13 research outputs found
Long-term perturbations due to a disturbing body in elliptic inclined orbit
In the current study, a double-averaged analytical model including the action
of the perturbing body's inclination is developed to study third-body
perturbations. The disturbing function is expanded in the form of Legendre
polynomials truncated up to the second-order term, and then is averaged over
the periods of the spacecraft and the perturbing body. The efficiency of the
double-averaged algorithm is verified with the full elliptic restricted
three-body model. Comparisons with the previous study for a lunar satellite
perturbed by Earth are presented to measure the effect of the perturbing body's
inclination, and illustrate that the lunar obliquity with the value 6.68\degree
is important for the mean motion of a lunar satellite. The application to the
Mars-Sun system is shown to prove the validity of the double-averaged model. It
can be seen that the algorithm is effective to predict the long-term behavior
of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged
model presented in this paper is also applicable to other celestial systems.Comment: 28 pages, 6 figure
Periodic orbits related to the equilibrium points in the potential of Irregular-shaped minor celestial bodies
Abstract
We presented an overview of detailed continuation results of periodic orbit families which emanate from the equilibrium points (EPs) of irregular-shaped minor celestial bodies (hereafter called minor bodies). The generation and annihilation of periodic orbits (POs) related to the EPs are discussed in detail. The branch points of families of POs are also investigated. We presented 3D bifurcation diagrams for periodic orbits families emanating from the EPs of minor bodies which have five EPs totally. Structures of the 3D bifurcation diagrams depend on the distribution of EPs with different topological classifications. We calculated orbit families emanating from the EPs of asteroids 433 Eros and 216 Kleopatra, including the Lyapunov orbit family, the Vertical orbit family, the orbit families bifurcating from the Vertical orbit family, as well as the nonplanar orbit family