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I have a question about Laplace angle-only method for orbit determination where the line of sight vectors are being interpolated. I read somewhere that the method fails (due to a matrix being singular) when the observation site is in the motion plane of the observed body, but failed to see proof for that. Could anyone explain to me why is that?

The Laplace method could be found here. In pages 8-12 it explains the method, and in page 12 it references to Escobal's book that should explain that, however I do not have access to that book.

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  • $\begingroup$ Well I found Escobal's book but it did not really clarify the matter. Instead, I realized that maybe they are assuming that t1,t2,t3 are close enough so R1,R2,R3, are approximately collinear and then the required result can be achieved. $\endgroup$ – Charles zi Britannia Jul 6 '14 at 14:41

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