A book I read recently says that the only firm date is the history of ancient India is the invasion of Alexander (327-326 B.C.).
Can anything more be said about this?
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Yes, if the events in scriptures are described with planetary positions at that time then exact dates can be calculated. And this is exactly what happened in case of Ramayana.
In Valmiki Ramayana, planetary positions are mentioned when events took place. Based on those positions, the dates calculated are:
Sri Rama Navami - Birth day 10th January 5114 BCE
Birth of Bharatha - 11th January 5114 BCE
Pre coronation eve - 4th January 5089 BCE Khar
Dushan episode - 7th October 5077 BCE
Vali Vadham - 3rd April 5076 BCE
Hanuman's Visit to Lanka - 12th September 5076 BCE
Hanuman's Return from Lanka - 14th September 5076 BCE
Army March to Lanka - 12th September 5076 BCE
You can also see that dates calculated are quite consistent. More details have been shared by those who did this research like Valmiki Ramayana says Rama was 25 years of age when he went to exile and based on the planetary positions they fed into the software and found out the difference of years between positions at his birth and at exile and the result was 25 years! Perfect match with Valmiki Ramayana!