Quasi-bielliptic three-body problem

In this paper, we first proposed the Quasi-Bielliptic Problem (QBEP) in the Sun-Earth-Moon three-body problem. In this model, we assume that the Moon revolves around the Earth in a quasi-elliptic orbit perturbed by the solar gravity, whereas the orbit of the Earth-Moon barycenter around the Sun has been known to be strictly elliptic. In addition, we assumed that these three celestial bodies move in the same orbital plane. The differential equations for the first-order analytical expansion of the lunar quasi-elliptic orbit were derived. Using a computational approach, these differential equations were transformed into a system of linear equations and then solved numerically. The validity of our semianalytical result was testified by comparing with the results of numerical integration. The differences between analytical results of the QBEP and the QBEP have been discussed in detail. The influences of these two eccentricities on analytical results were also investigated.