Yug in ved
Both versions of Vedaang Jyotish (Rig Ved and Yajur Ved) tell "Panch-Samvatsar mayam yugam". These have different meanings in different contexts -
(1) 1 Yug = 5 years, called Sam-vatsar, Pari-vatsar, Id-vatsar, Idaa-vatsar, and Anu-vatsar.
Vatsar is 12 x 30 = 360 days is civil year with 5 or 6 extra days at the end called Pancha-raatra or Shadaha.

(2) 1 Yug has 5 years of Samvatsar type and 14 years of other 4 types - Pari-vatsar, Id-vatsar, Idaa-vatsar, Anu-vatsar.

(3) Yug is decided by 5 types of Sam-vatsar - in same way as day is decided by 5 methods - Tithi, Vaar, Nakshatra, Yoga, Karan. 5 Samvatsar deciding Yug are - Baarhaspatya, Divya, Saptarshi, Dhruv or Kraunch, and Ayanabda.

(4) In Baarhaspatya system itself, a Yug is of 5 Samvatsar of 12 years (Aadityas) each, called Aangiras period of 5 x 12 = 60 years in Taittireeya Braahman (2.2.3.5), or Aitareya Braahman (18.3.7)

1 Yug = 5 years or 18 years in Rig Ved Jyotish has some distinctions -
(1) Year is tropical, sidereal, or combination of sidereal and greater part of Mandochcha cycle in 312,000 years which makes 24,000 year cycle of Ayanaabda Yug instead of 26,000 years called Manvantar in Brahmaand Puraan.

(2) Value of each year was different in ancient eras due to uncertain values of the Earth's axial rotation period which is the unit of measurement of year.

(3) Accuracy of measuring day and year lengths in each era and their revisions in each period.

Discussion about 3 Vishwaamitra and Pargiter in his Pauraanik chronology has devoted about 150 pages on it to show that Puraan are unreliable on this account and did arbitrary manipulations. Same authors have no hesitation in accepting 8 Edwards and 5 Georges within 300 years in much smaller area of England, or 2 George Bush as Presidents of USA in 10 years.

Finally, it comes down to the conclusion that Indian civilization started after the attack by Alexander in 326 BC and Vishwaamitra should be in 200 BC. But Megasthenese, Arian, Solinus have stated that in 6777 BC, April month Dyonisus had attacked India and carried his arms up to Pillar which stood at Palibothri on Yamunaa banks in time of Megasthenese. In that period, there was no king, but India had sufficient wealth for looting.

The third Vishwaamitra or Kalki are probably yet to be born and related parts will be after rule of World Bank or Wal-mart.
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1. 5 years x 365.24219 = 1826.2109 days
2. 62 Lunar months x 29.5305 = 1830.891 days
3. 62 Savan months x 30 = 1860 days
4. 19 years x 365.24219 = 6939.6016
5. 235 lunar months x 29.5305 = 6939.6675

Thus, they were following the calculation of years in Mahaabhaarat era :
1. A 5- year Yug of 62 Lunar Months
2. On completion of 19 years, they used to drop last Samvatsar of the 4th Yug of 5-years Yug cycle, so that the Lunar Tithi may fall in line with the solar year. This is mentioned in Mahaabhaarat.

The question is what was the method adopted to commence a 5-year Yug cycle.
As far as Chatur-Yug cycle, of 4,320,000 years is concerned, it is for astronomical calculations, and it has no religious significance

The Era of Vishwaamitra (24th Century BC)

1. Ingress of the Vernal Equinox into Krittikaa Nakshatra
Some authorities talk about three Vishwaamitra who lived in three different Eras. Here we will explore the achievements of the Rishi Vishwaamitra who lived in the 24th century BC. This can be proved with the help of the following verse which indicates the commencement of the Yudhishtra Era:

"This verse says that the Shak Era commenced after a lapse of 2526 years from the commencement of the Yudhishthir Era. Thus we can draw the simple conclusion that the Mahaabhaarat Era was before 2448 BC (ie 2526 years before 78 AD, the year of the commencement of the Shak Era). Some authorities believe that the original Shak Era actually commenced in 550 BC. This would push the commencement of the Yudhishtra Era back to 3076 BC. In any case, the Rishi Vishwaamitra, to whom we are referring to lived after the Mahaabhaarat Era. (see many Samvatsar names here)

We quote this verse to prove that the sage Vishwaamitra and the sage Paraashar whose achievements I am discussing, lived after the Era of the Mahaabhaarat. The sage Vishwaamitra of the Era of Raam and the sage Paraashar of Mahaabhaarat fame were different Rishi.

The Astronomical hymn of Vishwaamitra (RV III, 9.9) reads as follows:
trini shataa trï sahasraanya agnim trinshat cha devaa navaa chasaparyan
tri saharaani, trini sataa, trinshat cha nava cha devaa agnim asaparyan, --- i.e.
3339 Dev (Dyu or Tithi) worshipped Agni (Krittikaa = Alcyone 2) by perambulation in the sky.

Vishwaamitra’s astronomy thus contains the mystic number 3339 which can be factorized as follows:  3339 = 371 X 9 = 53 X 7 X 9
This is purely an astronomical hymn which refers to the worship of Agni, the Lord of the star Krittikaa, by perambulation in the sky.
The hymn yields the following concepts when the Full Moons in Krittikaa (Alcyone 2) are observed and studied continuously for 30 years:

2. The Length of the Year
A Solar Year is made up of 371 Lunar Tithi to a first approximation; a 9-year period is made up of 3339 Tithi.
In three years, there is one intercalary month. Vishwaamitra discovered that in 30 years, one extra intercalary month (in addition to the usual 10) is needed.

Hence 30 solar years
= 30 Synodic years + 11 Synodic months
= 30 X 360 Tithi + 11 X 30 Tithi
= 30 X 371 Tithi

Thus one solar year = 371 Tithis  =  = 371 X 29.531/30 = 365.20 days

The modern values are:
Mean length of a tropical year = 365.242190 days
Mean length of a sidereal year = 365.256363 days

Vishwaamitra's calculations are truly a wonderful achievement in so remote a period! (We should also remember that the duration of the rotation of the earth varies in different Eras and is not constant.)

Since ancient times, man has observed that day comes after night and night after day. Similarly, he has observed the phases of the Moon and the yearly cycle of seasons.

3. Eclipses – Cycle of Saros
The plane of the Moon’s orbit has an inclination of 5.15 degree to that of the Earth’s orbit. The two opposite points of intersection of these orbits are called Raahu and Ketu. These nodes regress, and in 6793.470 days (18.60 years) make a complete circle of the zodiac. When a conjunction or opposition of the Sun and the Moon occurs near either node, a solar or lunar eclipse occurs. Man has always been very curious about the occurrence of the eclipses in all Eras.

It is believed that the Chaldean astronomers discovered that eclipses recur in a cycle of 18 tropical years, 11 days and 8 hours, a period within which four leap years are contained. If there are five leap years, then it is one day shorter; and if there are three, then it is one day longer. The Indian Rishi discovered that the corresponding cycle contained 223 Synodic lunar months. This cycle is more appropriate and meaningful because the eclipses can take place only at the full or New Moons. The Indian law is, therefore, integrally rigorous.
Now, 3339 Tithi  = 111 Synodic months plus 9 Tithi.

If the above period is multiplied by two, the figure will come to 222 Synodic months plus 18 Tithis. This is only 12 Tithi shorter than the Saros cycle of 223 Synodic months. Thus, astronomers could predict the eclipse at the next full or new moon after the period arrived at by using the mystic number 3339. This establishes that the Vishwaamitra School knew about the cycle of eclipses.

4. Vishwaamitra Yug (Exeligmos)
The period of 3339 Synodic years equals 3240 solar years (3339 X 360.371). Actually one third the period ie 1080 solar years, was extensively used and applied in determining Eras in India up to the 5th century AD. (The period of 1080 solar years will include all intercalary Tithi in full number to first approximation. 1080 solar years will contain 1113 Synodic years.)

From this initial period of 1080 years they evolved the concept of a Chatur-Yug of 4320 years (1080 X 4). From this, Aaryabhatt derived the concept of 4,320,000 years as comprising a Cosmic Yug for higher accuracy. (This is called one day of the creator, Brahmaa) And Brahmgupt conceived of 4,320,000,000 years for still higher accuracy.

Some authorities believe that the value of the Cosmic Yug mentioned above is the LCM of the sidereal periods of all the seven planets. It is not possible to verify such a claim mathematically based on the astronomical data available at present.

Vishwaamitra’s mystic number 3339 gives a better and a more scientific explanation for the adoption, by different authorities, of the time durations of the Yug.

I may mention that some astrologers recommend the use of the Savan year of 360 days for the calculation of Dashaa and for other predictive purposes. This is not correct. The solar year must be used for Dashaa calculations as is clear from the discussions above. UNQUOTE