A plan-view Sun–Earth–Moon model is paired with an enlarged Earth-facing lunar disk. The disk is shaded from the same lighting geometry as the orbit. New, quarter and full phases result from the viewing angle, not Earth’s shadow.
• A real-time 3D scene with 5 inspectable parts (Earth observer, Orbiting Moon, Sunlight direction, Earth-view lunar disk, Viewing direction), with home view, focus-selected-part, auto-rotate, expand, instrument-cover and hide-labels scene tools, plus a model response curve beneath the scene. • Experiment controls: Starting synodic age (0-29 days); Lunar days per animation second (0-2 days/s); Observer orientation (Northern view / Southern view); pause/resume, 0.1 s and 1 s single-step buttons, four playback speeds and a restart button. • Live readouts: Synodic age; Sun–Moon elongation; Visible illuminated fraction; Lunar phase angle; Time to next full phase; Completed cycles. • A Geometry & measurements tab with a parameter-comparison chart, a live-measurements chart, the model equations and snapshot readouts. • An Experiments tab with 3 guided presets (First quarter; Full Moon; Southern orientation) and a Model verification bench that runs independent fresh models, plus a timestamped event log and a copyable trial report. • A Learn & assess tab with guided lessons, a knowledge-check quiz with reset and a written model-scope statement linking to a technical reference.
θ=2π age/29.5306, measured from new Moon f=(1−cosθ)/2; phase angle=acos(−cosθ) Visible disk normal n=(x,y,sqrt(1−x²−y²)); brightness=max(0,n·s) s=(sinθ,0,−cosθ); southern view rotates the disk 180°
Circular coplanar synodic geometry; orbital distance, eccentricity, libration and eclipses are omitted. Apparent sizes and distances are enlarged independently. The hemisphere control is a simplified orientation change, not a full altitude/parallactic-angle sky model.
No. Earth’s shadow produces a lunar eclipse, a separate alignment event.
No. It rotates the view without changing Sun–Moon–Earth geometry.
Circular coplanar synodic geometry; orbital distance, eccentricity, libration and eclipses are omitted. Apparent sizes and distances are enlarged independently. The hemisphere control is a simplified orientation change, not a full altitude/parallactic-angle sky model.