N-Body Particle Simulation

A real-time simulation of gravitational interactions between particles in 2D and 3D space, implemented in Python using Matplotlib.

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Features

• Simulates gravitational interactions in 2D and 3D
• Newtonian gravity with softening to prevent singularities
• Forward Euler integration for numerical updates
• Real-time animation with trajectory visualization
• Interactive controls for play, pause, and reset
• Demonstrates various three-body problem scenarios
• Built entirely with native Python libraries

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Requirements

• Python 3.6+
• matplotlib
• numpy

Install dependencies via pip:

pip install matplotlib numpy

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Usage

Run the main menu:

python Menu.py

Alternatively, you can run individual simulation scripts directly.

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Physics Implementation

Classical Newtonian gravity is used, with computations updated in real-time per frame:

Force Calculation

For each particle pair:

F = G * (m1 * m2) / (r² + ε²)

Where:

• G is the gravitational constant
• ε is the softening factor to avoid singularities

Velocity Update (Forward Euler)

v_new = v_old + a * Δt

Position Update

x_new = x_old + v * Δt

Visualization

Particle positions and trajectory trails are redrawn each frame to reflect current system state.

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Configuration Parameters

You can modify the following simulation settings in the source code:

Parameter	Description
t	Time step size
v	Initial velocity magnitude
L	Initial spacing between particles
soft	Gravity softening factor (reference)

These parameters allow you to model both periodic and chaotic solutions of the three-body problem.

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Customization

To modify the particle system, edit the create_particles() function:

• Adjust mass, position, and velocity per particle
• Change particle appearance (color, size)

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Additional Information

For an extended project overview and more physics-based simulations, visit:

jacobpoore.wescreates.wesleyan.edu/projects