What is a Saros cycle ?
Exactly 223 synodic months after an eclipse, a near similar eclipse will occur at the same place in the zodiac, a fact that has been known for more than two millennia. These two nearly identical eclipses occurring 18 years apart are said to belong to the same saros cycle (a saros being the time interval between two nearly identical eclipses). If you consider the chain of eclipses separated by 223 synodic months (a saros), they are said to belong to the same saros cycle (a Saros cycle can be about solar or lunar eclipses).
Every lunar and solar eclipses belong to a Saros cycle that spans throughout more than a millennium. At the very beginning of a Saros cycle, the sun, moon and earth are poorly aligned, resulting in partial eclipses. As time progresses, the Saros eclipses become more spectacular as the sun, moon, earth alignment improves and eclipses become total. Intensity reaches its climax when the three bodies are perfectly aligned. This is what I define as the culmination of the Saros cycle. Then, the perfect alignment relative to one Saros cycle gradually vanishes, its eclipses become partial again, then cease. This process, the rise, culmination and retraction of a Saros cycle spans over a millennium of years, and generally comprises 71-73 eclipses (figure 1).
Figure 1. Saros 133 and the evolution of sun-earth-moon alignment (gamma) over time. Each point represents an eclipse. A value of gamma equals to zero means perfect alignment. This saros cycle spanned over 450’000 days (more than 1’200 years).
Bernadette Brady’s approach
Bernadette Brady, in her seminal work, recognised the potency and the magic of Saros cycles, and invited astrologers to interpret eclipses in the light of their corresponding Saros cycle. But how do you derive a chart for a Saros cycle ? She answered this question by looking at the signature chart of the very first eclipse of a Saros cycle, which can be seen as corresponding to the birth of the Saros cycle (figure 2).
Figure 2. Bernadette Brady’s approach is to take the first eclipse of a saros cycle (green circle), and compute the corresponding chart, said to represent the birth of the saros cycle.
The heart of Saros cycles
Figure 3. My approach is to estimate the point in time where the gamma value of a saros cycle equates zero (i.e. perfect sun-moon-earth alignment), thus denoting its culmination. The corresponding time estimate is highlighted in the green box (7 Feb 1856, Gregorian calendar, 9:43:43 UTC). The line in red is the gamma as a function of time function inferred by regression.