Geocentric–Lunar System Barycenter via Geometric Construction

This example demonstrates the barycenter (center of mass) of the Earth–Moon two-body system in a geometric, interactive way. By introducing adjustable parameters and constructing intersection-based points, the app visualizes how the system’s center of mass location is determined and how it changes under scaling or mass/geometry settings. Key math ideas include center of mass/barycenter via geometric division (mass-ratio weighting), coordinate/analytic-geometry interpretation of positions, constraint-based point determination through intersections, and quantitative statistical indicators (distances/parameters/derived values) to report the computed results. Construction is driven by GeoGebra commands Intersect, Point, and Circle, together with objects such as M, m, R, r, Rs, S, A, d, and Moon-related quantities (e.g., MMond, rs), plus parameters/angles (e.g., α) and on-screen Text and control elements (buttons/sliders) to support the interactive investigation. Suitable for advanced high school and early university learners in geometry construction, coordinate geometry, and mathematical modeling for physics/engineering contexts.