I am still in the process of researching this significant question and have not come to a conclusion, but here is some evidence that, at least for now, seems to bear very significant weight in my mind.
Srimad Bhagavatam 1.4.14 says that Vyasa began his work when the Second Age was on the verge of beginning.1.4.20 says that he began by creating the Rg and other three Vedas. 1.4.23 indicates that the further development of literature took place as a combined effort of sages under Vyasa’s leadership over a span of many generations. The remainder of the chapter and beginning of the next makes it clear that after seeing the compilation of so many expansive upanishads and puranas, Vyasa remained dissatisfied and later became inspired by Narada to create the Bhagavatam to remedy his dissatisfaction. So Bhagavatam is the last effort.
We hear elsewhere in the text itself that Bhagavatam was created just after Krishna’s departure from the Earth and the beginning of Kali Yuga.
Astronomically speaking we know with sufficient confidence that the Rg Veda created roughly 5,000 years ago – because it specifies that the “first star” was Krittika (Pleiades) and we can reconstruct the movement of the vernal equinox (the starting point of the celestial circle) to see that it was last in Krttika about 5,000 years ago.
This indicates that 5,000 years ago is when Vyasa began his efforts, not when he completed them by creating the Bhagavatam. So it seems to be a clear indication that 5,000 years ago was the beginning of the Second Age (Dvapara). And that Kali Yuga began several generations of sages after that.
This assessment does not support the long version of yugas as multiples of 1,000 years multiplied by 360. Rather it supports the short version of yugas simply as multiples of 1,000 years.
Please see this addendum correcting a mistaken concept in this post.
– Vic DiCara