Circular restricted three-body problem when both the primaries are heterogeneous spheroid of three layers and infinitesimal body varies its mass
The circular restricted three-body problem, where two primaries are taken as heterogeneous oblate spheroid with three layers of different densities and infinitesimal body varies its mass according to the Jeans law, has been studied. The system of equations of motion have been evaluated by using the...
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| Veröffentlicht in: | Journal of astrophysics and astronomy 2018-10, Vol.39 (5), p.1-20, Article 57 |
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| creator | Ansari, Abdullah A. Alhussain, Ziyad Ali Prasad, Sada Nand |
| description | The circular restricted three-body problem, where two primaries are taken as heterogeneous oblate spheroid with three layers of different densities and infinitesimal body varies its mass according to the Jeans law, has been studied. The system of equations of motion have been evaluated by using the Jeans law and hence the Jacobi integral has been determined. With the help of system of equations of motion, we have plotted the equilibrium points in different planes (in-plane and out-of planes), zero velocity curves, regions of possible motion, surfaces (zero-velocity surfaces with projections and Poincaré surfaces of section) and the basins of convergence with the variation of mass parameter. Finally, we have examined the stability of the equilibrium points with the help of Meshcherskii space–time inverse transformation of the above said model and revealed that all the equilibrium points are unstable. |
| doi_str_mv | 10.1007/s12036-018-9540-7 |
| format | Article |
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The system of equations of motion have been evaluated by using the Jeans law and hence the Jacobi integral has been determined. With the help of system of equations of motion, we have plotted the equilibrium points in different planes (in-plane and out-of planes), zero velocity curves, regions of possible motion, surfaces (zero-velocity surfaces with projections and Poincaré surfaces of section) and the basins of convergence with the variation of mass parameter. Finally, we have examined the stability of the equilibrium points with the help of Meshcherskii space–time inverse transformation of the above said model and revealed that all the equilibrium points are unstable.</description><identifier>ISSN: 0250-6335</identifier><identifier>EISSN: 0973-7758</identifier><identifier>DOI: 10.1007/s12036-018-9540-7</identifier><language>eng</language><publisher>New Delhi: Springer India</publisher><subject>Astronomy ; Astrophysics and Astroparticles ; Chaos theory ; Equations of motion ; Equilibrium ; Jacobi integral ; Observations and Techniques ; Physics ; Physics and Astronomy ; Planes ; Three body problem</subject><ispartof>Journal of astrophysics and astronomy, 2018-10, Vol.39 (5), p.1-20, Article 57</ispartof><rights>Indian Academy of Sciences 2018</rights><rights>Journal of Astrophysics and Astronomy is a copyright of Springer, (2018). 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The system of equations of motion have been evaluated by using the Jeans law and hence the Jacobi integral has been determined. With the help of system of equations of motion, we have plotted the equilibrium points in different planes (in-plane and out-of planes), zero velocity curves, regions of possible motion, surfaces (zero-velocity surfaces with projections and Poincaré surfaces of section) and the basins of convergence with the variation of mass parameter. Finally, we have examined the stability of the equilibrium points with the help of Meshcherskii space–time inverse transformation of the above said model and revealed that all the equilibrium points are unstable.</description><subject>Astronomy</subject><subject>Astrophysics and Astroparticles</subject><subject>Chaos theory</subject><subject>Equations of motion</subject><subject>Equilibrium</subject><subject>Jacobi integral</subject><subject>Observations and Techniques</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Planes</subject><subject>Three body problem</subject><issn>0250-6335</issn><issn>0973-7758</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1UMtOwzAQtBBIlMIHcLPE2eBHbCdHVPGSkLjA2XKSdeMqTYrtgPoXfDIuQeLExevdnZnVDEKXjF4zSvVNZJwKRSgrSSULSvQRWtBKC6K1LI_zn0tKlBDyFJ3FuKGUVQWvFuhr5UMz9TbgADEF3yRoceoCAKnHdo93Yax72OLPDgZcj6nLS8hTv7XBQ8Q2AO4gQRjXMMA4RRx3Xe58i0c3C-He7iFk6NBiPzg_-AQx83v8c-FjFvIp4q2N8RydONtHuPitS_R2f_e6eiTPLw9Pq9tn0gimEhGqcTW1Or_OFVJXJdQ1B0kp8Eq3TAMocMLVrW1bxi21peQ1ayTnSiitxBJdzbrZ4fuUvZvNOIUhnzScMUFLVZQHFJtRTRhjDODMbH1vGDWH4M0cvMnBm0PwRmcOnzkxY4c1hD_l_0nfhB-KGA</recordid><startdate>20181001</startdate><enddate>20181001</enddate><creator>Ansari, Abdullah A.</creator><creator>Alhussain, Ziyad Ali</creator><creator>Prasad, Sada Nand</creator><general>Springer India</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7TG</scope><scope>7XB</scope><scope>88I</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>KL.</scope><scope>L7M</scope><scope>M2O</scope><scope>M2P</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>Q9U</scope></search><sort><creationdate>20181001</creationdate><title>Circular restricted three-body problem when both the primaries are heterogeneous spheroid of three layers and infinitesimal body varies its mass</title><author>Ansari, Abdullah A. ; Alhussain, Ziyad Ali ; Prasad, Sada Nand</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-36cfb0a7cfbff45798ebb2e500e297d17ee6ef3fbdadd12a0a852b1c522636763</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Astronomy</topic><topic>Astrophysics and Astroparticles</topic><topic>Chaos theory</topic><topic>Equations of motion</topic><topic>Equilibrium</topic><topic>Jacobi integral</topic><topic>Observations and Techniques</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Planes</topic><topic>Three body problem</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ansari, Abdullah A.</creatorcontrib><creatorcontrib>Alhussain, Ziyad Ali</creatorcontrib><creatorcontrib>Prasad, Sada Nand</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Meteorological & Geoastrophysical Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>Meteorological & Geoastrophysical Abstracts - Academic</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Research Library China</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central Basic</collection><jtitle>Journal of astrophysics and astronomy</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ansari, Abdullah A.</au><au>Alhussain, Ziyad Ali</au><au>Prasad, Sada Nand</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Circular restricted three-body problem when both the primaries are heterogeneous spheroid of three layers and infinitesimal body varies its mass</atitle><jtitle>Journal of astrophysics and astronomy</jtitle><stitle>J Astrophys Astron</stitle><date>2018-10-01</date><risdate>2018</risdate><volume>39</volume><issue>5</issue><spage>1</spage><epage>20</epage><pages>1-20</pages><artnum>57</artnum><issn>0250-6335</issn><eissn>0973-7758</eissn><abstract>The circular restricted three-body problem, where two primaries are taken as heterogeneous oblate spheroid with three layers of different densities and infinitesimal body varies its mass according to the Jeans law, has been studied. The system of equations of motion have been evaluated by using the Jeans law and hence the Jacobi integral has been determined. With the help of system of equations of motion, we have plotted the equilibrium points in different planes (in-plane and out-of planes), zero velocity curves, regions of possible motion, surfaces (zero-velocity surfaces with projections and Poincaré surfaces of section) and the basins of convergence with the variation of mass parameter. Finally, we have examined the stability of the equilibrium points with the help of Meshcherskii space–time inverse transformation of the above said model and revealed that all the equilibrium points are unstable.</abstract><cop>New Delhi</cop><pub>Springer India</pub><doi>10.1007/s12036-018-9540-7</doi><tpages>20</tpages></addata></record> |
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| source | Indian Academy of Sciences; EZB-FREE-00999 freely available EZB journals; SpringerLink Journals - AutoHoldings |
| subjects | Astronomy Astrophysics and Astroparticles Chaos theory Equations of motion Equilibrium Jacobi integral Observations and Techniques Physics Physics and Astronomy Planes Three body problem |
| title | Circular restricted three-body problem when both the primaries are heterogeneous spheroid of three layers and infinitesimal body varies its mass |
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