Hybrid Eclipses and Lunar Anomaly
A research overview of hybrid solar eclipses, lunar anomaly, and the anomalistic gate.
Introduction
Hybrid solar eclipses occupy the narrow transition between total and annular eclipse geometry. Because they occur near this boundary, they are unusually sensitive to small changes in lunar distance, observer position, and the profile of the lunar limb.
An examination of hybrid eclipses revealed a pattern: their associated lunar librations in longitude appeared far less dispersed than those of the general eclipse population. This observation suggested that hybrid eclipses might not be randomly distributed throughout the parameter space governing eclipse geometry.
Since the apparent size of the Moon is determined primarily by its distance from Earth, attention naturally turns to the Moon's anomalistic cycle—the progression from perigee to apogee and back again. The question investigated here is whether hybrid and near-hybrid eclipses exhibit preferred locations within that cycle, and whether those locations can be described by a simple geometric criterion.
The result is the anomalistic gate: a geometric framework that organizes hybrid and “hybrid-like” eclipses according to their proximity to the total-annular geometric boundary.
Background Concepts
Lunar Distance
The Moon does not orbit Earth in a perfect circle. Its distance varies continuously throughout the month, bringing it alternately closer to and farther from Earth. The closest point in the orbit is called perigee, while the farthest point is called apogee.
Because the apparent size of the Moon depends on its distance, lunar distance strongly influences eclipse type. A closer Moon appears larger and is more likely to produce a total eclipse. A more distant Moon appears smaller and is more likely to produce an annular eclipse.
Astronomers describe the Moon's position within this cycle using a quantity called anomaly. Anomalistic phase measures where the Moon lies within its progression from perigee to apogee, with 0° at perigee, 180° at apogee, and 360° completing the cycle back to perigee.
Lunar Libration
The Moon keeps nearly the same hemisphere facing Earth, but not perfectly. Because of the shape of its orbit and the orientation of its rotational axis, the Moon appears to rock slightly from side to side and up and down over time. This motion is known as libration.
Libration changes the portion of the lunar surface presented toward Earth and therefore alters the profile of the lunar limb. Since eclipse geometry depends on the exact profile of the Moon's silhouette, libration can become important when an eclipse lies near the boundary between total and annular conditions.
A Geometric View of Hybrid Eclipses
The darkest portion of the Moon's shadow forms a cone that extends toward Earth. If the tip of the umbral cone reaches Earth's surface, the eclipse is total. If it falls short of Earth's surface, the eclipse is annular. The tip of the umbral cone is known as the apex.
To describe this geometry, eclipse calculations traditionally employ the Fundamental Plane, introduced by the German mathematician and astronomer Friedrich Wilhelm Bessel. The Fundamental Plane passes through Earth's center and is perpendicular to the Sun-Moon line. It serves as the principal reference surface in classical eclipse calculations.
The Fundamental Plane (FP) should not be confused with Earth's physical surface. The plane passes through Earth's center, whereas observers reside on the curved surface of the planet, which may lie either closer to or farther from the Moon than the plane itself. This means that an eclipse can be annular on the Fundamental Plane while remaining total for observers on Earth's surface.
The position of the apex relative to the FP provides a useful measure of eclipse geometry. When the apex extends well beyond the plane, total eclipse conditions are generally favored. When it falls well short of the plane, annular conditions are generally favored. The most interesting cases occur when the apex lies near the plane. In this case, Earth's curvature becomes important: observers near the center of an eclipse track may lie slightly closer to the Moon than observers near the beginning or end of the track. As a result, the same eclipse can exhibit both total and annular characteristics. Hybrid eclipses occupy this transition region.
The Anomalistic Gate
The anomalistic gate provides a quantitative measure of where an eclipse lies relative to the total-annular boundary.
The gate is based on the position of the apex relative to the Earth-centered reference plane. A signed quantity is defined that measures whether the eclipse geometry lies on the total side of the boundary or the annular side. When the gate value is positive, the apex lies above the FP, and the eclipse geometry is annular-type. When the gate value is negative, the geometry is total-type. Values near zero identify eclipses that lie close to the transition between the two, regardless of whether they are called “total” or “annular” for Earth-based observers.
The gate places total, hybrid, and annular eclipses along a continuous geometric scale, and allows eclipses near the hybrid boundary to be studied together.
Survey of Solar Eclipses
To investigate the relationship between eclipse geometry and lunar anomaly, a survey was conducted using solar eclipses spanning the years 1600 through 2600.
For each eclipse, the anomalistic gate parameter was computed and compared with the Moon's anomalistic phase. Lunar and solar ephemerides were obtained from the NASA/JPL SPICE system, while lunar dimensions were based on the mean radius adopted by NASA's Lunar Reconnaissance Orbiter (LRO) mission. Two commonly used solar-radius models were examined in order to test the stability of the results.
Particular attention was given to eclipses lying near the gate. This includes not only formally classified hybrid eclipses but also total eclipses whose geometry lies close to the hybrid boundary.
Principal Findings
Libration Preference
An initial examination of hybrid eclipses revealed unusually concentrated values for libration in longitude. Because this libration is closely tied to the Moon's orbital position and varying distance from Earth, this observation motivated a broader investigation of anomalistic phase and eclipse geometry.
Anomalistic Clustering
If hybrid and near-hybrid eclipses were distributed randomly throughout the anomalistic cycle, their anomalistic phases would be expected to appear approximately uniform. Instead, strong concentrations emerge. Near-gate eclipses cluster around specific regions of anomalistic phase rather than being spread evenly throughout the cycle.
The strongest concentrations occur near approximately 52° and 308°, indicating that the geometry associated with hybrid and near-hybrid eclipses preferentially occurs at particular locations within the anomalistic cycle.
Hybrid Subclasses
Most hybrid eclipses belong to the familiar ATA class, in which the eclipse begins annular, becomes total near the middle of the track, and returns to annular conditions before ending. Much rarer are the single-transition hybrids, in which the eclipse crosses the total-annular boundary only once. The crossing may be from total to annular (TA) or vice versa (AT).
These very rare events are of particular interest because they represent geometries lying so close to the boundary itself that the gate is actually crossed during the eclipse.
When the hybrid subclasses are plotted against anomalistic phase, a striking separation emerges. The single-transition events occupy opposite sides of the anomalistic cycle, with one population (AT) occurring before perigee and the other (TA) after perigee. Rather than being randomly distributed, the rarest hybrid eclipses appear to respond systematically to the same geometric structure identified by the anomalistic gate.
This separation is particularly intriguing because a hybrid eclipse is, in effect, an observable crossing of the same geometric boundary represented by the anomalistic gate. The eclipse track itself passes through the transition region between annular and total conditions. The fact that the hybrid subclasses separate according to anomalistic phase suggests that the gate is responding to an underlying aspect of the Earth-Moon-Sun geometry.
Saros 145
Saros 145 provides a useful case study because it follows a single eclipse family as it passes through the transition region between annular and total eclipse geometry. Successive members of the series show a clear progression from annular eclipses, through hybrid eclipses, and onward into total eclipses.
The gate parameter tracks this evolution directly. As the series develops, the apex moves steadily from the annular to the total side of the FP, passing through the narrow interval in which hybrid eclipses occur. The transition is not abrupt. Multiple eclipses occupy intermediate positions near the boundary, illustrating the continuous nature of the underlying geometry.
This behavior helps explain that hybrid eclipses occur when an eclipse family passes through the geometric gate. Saros 145 captures this process in a particularly clear form, providing a direct example of the transition that the anomalistic gate is intended to measure.
What the Gate Shows
The anomalistic gate demonstrates that hybrid and near-hybrid eclipses are not distributed randomly throughout the lunar anomalistic cycle.
Instead, eclipses occupying the transition region between total and annular geometry respond to a well-defined geometric boundary. The strongest concentrations occur at preferred anomalistic phases, indicating that lunar distance plays a measurable role in determining when these boundary conditions arise.
An important aspect of this result is that the study extends beyond formally classified hybrid eclipses. Total eclipses that lie close to the hybrid boundary are part of the same geometric continuum and respond to the same gate structure. Restricting the analysis to catalog-designated hybrid eclipses would obscure much of the underlying pattern.
Viewed in this way, hybrid eclipses are not isolated curiosities. They represent one portion of a broader transition region governed by the geometry of the Earth-Moon-Sun system. The anomalistic gate provides a framework for identifying and studying that region.
Full Paper
The complete paper presents the mathematical derivation of the anomalistic gate, validation tests, eclipse surveys, figures, and supporting analysis.
Citation
Dan McGlaun. Hybrid Eclipses and Lunar Anomaly: The Anomalistic Gate. Zenodo, 2026. DOI: 10.5281/zenodo.20695449.