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Is there any animation of real trajectory (and real velocity profile) of any of the flown Apollo moon missions?

Something similar to what is shown in the two following links, but using actual data from a flight. Lunar Free Return Trajectory Simulation

https://en.wikipedia.org/wiki/File:Animation_of_Lunar_Reconnaissance_Orbiter_trajectory_around_Earth.gif

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Yes! The good folks at AGI (Makers of STK) simulated the entire Apollo 11 trajectory in STK: "Based on original NASA documentation, our engineers have built a high-fidelity, eight-day digital mission in Systems Tool Kit (STK). They modeled precise trajectories using STK Astrogator"

The web site has tutorials on how to do some of the simulation using STK/Astrogator (paid software unless you are a student).

I've talked to one of the guys who did it, and they ran into some interesting challenges, like typos, in the original record. There would be entries in long tables that were nonsensical given the rest of the table, for instance.

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