Periodic Orbits Close to That of the Moon in Hill's Problem

In the framework of the restricted, circular, 3-dimensional 3-body problem Sun-Earth-Moon, Valsecchi et al. (1993) found a set of 8 periodic orbits, with duration equal to that of the Saros cycle, and differing only for the initial phases, in which the motion of the massless Moon follows closely tha...

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Main Author: Giovanni B. Valsecchi
Format: Article
Language:English
Published: Frontiers Media S.A. 2018-06-01
Series:Frontiers in Astronomy and Space Sciences
Subjects:
Online Access:https://www.frontiersin.org/article/10.3389/fspas.2018.00020/full
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spelling doaj-2bf9e827e44f4a928fa4a7ef4a9d65102020-11-25T00:50:52ZengFrontiers Media S.A.Frontiers in Astronomy and Space Sciences2296-987X2018-06-01510.3389/fspas.2018.00020372642Periodic Orbits Close to That of the Moon in Hill's ProblemGiovanni B. Valsecchi0Giovanni B. Valsecchi1IAPS-INAF, Rome, ItalyIFAC-CNR, Sesto Fiorentino, ItalyIn the framework of the restricted, circular, 3-dimensional 3-body problem Sun-Earth-Moon, Valsecchi et al. (1993) found a set of 8 periodic orbits, with duration equal to that of the Saros cycle, and differing only for the initial phases, in which the motion of the massless Moon follows closely that of the real Moon. Of these, only 4 are actually independent, the other 4 being obtainable by symmetry about the plane of the ecliptic. In this paper the problem is treated in the framework of the 3-dimensional Hill's problem. It is shown that also in this problem there are 8 periodic orbits of duration equal to that of the Saros cycle, and that in these periodic orbits the motion of the Moon is very close to that of the real Moon. Moreover, as a consequence of the additional symmetry of Hill's problem about the y-axis, only 2 of the 8 periodic orbits are independent, the other ones being obtainable by exploiting the symmetries of the problem.https://www.frontiersin.org/article/10.3389/fspas.2018.00020/fullmoonlunar orbitperiodic orbitsHill's problemrestricted 3-body problem
collection DOAJ
language English
format Article
sources DOAJ
author Giovanni B. Valsecchi
Giovanni B. Valsecchi
spellingShingle Giovanni B. Valsecchi
Giovanni B. Valsecchi
Periodic Orbits Close to That of the Moon in Hill's Problem
Frontiers in Astronomy and Space Sciences
moon
lunar orbit
periodic orbits
Hill's problem
restricted 3-body problem
author_facet Giovanni B. Valsecchi
Giovanni B. Valsecchi
author_sort Giovanni B. Valsecchi
title Periodic Orbits Close to That of the Moon in Hill's Problem
title_short Periodic Orbits Close to That of the Moon in Hill's Problem
title_full Periodic Orbits Close to That of the Moon in Hill's Problem
title_fullStr Periodic Orbits Close to That of the Moon in Hill's Problem
title_full_unstemmed Periodic Orbits Close to That of the Moon in Hill's Problem
title_sort periodic orbits close to that of the moon in hill's problem
publisher Frontiers Media S.A.
series Frontiers in Astronomy and Space Sciences
issn 2296-987X
publishDate 2018-06-01
description In the framework of the restricted, circular, 3-dimensional 3-body problem Sun-Earth-Moon, Valsecchi et al. (1993) found a set of 8 periodic orbits, with duration equal to that of the Saros cycle, and differing only for the initial phases, in which the motion of the massless Moon follows closely that of the real Moon. Of these, only 4 are actually independent, the other 4 being obtainable by symmetry about the plane of the ecliptic. In this paper the problem is treated in the framework of the 3-dimensional Hill's problem. It is shown that also in this problem there are 8 periodic orbits of duration equal to that of the Saros cycle, and that in these periodic orbits the motion of the Moon is very close to that of the real Moon. Moreover, as a consequence of the additional symmetry of Hill's problem about the y-axis, only 2 of the 8 periodic orbits are independent, the other ones being obtainable by exploiting the symmetries of the problem.
topic moon
lunar orbit
periodic orbits
Hill's problem
restricted 3-body problem
url https://www.frontiersin.org/article/10.3389/fspas.2018.00020/full
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