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I'm making a videogame/simulator that works with the orbital parameters of this document, but it doesn't have data about moons, dwarf planets, asteroids, comets, or even artificial satellites like the ISS, which I'd like to put to in the simulation. Does anyone know where to find them?

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The JPL Solar System Dynamics site (where the document you mentioned is hosted) has several other resources for finding orbital elements of moons, asteroids, and comets. These are mainly for natural bodies, but they also recommend using the CelesTrak database for artificial spacecraft. The only information they may not have is the time derivatives (at least I didn't see them when taking quick glance through the output).

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