Scaled Sun-Earth-Moon Model with Shadow Cones

This applet demonstrates a geometric model of the Sun, Earth, and Moon scaled to their relative proportions, including the construction of their shadow cones. Using basic geometric objects such as points, circles, segments, rays, and polygons, it visually illustrates the spatial geometry behind solar and lunar eclipses. Ideal for exploring scale, solid geometry, and astronomical concepts. The applet presents an accurately proportioned three-body system in which the Sun, Earth, and Moon are rendered as spheres at their true size ratios, allowing students to grasp the vast differences in scale that characterize our solar neighborhood. Shadow cones—umbra and penumbra—are constructed by drawing tangent rays from the light source (the Sun) to each secondary body, making visible the conical regions of total and partial shadow that each planet casts into space. By manipulating the positions of the celestial bodies through interactive controls, learners can observe how eclipse events arise from the precise alignment of the Sun, Earth, and Moon along a common plane. When the Moon passes through Earth's shadow cone, a lunar eclipse is simulated; when the Moon's shadow cone falls upon Earth, a solar eclipse is demonstrated. The dynamic construction also reveals why eclipses do not occur every month: the tilt of the Moon's orbital plane relative to the ecliptic is represented, showing that most of the time the shadows miss their targets. This visual approach transforms abstract astronomical facts into tangible geometric relationships, reinforcing concepts in solid geometry such as cones of revolution, tangent lines to circles, and the intersection of lines with spherical bodies. The applet is particularly suited for secondary-level mathematics and science classes, providing a bridge between pure geometry and real-world applications. Teachers can guide students through explorations of scale modeling, proportional reasoning, and the geometric conditions required for shadow alignment. The interactive slider and draggable elements encourage hands-on experimentation, helping learners develop intuition about celestial mechanics and the nature of shadow formation. Whether used for individual exploration or classroom demonstration, this applet offers a rigorous yet accessible way to connect geometry with astronomy.