Application of the Shannon entropy in the planar (non-restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system

ABSTRACT In this paper, we present an application of the Shannon entropy in the case of the planar (non-restricted) four-body problem. Specifically, the Kepler-60 extrasolar system is being investigated with a primary interest in the resonant configuration of the planets that exhibit a chain of mean...

Full description

Saved in:
Bibliographic Details
Published in:Monthly notices of the Royal Astronomical Society 2022-01, Vol.509 (1), p.884-893
Main Authors: Kővári, E, Érdi, B, Sándor, Zs
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c203t-d7e0e4c73326a809ab4679f2f6be1af77eef7e64533099192f0298f6ed19daf73
cites cdi_FETCH-LOGICAL-c203t-d7e0e4c73326a809ab4679f2f6be1af77eef7e64533099192f0298f6ed19daf73
container_end_page 893
container_issue 1
container_start_page 884
container_title Monthly notices of the Royal Astronomical Society
container_volume 509
creator Kővári, E
Érdi, B
Sándor, Zs
description ABSTRACT In this paper, we present an application of the Shannon entropy in the case of the planar (non-restricted) four-body problem. Specifically, the Kepler-60 extrasolar system is being investigated with a primary interest in the resonant configuration of the planets that exhibit a chain of mean-motion commensurabilities with the ratios 5:4:3. In the dynamical maps provided, the Shannon entropy is utilized to explore the general structure of the phase space, while, based on the time evolution of the entropy, we also determine the extent and rate of the chaotic diffusion as well as the characteristic times of stability for the planets. Two cases are considered: (i) the pure Laplace resonance when the critical angles of the two-body resonances circulate and that of the three-body resonance librates; and (ii) the chain of two two-body resonances when all the critical angles librate. Our results suggest that case (ii) is the more favourable configuration, but we state too that, in either case, the relevant resonance plays an important role in stabilizing the system. The derived stability times are no shorter than 108 yr in the central parts of the resonances.
doi_str_mv 10.1093/mnras/stab2953
format article
fullrecord <record><control><sourceid>oup_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1093_mnras_stab2953</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><oup_id>10.1093/mnras/stab2953</oup_id><sourcerecordid>10.1093/mnras/stab2953</sourcerecordid><originalsourceid>FETCH-LOGICAL-c203t-d7e0e4c73326a809ab4679f2f6be1af77eef7e64533099192f0298f6ed19daf73</originalsourceid><addsrcrecordid>eNqFUD1PwzAQtRBIlMLK7JEObu04sWu2quJLVGIA5shJzjQosS3blcjP4B-TFjozne7ee3fvHkLXjM4ZVXzR26DjIiZdZargJ2jCuChIpoQ4RRNKeUGWkrFzdBHjJ6U055mYoO-V911b69Q6i53BaQv4dautHVuwKTg_4NYexr7TVgd8M0IkQEyhrRM0M2zcLpDKNQP2wVUd9LcHeufsB0kQery31HZtGo4HnsF3EIigGL7cfi0kHQYch5igv0RnRncRrv7qFL3f372tH8nm5eFpvdqQOqM8kUYChbyWfHxDL6nSVS6kMpkRFTBtpAQwEkRecE6VYiozNFNLI6BhqhlxPkXz3711cDEGMKUPbT_6KBkt94GWh0DLY6CjYPYrcDv_H_cHYLh83Q</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Application of the Shannon entropy in the planar (non-restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system</title><source>OUP_牛津大学出版社OA刊</source><source>EZB Electronic Journals Library</source><creator>Kővári, E ; Érdi, B ; Sándor, Zs</creator><creatorcontrib>Kővári, E ; Érdi, B ; Sándor, Zs</creatorcontrib><description>ABSTRACT In this paper, we present an application of the Shannon entropy in the case of the planar (non-restricted) four-body problem. Specifically, the Kepler-60 extrasolar system is being investigated with a primary interest in the resonant configuration of the planets that exhibit a chain of mean-motion commensurabilities with the ratios 5:4:3. In the dynamical maps provided, the Shannon entropy is utilized to explore the general structure of the phase space, while, based on the time evolution of the entropy, we also determine the extent and rate of the chaotic diffusion as well as the characteristic times of stability for the planets. Two cases are considered: (i) the pure Laplace resonance when the critical angles of the two-body resonances circulate and that of the three-body resonance librates; and (ii) the chain of two two-body resonances when all the critical angles librate. Our results suggest that case (ii) is the more favourable configuration, but we state too that, in either case, the relevant resonance plays an important role in stabilizing the system. The derived stability times are no shorter than 108 yr in the central parts of the resonances.</description><identifier>ISSN: 0035-8711</identifier><identifier>EISSN: 1365-2966</identifier><identifier>DOI: 10.1093/mnras/stab2953</identifier><language>eng</language><publisher>Oxford University Press</publisher><ispartof>Monthly notices of the Royal Astronomical Society, 2022-01, Vol.509 (1), p.884-893</ispartof><rights>The Author(s) 2021. Published by Oxford University Press on behalf of Royal Astronomical Society. 2021</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c203t-d7e0e4c73326a809ab4679f2f6be1af77eef7e64533099192f0298f6ed19daf73</citedby><cites>FETCH-LOGICAL-c203t-d7e0e4c73326a809ab4679f2f6be1af77eef7e64533099192f0298f6ed19daf73</cites><orcidid>0000-0002-4491-2824 ; 0000-0003-1216-913X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,1604,27924,27925</link.rule.ids></links><search><creatorcontrib>Kővári, E</creatorcontrib><creatorcontrib>Érdi, B</creatorcontrib><creatorcontrib>Sándor, Zs</creatorcontrib><title>Application of the Shannon entropy in the planar (non-restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system</title><title>Monthly notices of the Royal Astronomical Society</title><description>ABSTRACT In this paper, we present an application of the Shannon entropy in the case of the planar (non-restricted) four-body problem. Specifically, the Kepler-60 extrasolar system is being investigated with a primary interest in the resonant configuration of the planets that exhibit a chain of mean-motion commensurabilities with the ratios 5:4:3. In the dynamical maps provided, the Shannon entropy is utilized to explore the general structure of the phase space, while, based on the time evolution of the entropy, we also determine the extent and rate of the chaotic diffusion as well as the characteristic times of stability for the planets. Two cases are considered: (i) the pure Laplace resonance when the critical angles of the two-body resonances circulate and that of the three-body resonance librates; and (ii) the chain of two two-body resonances when all the critical angles librate. Our results suggest that case (ii) is the more favourable configuration, but we state too that, in either case, the relevant resonance plays an important role in stabilizing the system. The derived stability times are no shorter than 108 yr in the central parts of the resonances.</description><issn>0035-8711</issn><issn>1365-2966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>TOX</sourceid><recordid>eNqFUD1PwzAQtRBIlMLK7JEObu04sWu2quJLVGIA5shJzjQosS3blcjP4B-TFjozne7ee3fvHkLXjM4ZVXzR26DjIiZdZargJ2jCuChIpoQ4RRNKeUGWkrFzdBHjJ6U055mYoO-V911b69Q6i53BaQv4dautHVuwKTg_4NYexr7TVgd8M0IkQEyhrRM0M2zcLpDKNQP2wVUd9LcHeufsB0kQery31HZtGo4HnsF3EIigGL7cfi0kHQYch5igv0RnRncRrv7qFL3f372tH8nm5eFpvdqQOqM8kUYChbyWfHxDL6nSVS6kMpkRFTBtpAQwEkRecE6VYiozNFNLI6BhqhlxPkXz3711cDEGMKUPbT_6KBkt94GWh0DLY6CjYPYrcDv_H_cHYLh83Q</recordid><startdate>20220101</startdate><enddate>20220101</enddate><creator>Kővári, E</creator><creator>Érdi, B</creator><creator>Sándor, Zs</creator><general>Oxford University Press</general><scope>TOX</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-4491-2824</orcidid><orcidid>https://orcid.org/0000-0003-1216-913X</orcidid></search><sort><creationdate>20220101</creationdate><title>Application of the Shannon entropy in the planar (non-restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system</title><author>Kővári, E ; Érdi, B ; Sándor, Zs</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c203t-d7e0e4c73326a809ab4679f2f6be1af77eef7e64533099192f0298f6ed19daf73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kővári, E</creatorcontrib><creatorcontrib>Érdi, B</creatorcontrib><creatorcontrib>Sándor, Zs</creatorcontrib><collection>OUP_牛津大学出版社OA刊</collection><collection>CrossRef</collection><jtitle>Monthly notices of the Royal Astronomical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kővári, E</au><au>Érdi, B</au><au>Sándor, Zs</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Application of the Shannon entropy in the planar (non-restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system</atitle><jtitle>Monthly notices of the Royal Astronomical Society</jtitle><date>2022-01-01</date><risdate>2022</risdate><volume>509</volume><issue>1</issue><spage>884</spage><epage>893</epage><pages>884-893</pages><issn>0035-8711</issn><eissn>1365-2966</eissn><abstract>ABSTRACT In this paper, we present an application of the Shannon entropy in the case of the planar (non-restricted) four-body problem. Specifically, the Kepler-60 extrasolar system is being investigated with a primary interest in the resonant configuration of the planets that exhibit a chain of mean-motion commensurabilities with the ratios 5:4:3. In the dynamical maps provided, the Shannon entropy is utilized to explore the general structure of the phase space, while, based on the time evolution of the entropy, we also determine the extent and rate of the chaotic diffusion as well as the characteristic times of stability for the planets. Two cases are considered: (i) the pure Laplace resonance when the critical angles of the two-body resonances circulate and that of the three-body resonance librates; and (ii) the chain of two two-body resonances when all the critical angles librate. Our results suggest that case (ii) is the more favourable configuration, but we state too that, in either case, the relevant resonance plays an important role in stabilizing the system. The derived stability times are no shorter than 108 yr in the central parts of the resonances.</abstract><pub>Oxford University Press</pub><doi>10.1093/mnras/stab2953</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0002-4491-2824</orcidid><orcidid>https://orcid.org/0000-0003-1216-913X</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0035-8711
ispartof Monthly notices of the Royal Astronomical Society, 2022-01, Vol.509 (1), p.884-893
issn 0035-8711
1365-2966
language eng
recordid cdi_crossref_primary_10_1093_mnras_stab2953
source OUP_牛津大学出版社OA刊; EZB Electronic Journals Library
title Application of the Shannon entropy in the planar (non-restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-30T19%3A28%3A39IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-oup_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Application%20of%20the%20Shannon%20entropy%20in%20the%20planar%20(non-restricted)%20four-body%20problem:%20the%20long-term%20stability%20of%20the%20Kepler-60%20exoplanetary%20system&rft.jtitle=Monthly%20notices%20of%20the%20Royal%20Astronomical%20Society&rft.au=K%C5%91v%C3%A1ri,%20E&rft.date=2022-01-01&rft.volume=509&rft.issue=1&rft.spage=884&rft.epage=893&rft.pages=884-893&rft.issn=0035-8711&rft.eissn=1365-2966&rft_id=info:doi/10.1093/mnras/stab2953&rft_dat=%3Coup_cross%3E10.1093/mnras/stab2953%3C/oup_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c203t-d7e0e4c73326a809ab4679f2f6be1af77eef7e64533099192f0298f6ed19daf73%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_oup_id=10.1093/mnras/stab2953&rfr_iscdi=true