PyGravitySimulator

This is an interactive 2D simulation of gravitational interaction between objects with adjustable parameters.

Project structure

PyGravitySimulator
├── .github/            # Workflows (CI)
├── tests/              # Tests (Unit, UI)   
├── resources/          # Resourses (Icons, Textures etc.)
├── gravity_simulator/  # Main py package
├── .flake8             # Settings for flake8
├── .pylintrc           # Settings for pylint
├── README.md           # This file
└── readme.ru.md        # Ru-version for this file

Installation and Launch

pip install pygame
git clone https://github.com/Ewerall/PyGravitySimulator.git
python -m gravity_simulator.main

Mathematics

1. Gravitational Interaction

The simulator uses Newton's classical law of universal gravitation with regularization to prevent numerical instability:

Basic formulas:

dx = p₂.x - p₁.x

dy = p₂.y - p₁.y

r² = dx² + dy²

r = √(r² + ε²)

Where:

• dx, dy - components of the distance between objects
• r - regularized distance
• ε - softening parameter, preventing infinite forces at small distances

Gravitational force:

F = G·(m₁·m₂)/(r² + ε²)^(3/2)·(dx, dy)

Or in component form:

Fₓ = G·m₁·m₂·dx/(r²·r)

Fᵧ = G·m₁·m₂·dy/(r²·r)

Where:

• G - gravitational constant
• m₁, m₂ - masses of objects
• Fₓ, Fᵧ - force components

2. Particle Motion

Particle motion is calculated using the Euler method:

Acceleration:

aₓ = Fₓ/m

aᵧ = Fᵧ/m

Velocity:

vₓ(t+dt) = vₓ(t) + aₓ·dt

vᵧ(t+dt) = vᵧ(t) + aᵧ·dt

Position:

x(t+dt) = x(t) + vₓ(t+dt)·dt

y(t+dt) = y(t) + vᵧ(t+dt)·dt

Where:

• dt - time step
• a - acceleration
• v - velocity
• x, y - coordinates

3. Collision Handling

Collision detection

dx = p₂.x - p₁.x

dy = p₂.y - p₁.y

r² = dx² + dy²

r = √r²

if r < (R₁ + R₂), a collision has occurred

Where:

• R₁, R₂ - radii of objects

4. Particle Merging

When particles collide, they merge while conserving momentum and recalculating the center of mass:

Total mass:

M = m₁ + m₂

Velocity after merging (momentum conservation):

vₓ = (m₁·v₁ₓ + m₂·v₂ₓ)/M

vᵧ = (m₁·v₁ᵧ + m₂·v₂ᵧ)/M

Position after merging (center of mass):

x = (m₁·x₁ + m₂·x₂)/M

y = (m₁·y₁ + m₂·y₂)/M

Radius of the resulting object (for 2D):

R = √M

This follows from the fact that in 2D, mass is proportional to the area of a circle: M ∝ πR² ⇒ R ∝ √M