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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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 |
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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 |
work_keys_str_mv |
AT giovannibvalsecchi periodicorbitsclosetothatofthemooninhillsproblem AT giovannibvalsecchi periodicorbitsclosetothatofthemooninhillsproblem |
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1725246059113873408 |