remarkablemayonaise t1_je2h616 wrote
Reply to comment by TheJeeronian in ELI5 How do scientists know probes (Like Voyager I) aren't going to get swept up in the orbit of another celestial body? by remorsefulDownfall
I'm not sure which of us is confused. Conic sections are solutions to two body problems or similar (the Earth is orbiting the centre of mass of the solar system, not the sun itself).
Three body problems rely on second by second force simulations. Instantaneous force simulations lead to accelerations which lead to changes in velocity and location, which feedback to the force simulations.
Euler's method and similar are ways to solve differential equations like above.
TheJeeronian t1_je2u1zk wrote
Conic sections are just an approximation. The fairly minimal tidal gradient makes stitched together conical sections a decent approximation - when you're near Earth you follow a conic around Earth and your path around the sun otherwise mimics that of Earth.
The Earth orbits the solar system's barycenter, which approximates fairly nicely to the sun but if we ignore the sun and patch our conics around the barycenter it works even better.
The method is aptly named "patched conics".
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