ODYSSEY VSEPR Theory vs Simple Orbit Simulator

Why are some triatomic molecules linear (carbon dioxide, hydrogen cyanide) and others are bent (water, sulfur dioxide)? And why is the bond angle in water (~105°) smaller than that in sulfur dioxide (~119°)? Valence Shell Electron Pair Repulsion (VSEPR) theory provides surprisingly simple explanations in terms of the electron pairs that surround the central atom of a given molecule. VSEPR theory is described in detail in every introductory chemistry book. The ODYSSEY VSEPR Theory app provides three-dimensional models of 50 small molecules and ions as well as a set of generic models that illustrate the conceivable geometries of the theory. Each model can be moved and manipulated with simple touch gestures. Bond lengths and bond angles can be queried. Users can pick from multiple model styles (such as Ball and Spoke or Space Filling), request a schematic display of lone pair positions, and show the molecular dipole arrow. A glossary, comments section, and a set of multiple-choice questions (with randomized options) are also available. Most learners of chemistry are visually oriented. Complementing the presentation found in any introductory textbook, ODYSSEY VSEPR Theory enables exploration of one of the most fundamental concepts in general chemistry—molecular shape.

Simple Orbit Simulator brings the elegance of Einstein's general relativity to your fingertips. Watch two celestial bodies dance under the influence of gravity — not as a textbook approximation, but as a true Schwarzschild geodesic simulation — the same physics that governs real planets, stars, and black holes. Real Physics, Visually Beautiful Unlike typical orbit simulators that use Newtonian gravity, Simple Orbit Simulator traces actual curved-spacetime paths. Every orbit is a genuine geodesic of the Schwarzschild metric. The result: Mercury-style perihelion precession that slowly paints a rosette pattern on screen, gravitational time dilation that deepens as the planet plunges toward the star, and event horizon dynamics that are physically meaningful — not just decorative. Black Hole Mode Switch to Black Hole Mode and watch a supermassive compact object warp the simulation. The event horizon, photon sphere, and innermost stable circular orbit (ISCO) become visible boundaries. Push the planet too close and it crosses the point of no return. Accretion disk glow and a dynamically warped spacetime grid make the physics viscerally tangible. Full 3D Orbits Tilt the orbital plane with the inclination slider and drag the canvas to rotate the camera freely. Horizontal drag changes the azimuth — spinning the scene left and right. Vertical drag changes the elevation — from a top-down view to edge-on. A circular orbit becomes an ellipse, a line, or a spiral rosette depending on your viewpoint. Physics is computed in full three-dimensional space. Live Relativistic Metrics Track real-time data as the simulation runs: • Gravitational time dilation factor • Accumulated proper time of the orbiting body • Lorentz gamma factor • Orbital velocity as a fraction of the speed of light • Perihelion precession angle in degrees • Orbits completed Explore and Experiment Adjust star mass, planet mass, and orbital distance with intuitive logarithmic sliders. See how increasing the star's mass deepens the gravitational well. Increase separation and watch relativistic precession shrink as GR effects fade with distance. Combine an inclined orbit with Black Hole Mode for a dramatic 3D plunge trajectory. Built for Clarity Every design decision prioritises understanding over complexity. The simulation uses scaled constants so relativistic effects are visible at screen scale — preserving all qualitative behaviour predicted by general relativity in a form humans can actually see. Simple Orbit Simulator is for students, educators, curious minds, and anyone who has ever looked up at the night sky and wondered what holds it all together.