Continuation of some nearly circular symmetric periodic orbits in the elliptic restricted three-body problem

Some comet-and Hill-type families of nearly circular symmetric periodic orbits of the elliptic restricted three-body problem in the inertial frame are numerically explored by Broyden's method with a line search. Some basic knowledge is introduced for self-consistency. Set j/k as the period ratio between the inner and the outer orbits. The values of j/k are mainly 1/j with 2 < j < 10 and j = 15, 20, 98, 100, 102. Many sets of the initial values of these periodic orbits are given when the orbital eccentricity ep of the primaries equals 0.05. When the mass ratio mu = 0.5, both spatial and planar doubly-symmetric periodic orbits are numerically investigated. The spacial orbits are almost perpendicular to the orbital plane of the primaries. Generally, these orbits are linearly stable when the j/k is small enough, and there exist linearly stable orbits when j/k is not small. If mu &NOTEQUexpressionL; 0.5, there is only one symmetry for the high-inclination periodic orbits, and the accuracy of the periodic orbits is determined after one period. Some diagrams between the stability index and e(p) or mu are supplied. For mu = 0.5, we set j/k = 1/2, 1/4, 1/6, 1/8 and ep is an element of [0, 0.95]. For e(p) = 0.05 and 0.0489, we fix j/k = 1/8 and set mu is an element of [0, 0.5]. Some Hill-type high-inclination periodic orbits are numerically studied. When the mass of the central primary is very small, the elliptic Hill lunar model is suggested, and some numerical examples are given.