Abstract
The theory of complex variables is used to establish exact analytical solutions to a class of two-body problems. In view of Lambert's theorem, two points on the conic, the chord-distance between the two points, and the time interval are considered given, and subsequently the solutions for the semi-major axis required to define the orbit are developed and expressed ultimately in terms of elementary quadratures.
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References
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Burniston, E.E., Siewert, C.E. Exact analytical solutions basic to a class of two-body orbits. Celestial Mechanics 7, 225–235 (1973). https://doi.org/10.1007/BF01229949
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DOI: https://doi.org/10.1007/BF01229949