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Gravity Assist Slingshot

Hyperbolic flyby with turning angle $\delta = 2 \arcsin\left(\frac{1}{1 + \frac{r_{\min} v_{\infty}^2}{GM}}\right)$. Solar-system $\Delta v$ emerges from vector addition with the planet velocity; presets reproduce Voyager 1 at Jupiter and Cassini at Venus to within 20%.

Figure 1. Gravity-assist slingshot: a spacecraft's path bent by a flyby of a moving planet, gaining or losing speed in the Sun frame while its speed relative to the planet is unchanged. Method: planar restricted three-body flyby with before/after velocity vectors.

WHAT TO TRY

  • Vary each control and watch the rail readouts respond.
  • Compare the diagnostic plot against the live scene.