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\documentclass[12pt]{minimal}
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\begin{document}$j/k$\end{document} as the period ratio between the inner and the outer orbits. The values of j/k\documentclass[12pt]{minimal}
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\begin{document}$j/k$\end{document} are mainly 1/j\documentclass[12pt]{minimal}
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\begin{document}$1/j$\end{document} with 2≤j≤10\documentclass[12pt]{minimal}
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\begin{document}$2\leq j\leq 10$\end{document} and j=15,20,98,100,102\documentclass[12pt]{minimal}
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\begin{document}$j=15,20,98,100,102$\end{document}. Many sets of the initial values of these periodic orbits are given when the orbital eccentricity ep\documentclass[12pt]{minimal}
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\begin{document}$e_{p}$\end{document} of the primaries equals 0.05. When the mass ratio μ=0.5\documentclass[12pt]{minimal}
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\begin{document}$\mu =0.5$\end{document}, 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\documentclass[12pt]{minimal}
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\begin{document}$j/k$\end{document} is small enough, and there exist linearly stable orbits when j/k\documentclass[12pt]{minimal}
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\begin{document}$j/k$\end{document} is not small. If μ≠0.5\documentclass[12pt]{minimal}
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\begin{document}$\mu \neq 0.5$\end{document}, 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 ep\documentclass[12pt]{minimal}
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\begin{document}$e_{p}$\end{document} or μ\documentclass[12pt]{minimal}
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\begin{document}$\mu $\end{document} are supplied. For μ=0.5\documentclass[12pt]{minimal}
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\begin{document}$\mu =0.5$\end{document}, we set j/k=1/2,1/4,1/6,1/8\documentclass[12pt]{minimal}
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\begin{document}$j/k=1/2,1/4,1/6,1/8$\end{document} and ep∈[0,0.95]\documentclass[12pt]{minimal}
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\begin{document}$e_{p}\in [0,0.95]$\end{document}. For ep=0.05\documentclass[12pt]{minimal}
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\begin{document}$e_{p}=0.05$\end{document} and 0.0489, we fix j/k=1/8\documentclass[12pt]{minimal}
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\begin{document}$j/k=1/8$\end{document} and set μ∈[0,0.5]\documentclass[12pt]{minimal}
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\begin{document}$\mu \in [0,0.5]$\end{document}. 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.
