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When was Bhagiratha born? Are there any attempts to date his period? Because it is said that the incident of the drought occurred when Kapila Nakshatra was seen in the sky.

I think this might be helpful in mapping how long back Bhagiratha existed.

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According to Ikshvaku_dynasty, King Sagara was ancentor of king Bhagirataha. King sagara had 60,000 sons who became ghosts.

King -> Period

20 Sagara -> Satya Yuga
21 Asamanja -> Satya Yuga
22 Amsumana -> Satya Yuga

Amsumana was already there in the story where Kapiladeva returned the horse and told Anshuman that the sons of King Sagara could be delivered if the Ganges descended to earth and bathed them in her waters.

Kapila is vedic sage and king Sagara is considered to be vedic king. Now Anshumana sons

23 Dileepa ->
24 Bhagiratha ->

These two can have period of either satya yuga or Treta Yuga.

37 Rama -> Treta yuga

Rigveda

Ganga is mentioned in the Rigveda, the earliest and theoretically the holiest of the Hindu scriptures. Ganga is mentioned in the nadistuti (Rigveda 10.75), which lists the rivers from east to west. In RV 6.45.31, the word Ganga is also mentioned, but it is not clear if the reference is to the river.

So we can see that before Rigveda was composed Ganga was there on earth.

Years Calculation

According to Hindu numbers

Duration of Satya yuga 1,728,000 years
Duration of lifetime of human in Satya yuga around 100,000 years.
Duration of lifetime of human in Tretā-yuga around 10,000 years

Brahma is at number 1 so at number 24 years can be maximum of 840 *1000 years if we consider a person can have son at the age 35 which is in Gruhasthashram as per vedas.

Time passed after beginning of Kali-Yuga (Battle of Kurukṣetra) around 5,114 years

Calculation is

Year of Kaliyuga started 5,114 years
+ Time of Dwapar Yuga 864,000 years
+ Time of Treta yuga 1,296,000 years
= 2165114 Years

Period of Bhagirataha can be before 2165114 years minimum

Edits are invited to improve this answer

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  • 1
    In order to find out how old a particular hymn of the Rug Veda is, you can look at the Anukramani in my answer here: hinduism.stackexchange.com/a/2430/36 That will tell you who the seer of the hymn is, and then you can try to determine who long ago he lived. – Keshav Srinivasan Aug 27 '14 at 15:18

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