Description :

This is a page for experimenting with a virtual stellar system by manipulating its celestial bodies.
    A star like the Sun, a planet like the Earth, and a satellite like the Moon all move while exerting gravitational forces on one another. Here, using a simulation that computes the equations of motion for an imaginary stellar system and visualizes them with computer graphics, let’s explore various possible motions of celestial bodies.
    In this simulation, the mass of the planet is set to 1, the mass of the satellite to 0.1, and the mass of the star to 10. In reality, a star has an enormously larger mass and therefore appears almost stationary, but with a mass of around 10, it will be noticeably pulled and moved by the planet and other bodies. Also note that, for simplicity, the motion of the three bodies is restricted to a plane.
    At first, the satellite orbits the planet, but even a small change in the satellite’s velocity will disrupt this relationship, and the satellite may become a planet orbiting the star instead. Try experimenting to see whether you can make it a satellite again, and explore various possibilities. However, make sure the celestial bodies do not collide—such an event would be disastrous for any life on that world. If a collision does occur, the system will return to its initial state.
    It is known that problems involving three bodies cannot be solved analytically, and their solutions cannot be expressed in closed form. However, as we are doing here, numerical simulations allow us to obtain results case by case. Please enjoy exploring the various scenarios.

●With the "*Start/Stop" button, you can start or stop the flow of time. The light blue object represents the planet, the gray one the satellite, and the yellow one the star.
You can change the speed of the simulation time with the “Fast/Slow” button.
●You can view the shape of the orbit with the “Trail” button.
●You can return to the initial state with the “Reset” button.
●By selecting a celestial body using the control checkboxes and dragging near its velocity vector, you can adjust its speed and try new orbits. If the bodies collide, the system will return to the initial state.
●The “COM Frame” button shifts the view to the center of mass, allowing you to fix the system in the center-of-mass frame.
●You can change the scale using the slider at the bottom right of the screen. The initial distance between the star and the planet is set to 1.

Copyright 2025 KATO, Noriyoshi