At the top of Talmud Bavli Masechet Brachot 59b, the Baraita states:
The Rabbis have taught:
One that sees:
- The sun in its tekufah (equinox)
- The moon in its gevurah (strength)
- The stars in their paths and
- The constellations in order
says Blessed is the One that Makes Creation.
(See the Yerushalmi for a slightly different version)
For Halachah, only the sun is discussed, and from this we arrive at Birkat HaChamah.
So what is this gevurah? If, from "the sun in its tekufah", we arrived at there being something special regarding a certain equinox in the sun's 28 year cycle, then the parallel here would be something special in a certain part of the moon's 19 year cycle.
In Kabbalah, summer and winter are both related to gevurah: the summer, in that restraints are removed and the heat comes to the world, and the winter, in that restraints are applied to the maximum, and the extreme cold comes to the world. The summer is the active strength.
Shemot 12:1 - This month is for you the head of months, it is first for the months of the year.
The focal point in the year for the moon is Nissan, and the focal point of Nissan is of course Pesach. Our task for finding the Moon's Strength is to find the Pesach that is closest to the summer.
With the Hebrew calendar in effect since approximately the year 4119, the year of the latest Pesach is the 8th year out of the 19th year cycle.
8 + 19n where 217 <= x <= 303
- 8 + (19 * 217) = 4131
- 8 + (19 * 303) = 5765
Recent years of note in this series are x = 300 and 301. This is the year 5708 and 5727, both where monumental events took place for Am Yisrael shortly after Pesach. The visibility of these events are dependent on other factors.
G-d willing, the next occurrence of this strength will be the decision of the Sanhedrin, as it is the Sanhedrin's task to set the pattern of the 19 year cycle. This is much needed, as our current calendar is for the whole Golah, and not for afterwards.