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Lambert provides a solution as long as the transfer angle is not 0, 180 or 180-multiple degrees. Why is that?

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An integral multiple of 180° means that the initial point $r_1$, the central point, and the target point $r_2$ all lie on the same line. This in turn means the cross product between the displacement vector from the central point to the initial point and from the central point to the final point is zero. Note that except for these special cases, the cross product point between these two vectors indicates the orbital plane of the transfer orbit. But in the special case where the cross product is zero, the orbital plane of the transfer orbit is undefined.

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  • $\begingroup$ @OscarLanzi - I rolled back your edit as it does not make sense. You can try again if you do not think my answer makes sense, but please do not make an exact repeat of your previous edit. $\endgroup$ – David Hammen May 13 at 15:22
  • $\begingroup$ I wanted to communicate the geometric interpretation (the singularity comes because the points are collinear) rather than just rely on the vector product. Now, having seen my attempt rejected, I need to know how this can be done in a manner acceptable to you. $\endgroup$ – Oscar Lanzi May 13 at 15:38
  • $\begingroup$ @OscarLanzi I'm not even sure what it is you don't understand; your edit didn't make sense, and David already pointed out the geometrical interpretation -- the 3 points are all on the same line, and the orbital plane is thus undefined. $\endgroup$ – Yakk May 13 at 20:09
  • $\begingroup$ I was always told to repeat things so people are sure to understand. Hence my attempt at addition. I guess that was a wrong lesson <shrug>. $\endgroup$ – Oscar Lanzi May 13 at 20:27
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    $\begingroup$ Guys can you please recognize that I do not yet really know what was wrong? Offer some way that my original intent, emphasizing that the singularity comes from the points lying in a straight line, could have been better presented. Failing such constructive criticism please accept my admission that I failed and lay off. $\endgroup$ – Oscar Lanzi May 14 at 1:52

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