.

Astrologically a strange phenomenon occurred during the Mahabharata war.

The lunar cycle (paksha - normally is 15 days) sometimes happens in fourteen days. But during the Mahabharata war-time a rare thing happened - the paksha got compressed to 13 days. This aspect has been discussed in the Bhiishma parva - 3rd Adhyaaya. Guru and Shani are in Vaishaaka, Moon and the Sun entered in the same house one after the other making Amaavaasya on the Trayodasi tithi itself. Because, Trayodashi can converge with Chatrudashi, or Chaturdashi can converge with Amavasya, these are called tithi kshya. But, tryodashi can never converge with Amavasya, no not even in 36 years normally. Tbh, It was all play by Krishn himself, or you think anyone can dare to touch him :)

Thus, this peculiar condensation of the tithis into thirteen from fifteen is a rare phenomenon as discussed by Vyaasa in Mahabharat and has inevitably followed by mass destruction due to war.

Vyaasa himself writes:

चतुरदशिम पंचदशिम भूता पूर्वामंचा शोडषिम् ।  ईमान्तु नाभि जानेsहम अमावश्याम त्रयोदषिम ।।
चंद्र सूर्य भौग्रसतौ  एकमेवं त्रयोदशिम ।
अपर्वाणी ग्रहणे तौ प्रजा साक्षाप्यैश्यतः।।
"I have seen fourteen days a paksha, fifteen day completion or extension to sixteenth day also. This amaavaasya falling on the thirteenth day itself I have never seen before" - says Vyasa. That, on the same month, Sun and Moon eclipses falling during the missing tithis is a rare phenomenon, resulting in large-scale disaster to people.

Thus it can be concluded, that falling of Amavasya on Trayodashi is extremely RARE. And if it thus happens ever, as said disasters are unevitable.

कालिकार्पणमस्तु ।🌺

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