Require nodal alignment before an eclipse claim

1. Define the frame and evidence

New alignment places the Moon near the Sun’s direction, while full alignment places it near the opposite direction. Neither alone guarantees an eclipse because the lunar orbital plane is inclined to the ecliptic. Near the nodes, the two planes intersect and suitable alignment can allow disk or shadow overlap.

2. Connect the mechanism

The original orbit inclination is 5.1°. At orbital angleu from a node, latitude magnitude is asin(sin 5.1° sinu). Fixed source radii and distances give a lunar angular radius about 0.258965° and solar radius 0.266698°. At new alignment the geocentric disks overlap only if their center separation is below the sum of radii. The supplied Moon is slightly smaller than the Sun, so perfectly centered containment is annular, not total solar coverage.

At full alignment, an approximate straight-ray Earth umbra has radius RE−Dmoon(RSun−RE)/DSun at the Moon’s distance. Its angular radius is about 0.685324°. Compare the lunar disk with that shadow: overlap is possible below about 0.944288° center separation, while complete lunar containment requires a tighter alignment. Penumbral shading and atmospheric enlargement are not included.

This is a geocentric geometric discriminator, not a local eclipse forecast, observing path or safety assessment. Real topocentric parallax, distances and timing matter. The lesson is entirely screen based: never look directly at the Sun or aim optical instruments toward it for these exercises.

3. Reconstruct the worked case

At u 10°, latitude is about 0.884472°. The new-alignment disks do not overlap because this exceeds 0.525663°. At full alignment it is below the umbra-plus-Moon limit 0.944288°, so partial umbral overlap occurs; the Moon is not wholly contained.

4. Predict and investigate

Predict first: Why can the same nodal offset fail the solar disk-overlap test but satisfy a lunar umbra-overlap test?

Compare new/full at the sameu and retain the separate angular radii. Locate configurations with no overlap, partial overlap and containment. Explain why a geocentric result does not specify a safe local viewing location or an actual date.

5. Test a changed case

Apply the evidence to a changed case

At u 0°, compare the two conjunction types. At u 15°, does either supplied disk test overlap?

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

At the node, the centered smaller Moon lies inside the larger solar disk (annular geometry), while at full alignment the entire Moon lies inside the umbra. At u 15°, latitude about 1.318351° exceeds both overlap limits, so neither test overlaps. These are conditional geometric states, not event forecasts.

6. Retain an observation or image-comparison plan

Preserve the source, units, coordinate epoch/frame, orientation, first prediction and limitations. The screen-based source-image pathway is complete without outdoor viewing. No direct Sun viewing or instrument aiming is requested. Original teaching models are not operational pointing, eclipse or weather predictions; public practice is not independent observing competence.

Primary mechanism or source reference, checked 30 October 2026. Explanations, numerical examples, questions and geometric SVG are original. OpenStax is linked for factual scope, not copied artwork or text. Source NASA media retain their own credits and reuse terms; NASA has not reviewed or endorsed the AI-assisted course.