Geometric Modeling of Circular Orbits with Animation

This example demonstrates, through an animation, how a point’s position evolves along a circular orbit and how the underlying geometric relationships remain consistent as parameters change. Key concepts include circle properties, metric relationships derived from similar triangles and the Pythagorean theorem, and a parameter-based construction that links orbit radius and position. Construction highlights: Sphere is used to set up a 3D reference scene (e.g., a “tierra” object), Circle constructs the orbit itself, and If supports conditional resets/logic during the animation. The mean command is used to compute intermediate/average quantities that feed into the geometry. Time-parameter objects such as t, dt, t0, t1, ω/ω1, vueltas, reg, regDif, T, and vel drive the moving point (M1) and the evolution of its trajectory; axes (eje1) and text/labels (texto5, tPausa) provide readable guidance and control. Suitable for secondary to early college geometry/coordinate-geometry lessons and for teaching how parameterized motion connects to classical geometric measures.