This project numerically solves the two-body problem using Euler's method and the second-order Runge-Kutta method (RK2, Midpoint method). The goal is to compare the accuracy and stability of these numerical integrators in simulating orbital motion.
- Implements the Euler method (first-order) and RK2 (Midpoint method) to solve the equations of motion for a two-body system.
- Outputs position and velocity data over time.
- Visualizes the orbital trajectories using Mathematica to compare accuracy.
✅ C++ Implementation – Efficient numerical integration of Newtonian gravity equations.
✅ CSV Output – Saves computed trajectories for easy visualization.
✅ Mathematica Plots – Compares the divergence of Euler vs. RK2 solutions.
- Euler's method exhibits significant numerical errors, causing artificial orbital drift.
- RK2 (Midpoint method) provides a more stable and accurate trajectory, better preserving orbital shape.
