Sensitivity of a Ballistic Jupiter Gravity Assist to Initial Conditions and Integration Method

Gravity-assist trajectories are sensitive to flyby geometry and to the numerical methods used to simulate them, but the two effects are rarely separated. We use the Gravitational Slingshot Mechanics Laboratory (GSML), a deterministic N-body simulation code, to study a Voyager-inspired ballistic Jupiter flyby. Starting from a baseline case (420 km parking-orbit altitude, 280 km Jupiter periapsis altitude), we change one parameter at a time: periapsis altitude, parking-orbit altitude, arrival inclination, engine thrust, specific impulse, and the integration method. With an adaptive Runge–Kutta–Fehlberg (RK45) integrator, only periapsis altitude changed the heliocentric velocity gain: moving periapsis by ±5 km changed the gain by +0.04 and −0.05 km/s. The other four physical parameters produced no change at the reported precision, as expected for an unpowered flyby. Replacing RK45 with a first-order Euler integrator made the solution invalid. These results illustrate why physical sensitivity must be separated from numerical error when validating trajectory software. They come from a single case study and a local, one-factor-at-a-time design.