Abstract
Formulas for the time of orbital flight in terms of the kinematic parameters are developed, and a kinematic theorem of orbital isochronism is introduced. Through this new theorem, the connection between the celebrated Lambart's theorem and the rather obscure theorem of Hamilton's hodographic isochronism is demonstrated, and the significance and implications of the latter are explored. In the light of Hamilton's hodographic representation, the characteristic features of an isochronal and isoenergetic family of Keplerian trajectories are observed, and a simple geometric method for the construction of such a family is proposed. Finally, Hamilton's time integral is briefly treated, resulting in another set of useful formulas for the time of flight.
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Sun, F.T. On the orbital isochronism. Celestial Mechanics 3, 272–288 (1971). https://doi.org/10.1007/BF01231801
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DOI: https://doi.org/10.1007/BF01231801