🛰️ Circular Restricted Three Body Problem

EP 471 — Project Summary

This project explores how small disturbances in launch angle and velocity affect a single Moon flyby and return to Earth orbit.
The orbit is simulated numerically using a Backward Differentiation Formula (BDF) — chosen because other methods become unstable when trajectories pass near the Moon.

The system is modeled using the Circular Restricted Three Body Problem (CR3BP) approximation.

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Methodology

The numerical simulation:

• Integrates the motion of a spacecraft under Earth–Moon gravity.
• Perturbs both initial velocity and launch angle to observe sensitivity.
• Uses stable numerical integration suitable for close-approach dynamics.

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Code Access

You can view or download the full Python code here:

👉 CR3BP.py

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Input Parameters

Parameter	Description
total_sample	The total number of sample iterations.
v_mag_nominal	The nominal velocity magnitude at launch.
phi_nominal	The launch angle relative to Earth’s position from the Moon (counterclockwise orbit).
phi_range	The range of perturbation angle values the simulation will iterate over.
vel_range	The range of perturbation velocity values the simulation will iterate over.

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Output

The simulation outputs trajectory data and plots illustrating how small variations in the initial conditions affect the resulting orbit.

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Notes

This project demonstrates:

• The sensitivity of orbital trajectories to small perturbations.
• The usefulness of implicit integration methods for close approaches.
• The practical application of the CR3BP in trajectory planning.

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