Three-Body Problem Simulation

This project is a real-time interactive simulation of the classical three-body problem in physics. It demonstrates chaotic orbital dynamics of three point masses under Newton’s law of gravitation.

Users can tweak initial conditions, pause/resume/reset the simulation.

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Demo

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Details

• Language: Go (Golang)

• Graphics Library: Ebiten v2

• Numerical Method: Explicit Euler integration (basic), extendable to Runge-Kutta or other ODE solvers

• User Controls:

  • Arrow keys: Adjust positions/velocities of bodies
  • P/O: Pause/Resume simulation
  • R: Reset simulation
  • Esc: Quit

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Physics

• Newton’s Law of Gravitation: $F = G \frac{m_1 m_2}{r^2} \hat{r}$

• Newton’s Second Law of Motion: $F = m a$ → $a = \frac{F}{m}$

• Each body experiences the gravitational pull of the other two, resulting in a system of coupled second-order differential equations.

• The three-body system is chaotic, meaning that small changes in initial conditions can lead to vastly different outcomes.

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Equations in action

• Equations of Motion:

  • Position update: $\mathbf{x}_{t+dt} = \mathbf{x}_t + \mathbf{v}_t , dt$
  • Velocity update: $\mathbf{v}_{t+dt} = \mathbf{v}_t + \mathbf{a}_t , dt$

• Numerical Integration:

  • Current version uses the Euler method (simple, but may accumulate error).
  • Can be upgraded to RK4 (Runge-Kutta 4th order) for better stability.

• Complexity:

  • For N bodies, the force computation is $O(N^2)$.
  • Here N = 3, so updates are efficient in real-time.

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How to Run

Prerequisites

• Go 1.20+
• Ebiten v2 (go get github.com/hajimehoshi/ebiten/v2)

Run Locally

git clone https://github.com/omgupta1608/three-body-simulation.git
cd three-body-simulation
go run main.go

Build

go build -o threebody main.go
./threebody