Solar System Simulation

A simple n-body gravity simulation built with C++ and SFML 3. The Sun and planets attract each other using Newtonian gravity, and each body's orbit emerges from real physics rather than a scripted animation.

Features

• Real pairwise gravitational forces (F = G·m₁·m₂ / d²) applied to every body each frame
• Velocity/position integration via simple Euler stepping
• Starting velocities computed for roughly circular orbits (v = √(GM/r))
• The Moon orbits the Earth (inheriting Earth's velocity plus its own orbital velocity), while the planets orbit the Sun
• Rendered in real time with SFML's 2D graphics API

Requirements

• C++17 (or newer) compiler
• SFML 3.x (Graphics, Window, and System modules)
• CMake (recommended) or your preferred build setup

Building

Using g++ directly

g++ -std=c++17 solar_system.cpp -o solar_system \
    -lsfml-graphics -lsfml-window -lsfml-system

Using CMake

cmake_minimum_required(VERSION 3.16)
project(SolarSystem)

set(CMAKE_CXX_STANDARD 17)
find_package(SFML 3 COMPONENTS Graphics Window System REQUIRED)

add_executable(solar_system solar_system.cpp)
target_link_libraries(solar_system PRIVATE SFML::Graphics SFML::Window SFML::System)

mkdir build && cd build
cmake ..
cmake --build .

Running

./solar_system

A window opens showing the Sun and planets orbiting under gravity. Close the window to exit.

Project Structure

.
├── solar_system.cpp   # Main simulation source
└── README.md

Physics Notes

• G and DT (the gravitational constant and timestep) are tuned for visual clarity, not real-world units — the simulation is scaled to fit an 800×600 window.
• Because forces are computed pairwise, orbits are not perfectly stable circles; you'll see gradual perturbation from other bodies' gravity, which is expected n-body behavior.

Possible Improvements

• Spread initial planet angles around the Sun instead of stacking them vertically
• Add a fixed/variable timestep toggle for numerical stability at higher speeds
• Add trails to visualize orbital paths
• Add UI controls to adjust G, speed, or add/remove bodies at runtime