The classic diagram of Apollo 13's trajectory is a figure-8 (eg. Wikipedia's illustration). This is clearly drawn in a reference frame that's rotated to align with the Earth-Moon axis. What shape would the trajectory be when drawn in a non-rotating Earth-centered reference frame? My experience with Kerbal Space Program says it would be a near-ellipse, with the "crossover" in the rotating frame being the result of the Moon moving prograde faster than Apollo 13 at that point.
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Here is a great GIF showing what it looks like (I modified to speed it up), From this archived page:
You can see that the rotating reference frame view is the same as the inertial. I was trying to find to find enough info to plot it in GMAT to get more data and views, but as of the time of writing I cannot.
Mark Omo
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I didn't see this here when I'd posted my answer. Very nice! Also referenced in this answer – uhoh Mar 27 '18 at 02:08
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1@uhoh we probably made them at the same time – Mark Omo Mar 27 '18 at 02:09
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Link in this answer appears broken, at least for me.. – Innovine Apr 04 '18 at 18:32