(Make sure to read all posts on Birkat HaChamah here)
Birkat HaChamah occurs once every 28 years as discussed before. Let me review some of the math.
For these calculations we are assuming a year length of 365.25 days derived from Tekufat Shmuel (That each year is made of 4 equal seasons of 91 days and 7.5 hours. Not scientifically accurate, but remember that physical reality is not the entirety of the existence).
If event X occurs Tuesday night at 6pm (or any time for that matter), the following year, it will occur 30 hours later in the week (7 days * 52 weeks = 364, leaving 1.25 days remainder per year). After 28 years, it will cycle through week to make it back to the starting point. For further illustration, you can create an Excel spreadsheet to show the cycle, Column A being the year #, Column B being the hour of the week (7*24=168 hours per week).
Leave that on the side. We've established a 28 year cycle for the Jewish calendar due to the year length being 365.25 days, aside from the 19 year cycle linking the solar and the lunar years.
However, that is not the way the Gemara and Pirkei D'Rebbi Eliezer present the creation of the Sun. It is not just that it is the beginning of the Fourth Night, but also at the hour of Shabbtai.
Chazal bring down a cycle of 7 different bodies in our solar system, and tell us that they cycle through in a 7-hour cycle, each one having its own hour of influence. Interestingly enough is that this necessitates another independent cycle within the 28 year cycle. It does not matter what the yearly remainder is in hours (i.e. 365.25 days per year gives us 30 hour remainder, but it doesn't matter if this is 31 hours or 29 hours), the result is a 7-year cycle.
For example: In year 1, Tekufat Nissan fell in Shabbtai. That means that it also fell in Shabbtai in year 8. Shmitah years are (in our time) always in a year that Tekufat Nissan falls in Kokhav.
The difference between the two cycles:
In the 7-year cycle, we mark the 7th year (the end of the cycle), just like the 7th day.
In the 28-year cycle, we mark the 1st year (the beginning of a new cycle).
That is why this year is Shmitah and next year is Birkat HaChamah.
They seem so related, 4 cycles of 7 takes us to the beginning of the next 28 year cycle, yet they are mathematically independent, one based on the year-length, the other based on the hourly-cycle.
Neither is based on anything which is astronomically observable (the actual physical solar year is not 365.25 days long, and there is no observable 7 hour cycle among the planets), yet both are based on objects in our solar system.
The significance of these cycles is great, each cycle's significance is a secret of Torah which I am not here today to reveal. Also note that everything mentioned here is based on the year length and the cycle being based on an integer number of hours. This becomes more glaring in another cycle in Pirkei D'Rebbi Eliezer.
For further reading:
- Bavli Brachot 59b
- Bavli Eiruvin 56a
- Pirkei D'Rebbi Eliezer chapter 6-8