The wise men of ancient Babylon made very accurate observations of the positions of the sun and the moon over several centuries. Their observations made over several generations revealed that the positions of the sun and moon relative to the earth followed a cycle of 19 years.
It is likely that this would have been known to Daniel, as according to Daniel 2:48, king Nebuchadnezzar made Daniel “chief of the governors over all the wise men of Babylon.”
Knowledge of the 19-year cycle was used to regulate the calendar a few decades after Daniel’s time. It led to a more accurate determination of the length of the year and of the lunar month (or the synodic month).
In modern astronomy, the synodic month, the time between two successive New Moons, is 29.53059 days (29 days, 12 hours, 44 minutes, 2.8 seconds). A tropical year is 365.24218967 days (365 days, 5 hours, 48 minutes and 45.1875 seconds).
In ancient Babylon, observations and calculations were made, and recorded on clay tablets. The number system they employed was sexagesimal (base 60). In that system we would write, “1 year = 12;22,6,20 months.” The Babylonians determined that “19 years contain 7 intercalary months.”
19 years = 19 × 12 + 7 = 235 synodic months
Thus, 19 years is a “week” of leap years.
Otto Neugebauer said the 19-year cycle was incorporated in the Babylonian calendar since the 5th century B.C. 
James Evans wrote: 
The tropical year is longer than twelve synodic months by 0.3693 month. We search for an integer n such that n × 0.3683 is a whole number. A very satisfactory solution is n = 19.
19 × 0.3683 = 6.9977, which is very nearly 7.
Thus, we may construct a nineteen-year luni-solar cycle. In nineteen calendar years, we insert seven additional months. Of the nineteen years, twelve will consist of twelve months and seven will consist of thirteen months.
12 years of 12 months = 144 months
7 years of 13 months = 91 months
so, 19 calendar years = 235 months
The average length of the calendar year in this system is 235 months/19 = 12.3684 months, which agrees very well with the length of the solar years (12.3683 months)
Nineteen tropical years therefore contain 235 synodic months, almost exactly. The astronomical meaning of this statement is that after nineteen tropical years, both the Sun and the Moon return to the same positions on the ecliptic. The sun returns to the same longitude after any interval containing a whole number of tropical years. The special feature of the nineteen-year period is that it also contains a whole number of synodic months. Thus, the Moon will be in the same phase on two dates that are nineteen years apart.
The explanation of the eight- and nineteen-year cycles given above is not meant to reflect the actual process of discovery: the ancient Greeks and Babylonians did not begin with a knowledge of the lengths of the year and the month. Rather, a knowledge of these cycles emerged after several generations of keeping track of the Moon.
Evans said that in Babylon, “There is some evidence that an eight-year cycle was used for the brief period from 529 to 503 B.C. From 499, the nineteen-year cycle was probably in use (seven intercalary months inserted every nineteen years).” 
In the prophecy of the 70 weeks, which dates from about 539 B.C., Daniel divides the time from the decree of Cyrus to the appearance of Christ into two sections, of 7 weeks, and 62 weeks. The number 62 is mentioned in chapter 5, where the age of Darius when he became king was 62. When the second section of 62 weeks is viewed in terms of “seven times,” the unit of “times” is 62 years. The second section is 434 years.
In the New Testament, the beginning of John’s ministry is dated as the 15th year of Tiberius. [Luke 3:1] Tiberius was established as co-emperor with Augustus, two years before the death of Augustus, which occurred in August 14 A.D. Thus, if the two years as co-regent are included, the 15th year of Tiberius was probably 26 A.D. Jesus began his ministry after John.
Daniel specified the time period from Cyrus to the beginning of the ministry of Jesus in two sections, because different units for “times” apply in each section. In the second section, a “time” is 62 years. I suggest the units of the first section are weeks of leap years; the seven sevens are seven sevens of leap years. A week of leap years is 19 years. This accurately fulfills the prophecy as a prediction of the date of the appearance of the Messiah.
First section (time = 19 years): seven times = 133 years
Second section (time = 62 years): seven times = 434 years
Time from Cyrus’ decree to Jesus = 567 years
What clues support Daniel’s use of leap years for the first section?
The two numbers provided in Daniel 12:11-12, 1290 days, and 1335 days, are cryptic representations of periods that fit the pattern of a time, times and a half. They involve years of 12 months, and years of 13 months.
And I heard, but I understood not: then said I, O my Lord, what shall be the end of these things?
And he said, Go thy way, Daniel: for the words are closed up and sealed till the time of the end.
Many shall be purified, and made white, and tried; but the wicked shall do wickedly: and none of the wicked shall understand; but the wise shall understand.
And from the time that the daily sacrifice shall be taken away, and the abomination that maketh desolate set up, there shall be a thousand two hundred and ninety days.
Blessed is he that waiteth, and cometh to the thousand three hundred and five and thirty days.
The numbers fit the pattern of a time, times and a half, as follows:
1,290 days = 13 × 30 + 2 × 12 x 30 + 12
× 30 / 2
1,335 days = 12 × 30 + 2 × 13 x 30 + 13 × 30 / 2
The number of leap years in these expressions equals the number of regular years. In reality, there are seven leap years for every 12 regular years. In the above expressions the “months” are exactly 30 days, which indicates they are not real months. The expressions do not fit any literal three and a half year periods, but they are symbolic.
In each of the expressions above, the units for the first section differ from the rest. The same principle applies to the 70 weeks; the units of the first section are weeks of leap years. A period of 49 leap years spans 133 years.
Since Daniel was put over all the wise men of Babylon, he must have been well aware of their astronomical knowledge and of their measurements of the synodic month that dated back for centuries. And so his use of the 30 day month in formulating the above numbers demonstrates that they represent symbolic periods, not literal days, or a literal three and a half years. The pattern of the “time, times and a half” applied to the numbers shows the significance of leap years, which are units employed in the first section of the 70 weeks prophecy, part of the time periods relating the decree of Cyrus and the appearance of Christ.
1. Otto Neugebauer. A history of ancient mathematical astronomy, Volume 2. Birkhäuser, 1975. pp. 616, 622.
2. James Evans. History and practice of ancient astronomy. Oxford University Press, 1998. p. 185.
3. Ibid., p. 188.