Quick guide to the UI:
You will find here different classes of examples of periodic 3 body orbits
Choose here the numerical integration method used to solve the there body problem (Recommended DOP853)
The differential equation is solved in a web-worker
Dormand-Prince method of order 8. This is the recommended method for most problems.
Very high-order explicit RK with embedded error. Heavy but superb when you need extreme accuracy/precision.
Uses multiple precision arithmetic. Solving an example might take minutes or hours.
Classic fixed-step 4th order. Simple to code and understand. It generally doesn't perform well in these examples
Symplectic 2nd order—great long-term energy behavior for Hamiltonian systems with a suitably small dt.
It is here just as an example
The three-body problem simulator helps users visualize and understand the complex gravitational interactions between three celestial bodies.
It features a collection of known periodic orbits, allowing users to explore and learn about these fascinating solutions to the three-body problem.
Users can select different example classes, control the simulation, and even create and save their own initial conditions.
The simulator is built using Rust, Wasm, JavaScript and HTML5, leveraging the power of modern web technologies to provide an interactive and educational experience.
All three bodies share the same orbit.
It is hypnotic to see them dance around the same path.
The by now well known "eight-figure" choreography is a remarkable example (discovered by Moore in 1993), and by Chenciner and Montgomery in 2000).
The examples here where discovered by Carles Simó (Paul Masson rescued the initial conditions in here)
Periodic orbits with equal masses. Initiated by Šuvakov and Dmitrašinović in their paper Three Classes of Newtonian Three-Body Planar Periodic Orbits, here we have the list from More than six hundreds new families of Newtonian periodic planar collisionless three-body orbits
See also their website
Periodic orbits with unequal masses. Many were found by Li and Liao in their paper The 1223 new periodic orbits of planar three-body problem with unequal mass and zero angular momentum
See also their GitHub repo
Some periodic orbits in 3D. These are not as well studied as the planar case
See for example the paper Discovery of 10,059 new three-dimensional periodic orbits of general three-body problem by Li and Liao
The 316 periodic orbits discovered by Xiaoming Li and Shijun Liao in their paper Collisionless periodic orbits in the free-fall three-body problem
These are 2D solutions with no initial speed. See also their GitHub repo
These solutions were found by I. Hristov, R. Hristova, T. Puzynina, Z. Sharipov and Z. Tukhliev in their paper Numerical search for three-body periodic free-fall orbits with central symmetry
I call it the Puzynin solutions, in honour of their teacher Igor Viktorovich Puzynin
These are 2D solutions with no initial speed. I have included here only the so called
See also their website https://db2.fmi.uni-sofia.bg/3bodyfree/
Some of this orbits require a multiple precision method for their solution
These solutions were found by I. Hristov, R. Hristova, T. Puzynina, Z. Sharipov and Z. Tukhliev in their paper Numerical search for three-body periodic free-fall orbits with central symmetry
I call it the Puzynin solutions, in honour of their teacher Igor Viktorovich Puzynin
These are 2D solutions with no initial speed. I have included here the first 600 solutions
See also their website https://db2.fmi.uni-sofia.bg/3bodyfree/
Some of this orbits require a multiple precision method for their solution
These are not periodic orbits, this are periodic in a rotating frame of reference
You can create those examples by clicking edit.