{
  "id": "1611.07550",
  "version": "v1",
  "published": "2016-11-22T22:06:41.000Z",
  "updated": "2016-11-22T22:06:41.000Z",
  "title": "On the period of the periodic orbits of the restricted three body problem",
  "authors": [
    "Oscar M Perdomo"
  ],
  "comment": "5 figures",
  "categories": [
    "math.DS",
    "astro-ph.EP",
    "math.DG"
  ],
  "abstract": "We will show that the period $T$ of a closed orbit of the planar circular restricted three-body problem (viewed on rotating coordinates) depends on the region it encloses. Roughly speaking, we show that, $2 T=k\\pi+\\int_\\Omega g$ where $k$ is an integer, $\\Omega$ is the region enclosed by the periodic orbit and $g:\\mathbb{R}^2\\to \\mathbb{R}$ is a function that only depends on the constant $C$ known as the Jacobian integral; it does not depend on $\\Omega$. This theorem has a Keplerian flavor in the sense that it relates the period with the space \"swept\" by the orbit. As an application, we prove that there is a neighborhood around $L_4$ such that every periodic solution contained in this neighborhood must move clockwise. The same result holds true for $L_5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-22T22:06:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic orbit",
      "planar circular restricted three-body problem",
      "result holds true",
      "jacobian integral",
      "keplerian flavor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}