{
  "annotation_id": "4aa2622e-9bff-4504-a4a0-e5f59b1209b8",
  "date_created": "2026-02-17T05:53:07.768000Z",
  "date_modified": "2026-02-17T05:53:07.768000Z",
  "file_hash": "5163babc5b6dc584311e69f06f21b58507b61beafe906cc408954332994dae91",
  "private": false,
  "record": {
    "abstract": "Multi-revolution elliptic Halo (ME-Halo) orbits are a special class of symmetric and periodic solutions within the framework of the elliptic restricted three-body problem (ERTBP). During a single period, an M:N ME-Halo orbit completes $M$ revolutions around a libration point and the primaries revolve N times around each other. Owing to the repeated configurations, ME-Halo orbits hold great promise as nominal trajectories for space mission design. However, a major challenge associated with ME-Halo orbits lies in their mathematical description. To this end, we propose a novel method to derive high-order analytical expansions of ME-Halo orbits in the ERTBP by introducing two correction terms into the equations of motion in the y- and z-directions. Specifically, both the coordinate variables and correction terms are expanded as power series in terms of the primary eccentricity, the in-plane amplitude, and the out-of-plane amplitude. High-order approximations are constructed using a perturbation method, and their accuracy is validated through numerical analysis. Due to the inherent symmetry, ME-Halo orbits can be classified into four distinct families: southern/northern and periapsis/apoapsis groups. The analytical approximations developed in this study not only provide high-accuracy initial guesses for the numerical computation of ME-Halo orbits, but also offer new insights into the dynamical environment near collinear libration points in the ERTBP, thereby advancing practical applications in mission design.",
    "arxiv_id": "2601.06563",
    "authors": [
      "Xiaoyan Leng",
      "Hanlun Lei"
    ],
    "categories": [
      "astro-ph.EP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "High-order expansions of multi-revolution elliptic Halo orbits in the elliptic restricted three-body problem",
    "url": "https://arxiv.org/abs/2601.06563",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6e98378e-0686-413b-afed-53343d0d5774",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}