In Daniel 9 we read how an angel announced to Daniel that 70 periods of 7 years ("weeks" of years) have been decided over Israel [1, 2]. According to the prophecy, this period would commence with the command to rebuild the city of Jerusalem. Then the first 69 periods (weeks of years) would continue until a Messiah (Anointed One), a Prince, arrives. After that, the Messiah would be "cut off" (i.e. die) (Dan. 9:25-6). In this short note, we focus on the calculation of this first 69 weeks of years (483 years). The relation between these 69 weeks and the final week is discussed elsewhere (see [1] where all the different views on Daniel's 70 weeks of years are discussed).
The only command that was ever given to rebuild the city of Jerusalem (as mentioned in the prophecy), was the one given in the month of Nisan in the twentieth year of the Persian king Artaxerxes Longimanus (Neh. 2:5). This was in the year 445 BC (Artaxerxes's rule is calculated from the death of his father Xerxes in July 465 BC; Anderson 1984:253). The three previous commands that were given by Persian rulers, were all concerned with the building of the temple – not the city of Jerusalem (Ezra 1:2-4; 5:13; 6:3-14; 7:12-26).
The period of 69 weeks of years would come to an end when Messiah, a Prince, appears. There can be no doubt that this prophecy may be taken as referring to Jesus Christ since the period clearly continues until his time. In the King James Bible the word "anointed one" is accordingly translated as "Messiah". The question that now confronts us is: To which event during the earthly ministry of Jesus does the prophecy refer? Or to put it differently: when did Jesus present himself as Messiah and King (Prince) to Israel?
This clearly happened when Jesus rode upon the donkey into Jerusalem in accordance with the prophecy of Zechariah: "Rejoice greatly, O daughter of Sion; shout, O daughter of Jerusalem: behold, thy King cometh unto thee: he is just, and having salvation; lowly, and riding upon an ass, and upon a colt the foal of an ass" (Zech. 9:9). When that happened, the crowd cried out: "Hosanna, Blessed is the King of Israel that cometh in the name of the Lord" (Joh. 12:13 – King James Bible).
From the details in the Gospel of St. Luke, we know that John the Baptist started his ministry in the fifteenth year of Cesar Tiberius (Luk. 3:1-3). The fifteenth year of Tiberius commenced on 19 August 28 AD. Jesus was therefore baptized in the autumn of 28 AD. This means that he was crucified three-and-a-half years later in the year 32 AD (Anderson 1984:97). The year 32 AD is also the only year in which the calendar agrees with the events of that time. Jesus, therefore, entered Jerusalem on the donkey on the Sunday before the crucifixion in the year 32 AD (see Joh. 12:1, 12).
This period of 69 weeks of years, i.e. 483 years, that is from 445 BC to 32 AD, ends long after the latest possible date that the text could have been written (somewhere after 164 BC; i.e as is accepted in Biblical Criticism circles). This means that a considerable part of the prophecy refers to events that happened long after the text was written (by the latest estimates). Traditional Christians believe that the prophecy dates much earlier, namely to the time mentioned in the Book of Daniel (538 BC; right at the beginning of the Persian rule over Babylon). Irrespective of the position taken, the 483 years obviously ends long after the latest accepted date for the writing of the book [3]. One can also not think that Jesus could have calculated the date to superficially "fulfil" the prophecy because (as we will now show) the kind of mathematics necessary to do the calculations was not available at that time.
This period of 69 weeks of years, i.e. 483 years, that is from 445 BC to 32 AD, ends long after the latest possible date that the text could have been written (somewhere after 164 BC; i.e as is accepted in Biblical Criticism circles). This means that a considerable part of the prophecy refers to events that happened long after the text was written (by the latest estimates). Traditional Christians believe that the prophecy dates much earlier, namely to the time mentioned in the Book of Daniel (538 BC; right at the beginning of the Persian rule over Babylon). Irrespective of the position taken, the 483 years obviously ends long after the latest accepted date for the writing of the book [3]. One can also not think that Jesus could have calculated the date to superficially "fulfil" the prophecy because (as we will now show) the kind of mathematics necessary to do the calculations was not available at that time.
Background for the calculations
Before we can proceed to calculate the period from the command given by Artaxerxes Longimanus to rebuild Jerusalem in 445 BC until Jesus' entrance on Palm Sunday into Jerusalem in 32 AD, we need certain background information.
It was already known from early times that the moon period (from new moon to new moon) is 29 1/2 days and that the seasonal year is 365 1/4 days. Twelve moon months of 30 and 29 days respectively (with an average of 29.5) give 354 days (one moon year) which are 11 days short of a seasonal year. By including a moon month of 30 or 29 days from time to time (more or less every third year), the ancients were able to synchronize the moon and seasonal (solar) years.
In the year 432 BC, the Greek astronomer Meton calculated that these moon and seasonal years would synchronize precisely over a period of 19 years if 4 or 5 days are added by some moon years over a period of 19 years. For each 19-year cycle for which 4 days are added, there must be three such cycles for which 5 days are added. The 19-year cycles are calculated as follows:
Cycle 1: 19 x 354 days + 6 x 30 days + 29 days + 5 days = 6940 days
Cycle 2: 19 x 354 days + 6 x 30 days + 29 days + 4 days = 6939 days
The average over four such 19-year cycles is therefore
1/4 (3 x 6940 + 6939) = 6939 3/4 days
which is precisely the amount of days in 19 seasonal years:
19 x 365 1/4 days = 6939 3/4 days.
Although it might seem strange that 4 or 5 days are added in this manner, the result is that the calculated moon cycle is much closer to the real moon cycle than would otherwise be the case (when those days are not added). This is shown below:
The assumed moon cycle that was known from early times: 29.5 days
Average calculated moon cycle in accordance with Meton's synchronizing procedure (235 moon months in 19 years): (6939 3/4)/235 = 29.53085 days
Real (average) moon cycle (current calculation): 29.530588 days
The difference between Meton's procedure and the real moon cycle is about 1 day in 307 years!
If Meton's procedure is followed, then the moon will show the same phases on the same dates after 19 years. Since the moon and seasonal years synchronize so precisely, the moon would, in any case, show the same phases on the same dates even when the procedure is not followed – the moon and earth rotations are obviously not dependent on the way in which the moon months are kept on earth. If the moon months are just continuously kept in line with the moon phases (for example, from new moon to new moon), then the moon months would also after 19 years fall on the same days calculated by Meton's procedure. Meton's procedure merely facilitate the process of calculation.
Another important calculation that we can make, is to show that every 28 years the same days of the week fall on the same dates (the "solar cycle"). This follows from the combined effect of adding a leap year every 4 years and the 7 days in the week (4 x 7 = 28). Already in 457 AD, Victorius of Aquitaine brought this solar cycle and Meton's calculations together in one procedure to calculate the dates for Easter Sunday.
In 1977 Roode (1977:4) rewrote these calculations mathematically, allowing us to calculate any Easter dates with ease. The reader should not be overwhelmed by the symbols used as part of this algorithm to calculate those dates for any year AD. One merely stick the information of the relevant year into the algorithm and then the details of that year become available. This is shown below:
In 1977 Roode (1977:4) rewrote these calculations mathematically, allowing us to calculate any Easter dates with ease. The reader should not be overwhelmed by the symbols used as part of this algorithm to calculate those dates for any year AD. One merely stick the information of the relevant year into the algorithm and then the details of that year become available. This is shown below:
G = (J) mod(19) + 1
(J is the year of interest, G is the golden number of that year, X mod(Y) = fraction(X/Y).Y)
E = (11 G – 4) mod(30) + 1 (1 for leap years)
(E gives the "age" of the moon on 31 December before year J)
N = 44 – E (43 – E for leap years)
(N gives the full moon date in March)
D = 5 J/4
M = N + 7 – ((D +N) mod(7))
(M is the date in March before the first Sunday after the relevant full moon).
The date of Jesus' entrance
We have already shown that Jesus entered Jerusalem in the year 32 AD on the donkey. To get all the necessary information for this year, we use the year 32 AD in the above algorithm. This is done below:
J = 32
G = 14
E = 1 (leap year)
N = 42 March (11 April)
D = 40
M = 44 March (13 April).
The calendar for March/April looks as follow
The Jews usually began their months on or just after the new moon, which is 13 days before full moon. This implies that the relevant month, namely Nisan, began with the new moon on Saturday 29 March 32 AD (on the Sabbath). This date is marked on the calendar given above. The full moon 13 days later on 14 Nisan was therefore on Friday 11 April 32 AD. This was also the day of the Passover (Pesach) and the day on which Jesus was crucified. Jesus, therefore, entered Jerusalem on Sunday 6 April 32 AD on the donkey.
The date on which the royal command was given
We must now consider the possibility of determining on which date Artaxerxes Longimanus gave the command to rebuild Jerusalem. We know already that it was in the year 445 BC. How can we find the details for this year? An easy way follows from the algorithm given above. We have shown that the phases of the moon fall every 19 years on the same date. Furthermore, the same weekdays fall every 28 years on the same date. The combined effect of these two principles is that after each 532 (19 x 28) years the phases of the moon would not only fall on the same dates but also on the same day of the week. Every 532 years are therefore identical!
We can now consider which AD year – for which we have the algorithm – would be identical with the year 445 BC. This is the year 88 AD. The period between any date during the year 445 BC and the same date during the year 88 AD is 532 years (there is no year 0). This is shown below:
For the year 88 AD we have
G = 13
E = 20
N = 24 March
D = 110
M = 30 March.
The calendar for that year is given below:
We can now make some small changes to the above calculations to accommodate those corrections that are necessary given our current knowledge. These corrections are only necessary for our data from 445 BC (the calculations for 32 AD involve a relatively short period, namely from 1-32 AD, for which no changes to the moon cycle and leap years are necessary). Meton's procedure results in the moon being allocated one day too far on the calendar after 307 years. We, therefore, have to "move" the moon backwards by about 1 1/2 days (that is for 445 years) in the direction of the date that we used as the point of departure for the algorithm (the year 1 BC). This means that the real new moon was on 13 March 445 (instead of 11 March) and the real full moon was on 26 March 445 BC.
Another important point concerns the leap year calculations. In the above algorithm, it is assumed that the seasonal year is 365 1/4 days long. This is not really correct and must be reduced by 11 minutes and 14 seconds (there are 365.2422 days in the year). Since no corrections were made in this regard since the procedure was first developed (starting in 64 BC), this error has grown throughout the centuries until the sixteenth century to 10 days. To rectify this error, the calendar of the year 1582 has the strange feature that 4 October was changed to 14 October (with the switch from the Julian to the Georgian calendar)! The ten days that were held as leap years through the ages but which never really were such were in this manner removed from the calendar. If those days were not added on 29 February, the calendar would have stood 10 days later.
We must now do a similar correction on the calendar for the year 445 BC. For every 400 years 3 leap years have to be removed. This implies that Wednesday 26 March 445 BC (full moon) should actually be Wednesday 23 March 445 BC. The new moon on March 445 BC was therefore on 10 March. This is shown below:
The eventual question that we must answer is: On what day did Artaxerxes Longimanus gave the command that Jerusalem should be rebuilt? In the Book of Nehemiah, we read that it was in the month of Nisan. This is the first month in the Jewish religious calendar. At that time, the Jewish months commenced either on the new moon or maybe when the first crescent appeared (according to the Mishnah – Anderson 1984:101) which could have been a day or so later.
In the year 445 BC, this new moon was on a Thursday (10 March). It is, therefore, possible that the religious new year could have commenced on any day from the Thursday to the Saturday. In those days the Jews also kept the New Year's day as a Sabbath (Amos 8:5; Hos. 2:10; Is. 1:13; 66:23). Since this New Year and the next Sabbath were so close to each other, it is likely that they would have coincided (these Sabbaths were not allowed to follow on subsequent days directly after each other). This means that the first working day of the week thereafter would have been the Sunday (13 March 445 BC). Nehemiah would have appeared before the king on this day.
The royal command must have been given early in the month of Nisan – maybe on this Sunday (2 Nisan). We can see this from other information in the Book of Nehemiah. We know that after Nehemiah's return to Jerusalem, they started building the wall around the city on the third of the month Ab (the wall was finished 52 days later on 25 Elul). Nehemiah would therefore have arrived on the 1st Ab in Jerusalem (Neh. 2:11; 6:15). Thirteen years earlier Ezra also arrived on this date in Jerusalem after departing five months earlier from Babylon (Ezra 7:9). This implies that Nehemiah must also have started his journey early in Nisan.
The reason why Sunday 13 March seems to be the correct date, is that this would have been the first day of the new year and month when Nehemiah appeared before the king. It might be that he humbled himself the previous day during the great Sabbath before God since another year has passed with the wall and gates of Jerusalem lying in ruins. He was clearly still grieving over the conditions in Jerusalem when he appeared before the king (Neh. 2:1-2).
The period from 445 BC to 32 AD
We can now proceed to calculate the period from Sunday 13 March 445 BC when the royal command was given to Sunday 6 April 32 AD when Jesus entered Jerusalem on the donkey. From 13 March 445 BC to 13 March 32 AD are 476 years which includes 365 x 476 days + 116 leap days = 173856 days. The period between 13 March and 6 April 32 AD is 24 days. The total is therefore 173880 days. This is precisely 69 prophetic years of 360 days each (see Rev. 11:1-2) – even to the exact day!
Day on which the royal command was given: Sunday 13 March 445 BC
Day on which Jesus entered Jerusalem: Sunday 6 April 32 AD
The period in between:
13 March 445 BC to 13 March 32 AD
(476 years = 476 x 365 days) 173740 days
13 March – 6 April 32 AD + 24 days
Leap years in the period + 116 days
Total 173880 days
For 69 x 7 prophetic years (360 days in the year)
(69 x 7 x 360) 173880 days
The fact that 173880 days are precisely dividable by 7 shows that the first and last dates must fall on the same day of the week (if those days are not calculated inclusively). We have indeed shown that both the royal command and the entrance in Jerusalem happened on Sundays – which is the day of the One about whom the prophecy is. Both events probably happened in the morning, with precisely 173880 days in between.
To confirm that the new moon did fall on 10 March 445 BC, we can apply a simple test. We know the average period between new moons and know that it did not change significantly since the time of Meton's procedure (432 BC). The period between any two new moons must now be dividable through this moon period (29.530588 days) – so also the period between the new moons of 10 March 445 BC and 29 March 32 AD.
We can now move the calculated period three days back such that it commences on the relevant new moon in 445 BC, which would mean that it ends just 5 days after the relevant new moon in 32 AD (3 days before Jesus' entrance into Jerusalem). The average period between these new moons would then be 173880 – 5 = 173875 days. This period is one day less than 173876 days which are exactly dividable by the average moon period of 29.530588 days (5888 times). The reason for the one day difference is that the first and last days of the total period (or of the period between these new moons) are not taken inclusively (which would add another day); the exact time of the new moons may, therefore, vary as much as one day. The new moon date in 445 BC has therefore been calculated correctly.
Other calculations
There have been various efforts to calculate this period of 69 weeks of years. The first and best known was done by Sir Robert Anderson. He used the same date for the time of Christ but for the year 445 BC, he took 13 March as the date for the new moon (as calculated in 1877 by the British Royal Observatory). My date is 10 March. Since we do not have access to the details of his calculation, it is difficult to give precise commentary on it. If one uses the Julian calendar (365.25 days in a year), one finds that the new moon is indeed on that day (this is the uncorrected date in our calculation). This means that he included three leap years too many (119 in total). He would have had 3 days too many in his calculation. According to him, the royal command was given on the Friday – the day after the new moon – 1 Nisan according to him). This is 2 days before the date that we used. The third surplus day originated from him taking the first and last days inclusive. Anderson, however, removed three days from his total when he assumed 116 leap days. His calculations, therefore, add up.
In 1984 another calculation of this period was published in Boodskap van die Basuin (April 1984) in which Prof. J.M. Schepers did the calculation. He used the same dates for the time of Christ. He, however, assumed that the new moon was on 23 March 445 BC – based on a calculation by Prof. Gawie Cellié of a solar eclipse which took place on 1 July 446 BC. This date agrees with our date for the full moon (!) although Prof. Schepers assumed 119 leap years. According to this calculation, the period ends with the date of the crucifixion. In our view, this is not what the prophecy says. According to the prophecy, the period of 69 weeks of years ends when the Messiah reveals himself as Prince (King), and it is only thereafter that the Messiah would die. The new moon date of 23 March 445 BC are also 13 days off when the new moons are calculated back from 29 March 32 AD.
Conclusion
In this note, I performed the calculation of the first 69 weeks of years in Daniel's prophecy (Dan. 9). The period stretches from Sunday 13 March 445 BC when Artaxerxes gave the command that Jerusalem must be rebuilt until the Sunday before the crucifixion (6 April 32 AD) when Jesus entered Jerusalem on the donkey. The period is 173880 days long and is precisely 69 weeks of years – to the day.
Sources
Anderson, Robert. 1984. The Coming Prince. Michigan: Kregel.
Malan, J. S. 1984. Boodskap van die Basuin. April edition. Alberton: Basuin Uitgewers.
Roode, J. D. 1977. Metoniese siklusse, epakta's en paasfees, of hoe Christopher C nie Amerika nie, maar 'n algoritme vir Paassondag ontdek het. Epsilon 7(1).
[1] For a detailed discussion of the various interpretations of this prophecy, click on The final seven years: the different views
[2] This essay was originally published in Afrikaans as note 6 in Dr Willie Mc Loud's book Op pad na Armageddon (1995).
[3] Those of the Biblical Criticism school that regard the prophecy as "history", i.e. as written after the events, have serious problems in explaining the period of 483 (or 490) years (see [1] for a detailed discussion).
Author: Dr Willie Mc Loud (Ref. wmcloud.blogspot.com)
The author is a scientist-philosopher (PhD in Physics; MA in philosophy). He writes on issues of religion, philosophy, science and eschatology.
