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    $\begingroup$Does reversing the sign of your cross product help? That ought to make it left handed.$\endgroup$
    – user53400
    CommentedJul 27, 2024 at 16:33
  • $\begingroup$It does make a difference, we end up hitting a quadrant check for ascending node, but it returns 314 deg/5.497787 rad, and argument of perigee is 135 deg/ 2.3561950 rad now$\endgroup$CommentedJul 27, 2024 at 16:56
  • $\begingroup$Right, COE stands for Classical Orbital Elements, which are the parameters that define an elliptical orbit.$\endgroup$CommentedJul 27, 2024 at 22:45
  • $\begingroup$Thanks! I'm just curious, are COEs and Keplerian elements two names for the same thing or are there some differences? I'm just curious.$\endgroup$
    – uhoh
    CommentedJul 27, 2024 at 23:45
  • $\begingroup$I'm curious as to why you want to compute this in a non-right-hand coordinate system. Right-hand coordinate systems are extremely useful.$\endgroup$
    – ChrisR
    CommentedApr 24 at 20:26

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