(Physics, Celestial mechanics, Computational method)
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities of three point masses and solving for their subsequent motion.
Example gif from Wikipedia:
There is no general analytical solution to the three-body problem given by simple algebraic expressions and integrals. Moreover, the motion of three bodies is generally non-repeating, except in special cases.
The Sitnikov problem is a sub-case of the spatial elliptic restricted three-body problem that allows oscillatory type of motions:
a massless body moves (oscillates) along a straight line that is perpendicular to the orbital plane that is formed by two equally massed primary bodies moving on symmetric Keplerian orbits.
Example gif from Scholarpedia:
By using JavaFX to visualize Sitnikov Problem and allow interactions, that users are able to change different variables to observe the fate of the system, (for now) these include:
- Masses of the bodies (including the massless body)
- Eccentricity of the orbit
- Time step (used in Euler's method, the smaller the time step, the more accurate the result which also consumes more time to complete a cycle)
- Initial velocities of the bodies
- Initial position (z) of the massless body