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Previously it was shown analytically that it is possible for a planet around a binary star to have stable or metastable conic-helical orbits, whose axis of symmetry coincides with the interstellar axis. That study was performed in frames of the nonrelativistic classical mechanics. In the present paper, first, we extend that study to star-planet-moon systemsalso in frames of the nonrelativistic classical mechanics. We complement analytical results by simulations showing that the moon can have practically stable conic-helical orbits around the planet, the average plane of the orbits being perpendicular to the axis connecting the planet and the star. Second, we extend that study to the relativistic classical mechanics. We show that relativistic effects can become significant in conic-helical orbits of a planet around a binary star for the situations where the mass of the planet is relatively small (such planets are so-called planetoids). Again, we complement analytical results by simulations showing that the planet can have relatively stable conic-helical orbits around the lighter star, the average plane of the orbits being perpendicular to the interstellar axis.

Conic-Helical Motion in the Three-Body Problem: Star-Planet-Moon Systems and Relativistic Effects in Binary-Star-Planet Systems