Moon around Sun: Parametric Curves and Tangent Animation

This GeoGebra example demonstrates a dynamic simulation of a moon (small circle) orbiting around the sun (large circle), while simultaneously displaying tangent lines, quadrilaterals, and related function graphs along the motion. The core mathematical concepts include parametric curves, tangent lines, trigonometric functions, multiplication, and quadrilateral properties. The construction uses GeoGebra commands such as Circle, Sphere, Rotate, If, and CurveCartesian, with objects like r_1, S, r, c, t, re, E, a, t_1, vz, w0, SF0, u, j, w1, SF1, fr, b, M, and sliders to control rotation angles and speed, enabling real-time visualization of the moon's position and its trajectory tangents. Suitable for high school or university mathematics education, this example helps students understand parametric equations, trigonometric functions, and geometric transformations, and can also serve as a visual tool for astronomical orbital motion.