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I have a solar system where each body interacts with each other by force F = Gm1m2/R^2

Is it possible to predict future position of some random body after t seconds since bodies velocity and position measurement?

I guess, it is possible only with numerical methods, but how to to it fast without calculating system state for each future frame? I don't need a big precise, just a rough estimation to target into sphere of influence of planet.

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    \$\begingroup\$ Yes, this is definitely possible. But the exact math eludes me. Perhaps astronomy.stackexchange.com can provide a better answer to this question than we could. \$\endgroup\$ Commented Oct 7, 2021 at 13:55
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    \$\begingroup\$ The three (or more) body problem is notoriously chaotic, with only a few predictable solutions. If your your star dominates and you can neglect interactions between planets, then you can run them on Kepler orbit "rails". That's a good approximation for the motion of the planets in our solar system, for instance. We have past Q&A about how to do that. If you need 3+ bodies all interacting strongly then short timesteps are your best bet. Can you clarify which direction you want to go? \$\endgroup\$ Commented Oct 7, 2021 at 13:59
  • \$\begingroup\$ I can't use kepler's orbit. I want different types of systems: double stars, two-three bodies with same mass, etc \$\endgroup\$ Commented Oct 7, 2021 at 14:04
  • \$\begingroup\$ Comments are not for extended discussion; this conversation has been moved to chat. \$\endgroup\$ Commented Oct 7, 2021 at 15:59

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