As with all of science, in the context of eclipse prediction and astronomical modeling, terms like "correct", "accurate" or "true" can easily mislead — especially when removed from whichever associated framework of assumptions has been used. It is a critical principle of science that:
No result is absolutely, or even inherently, "correct". Every result is only conditionally and temporarily valid within a specified model, a given set of assumptions, and the bounds of observational and testable resolution.
This is not a weakness of the process; it is the core strength of scientific thinking. Unlike dogma, which clings to the false comfort of zero-tolerance acceptance and divine immutability, science simultaneously expands and constrains its ignorance by continually testing, questioning, refining and improving upon prior models. Every eclipse prediction, every lunar and solar radius, every contact timing or path limit prediction exists only within a structured geometric model — and that geometry is always conditional.
For instance, we use a slightly different value for the Moon's radius than did the master Fred Espenak. This in absolutely no way means that we believe Fred’s use of two different lunar radii for his canons (one of which being the IAU value of 1738.091 km) was in any sense “wrong”. His model was correct within his defined framework, which deliberately optimized for consistency across a canonical eclipse series, and which was carefully and painstakingly chosen by him to achieve the maximum accuracy in his work with respect to its stated goal. By contrast, a modern topographic model derived from LOLA or GDR/SLDEM data must assume 1737.4 km as its datum — not because it is “more true,” but because it is internally consistent with the shape model used by NASA to describe the lunar limb.
How do we know what Fred was thinking? Well, he published very detailed narratives about his philosophy, and so we have that to go by. But even more, the author had the rare opportunity to discuss Fred's philosophy with him on several occasions. I believe very strongly that he knew EXACTLY what he was doing!
Science does not claim certainty. It claims internal consistency, falsifiability, and reproducibility — framed by assumptions we are obliged to share, and within whose bounds we remain constrained.
The present work adheres to this philosophy. Every number used here — from the lunar radius to the Sun’s distance — is derived not from tradition, but from the logical structure of the model being applied. Where historical values differ, those differences are honored, explained, and updated only when doing so increases the fidelity of the prediction.
This model prioritizes internal consistency over inherited norms. When modern data sources, such as LRO-derived topography, define the limb with respect to a specific radius, we must adhere to that datum in all subsequent calculations. Failure to do so introduces systemic error that compounds across projection geometry, Besselian element construction, and ultimately the eclipse path and local circumstance predictions.
Thus, the solar radius is also treated as a variable. While tradition and practicality have preserved Auwers' value in many canonical predictions, recent measurements suggest a more refined angular semi-diameter. This model allows for eclipse-specific values, allowing radius adjustments on a per-ephemeris basis, rather than defaulting to tabular norms. This gives us the flexibility to adapt to updated science, as the experimental results allow.
This is not a rejection of classical methods — far from it. It is an extension of their philosophy, honoring the exactitude and transparency that early pioneers like Meeus, Espenak, Duncombe, Herald and Watts embraced. The goal is not to replace, but to clarify: to show that each assumption matters, and that each adjustment or refinement is a step toward better alignment between predictive geometry and observable reality.
This study uses the INPOP19a ephemeris, developed by the SYRTE-IMCCE division of the Observatoire de Paris-PSL. INPOP (Intégrateur Numérique Planétaire de l’Observatoire de Paris) provides high-precision planetary and lunar positions and velocities in Terrestrial Time (TT), aligned to the ICRF celestial reference frame.
All ephemeris vectors are drawn from INPOP19a, which — as with the JPL DE series — internally accounts for light-time and relativistic corrections.
All celestial positions are computed in Terrestrial Time (TT). The difference TT - UT1 = \(\Delta T\) is never applied during Besselian element derivation to preserve modularity. It is introduced only during Bessel’s projection step, where it accounts for Earth's rotation and local hour angle. This separation allows reusability of the ephemeris-derived shadow geometry across varying \(\Delta T\) assumptions.
Although this model reproduces Besselian elements generally matching those from the JPL DE series to at least the 8th decimal place, only the first six to seven digits are retained in practice. Given that the Moon moves just slightly more than 1 m/ms in its orbit, any timing precision beyond this scale implies sub-meter or sub-millisecond certainty in lunar position — a threshold not practically achievable or observationally meaningful given the current limitations of current topographic/atmospheric models or \(\Delta T\) estimates.