Before we work on Age of Lord Rama we need to understand the Vedic division of the time which measures time in Kalpa, Mahayuga and Yuga.
For this discussion we assume that a Kalpa, the half day of Lord Brahma, is the greatest Vedic division of the time. It consists of 1000 Mahayugas. A Mahayuga is composed of four Yugas of different lengths, named as Krita or Satya, Treta, Dvapara and Kali. The Kali Yuga consists of 432,000 solar years. The Dvapara Yuga is double of the Kali Yuga. The Treta Yuga is triple and the Krita Yuga is quadruple of the Kali Yuga.
A Mahayuga therefore contains 10 times the years of a Kali Yuga i.e. 4,320,000 solar years. According to Hindu belief a Kalpa is the half day (excluding night) of Brahma, the god of creation.
If we take 'x' as the duration of one Kali Yuga then x = 432,000 solar years. Hence,
1 Kalpa = 1000 Mahayugas = 1 half day of Brahma = 10,000x
1 Mahayuga = 4,320,000 solar years = 10x
Satya Yuga = 1,728,000 solar years = 4x
Treta Yuga = 1,296,000 solar years = 3x
Dvapara Yuga = 864,000 solar years = 2x
Kali Yuga = 432,000 solar years = x
As per various Puranas Lord Rama was born in Treta Yuga and 5114 Kali Yugas are over as on April 17, 2013. Even if we assume that Lord Rama was born at the end of Treta Yuga, a total 869,114 (864,000+5114) solar years have passed. According to some scholars, the war between Rama and Ravana is supposed to have happened 880,155 solar years ago as of April 17, 2013.
Epic Ramayana has many references to astronomical events which occurred during the life time of Lord Rama. Based on those astronomical events, many scholars try to plot planetary positions in the sky to ascertain the birth time of Lord Rama. Such calculations need software which can perform astronomical calculations in the past up to 1,000,000 solar years (or about 1 million solar years in the past).
Pushkar Bhatnagar has done some work to date the birth time of Lord Rama. According to him "By using a powerful planetarium software, I found that the planetary positions mentioned in Ramayana for the date of birth of Lord Ram had occurred in the sky at around 12.30 p.m. of 10th January 5114 BC."
To prove his theory Pushkar Bhatnagar has considered the duration of one Kali Yuga as 1200 solar years.
If we take 'y' as the duration of one Kali Yuga then y = 1200 solar years. Hence,
1 Mahayuga = 12,000 solar years = 12y
Satya Yuga = 4800 solar years = 4y
Treta Yuga = 3600 solar years = 3y
Dvapara Yuga = 2400 solar years = 2y
Kali Yuga = 1200 solar years = y
After considering above time durations for various Yugas, which is already against various Puranas, Pushkar Bhatnagar further assumes that 1 Mahayuga should have been 10,000 solar years long rather than 12,000 solar years to fix 5114 BC as the birth date of Lord Rama.
Pushkar Bhatnagar doesn't explain if Kali Yuga spans for just 1200/1000 solar years then we all should be living in Satya Yuga. According to Vedic wisdom all Yugas are cyclic and Pushkar has taken 3012 BC as the starting year of the Kali Yuga. It is well known that all planetary positions are cyclic and keep repeating in similar patterns including solar and lunar eclipses. There is no work to prove that the similar astronomical events as described in Ramayana didn't occur before 5114 BC.
One needs to look back up to 1 million solar years in the past to ascertain birth time of Lord Rama. As per Pushkar Bhatnagar, his software was capable to look back 99,999 BC in the past which is only 10% of the needed time span. Any such studies should consider all instances of similar astronomical events during last 1 million solar years.
Till we don't have any concrete historical and astronomical proofs, it would be more appropriate and accurate to say that Lord Rama was born much earlier than 869,114 solar years in the past and according to Hindu calendar it was Navami of Chaitra Shukla Paksha.