It's not really that simple. You need high fidelity symplectic integrators to get stable orbits if you are going to go the numerical route. Otherwise energy is not conserved and orbits will diverge and become horribly unstable. It's far simpler using patched conics because the orbits are known EXACTLY with mathematical functions. Once you're in a sphere of influence you use math to determine the exact shape (a conic section) of your orbit and boom; you're done. Your spacecraft is now on rails; t
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