Periodic librations about the triangular solutions of the restricted earth-moon problem and their orbital stabilities

Abstract

view Abstract Citations (8) References (3) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Periodic librations about the triangular solutions of the restricted earth-moon problem and their orbital stabilities Rabe, Euggene ; Schanzle, Allan Abstract The methods previously used in the search for periodic Trojan orbits (Rabe 1961, 1962) are applied here to the determination of periodic orbits in the plane restricted earth-moon problem. Fourteen periodic orbits have been established, on the IBM 650 electronic computer, to the same degree of numerical accuracy. The orbits of larger amplitudes are of rather unexpected geometric shapes, which are related to the emer- gence of four points of minimum orbital velocity, instead of the familiar two for all the long-period librations in the corresponding Trojan problem. Harmonic analysis is used to obtain the Fourier expansions repre- senting all these periodic solutions. All the orbits are found to be stable in the ordinary sense, while the additional "X- r stability" (Rabe 1962) of the satellite's perigee motion exists only for librations with ampli- tudes up to those associated approximately with the emergence of Jonr points of minimum velocity, or only for orbits of "simple" shape. Publication: The Astronomical Journal Pub Date: December 1962 DOI: 10.1086/108802 Bibcode: 1962AJ.....67..732R full text sources ADS |