Black Holes & Satellites: Elliptical Orbits and Geometric Construction

① This GeoGebra example dynamically simulates the gravitational interaction between a black hole (BlackHole) and a satellite (Satellite), visually demonstrating the elliptical orbit of the satellite around the black hole and the geometric distribution of related celestial bodies. ② Core mathematical concepts involve ellipses, circles/circumcircles, midpoints, perpendicular bisectors (LineBisector), symmetry, reflection, and translation transformations, along with the idea of centroid/barycenter and gravitational centers. ③ Construction highlights: Based on the construction summary, the example uses GeoGebra commands such as Midpoint, Segment, LineBisector, Point, Ellipse, Circle, and Line, creating objects like A, b, B, C, g, h, D, c, E, ExoPlanet, d, Satellite, e, a, i, BlackHole, f, and text1–text5 to label key elements, forming a complete figure with elliptical orbits, auxiliary circles, and symmetric structures. ④ It is suitable for upper secondary to early university students in mathematics or physics, helping them understand the geometric properties of conic sections (ellipses), applications of geometric transformations, and mathematical modeling of celestial motion. It can also serve as a classroom demonstration or a self-study exploration tool for teachers and learners.