Triangular libration points in the R3BP under combined effects of oblateness, radiation and power-law profile
We study the effects of oblateness up to J4 of the primaries and power-law density profile (PDP) on the linear stability of libration location of an infinitesimal mass within the framework of restricted three body problem (R3BP), by using a more realistic model in which a disc with PDP is rotating a...
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| Veröffentlicht in: | Advances in space research 2016-01, Vol.57 (1), p.189-201 |
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| creator | Falaye, B.J. Dong, Shi-Hai Oyewumi, K.J. Falaiye, O.A. Joshua, E.S. Omojola, J. Abimbola, O.J. Kalu, O. Ikhdair, S.M. |
| description | We study the effects of oblateness up to J4 of the primaries and power-law density profile (PDP) on the linear stability of libration location of an infinitesimal mass within the framework of restricted three body problem (R3BP), by using a more realistic model in which a disc with PDP is rotating around the common center of the system mass with perturbed mean motion. The existence and stability of triangular equilibrium points have been explored. It has been shown that triangular equilibrium points are stable for 0 |
| doi_str_mv | 10.1016/j.asr.2015.10.030 |
| format | Article |
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The existence and stability of triangular equilibrium points have been explored. It has been shown that triangular equilibrium points are stable for 0<μ<μc and unstable for μc⩽μ≤1/2, where μc denotes the critical mass parameter. We find that, the oblateness up to J2 of the primaries and the radiation reduces the stability range while the oblateness up to J4 of the primaries increases the size of stability both in the context where PDP is considered and ignored. The PDP has an effect of about ≈0.01 reduction on the application of μc to Earth–Moon and Jupiter–Moons systems. We find that the comprehensive effects of the perturbations have a stabilizing proclivity. However, the oblateness up to J2 of the primaries and the radiation of the primaries have tendency for instability, while coefficients up to J4 of the primaries have stability predisposition. In the limiting case c=0, and also by setting appropriate parameter(s) to zero, our results are in excellent agreement with the ones obtained previously. Libration points play a very important role in space mission and as a consequence, our results have a practical application in space dynamics and related areas. The model may be applied to study the navigation and stationkeeping operations of spacecraft (infinitesimal mass) around the Jupiter (more massive) -Callisto (less massive) system, where PDP accounts for the circumsolar ring of asteroidal dust, which has a cloud of dust permanently in its wake.</description><identifier>ISSN: 0273-1177</identifier><identifier>EISSN: 1879-1948</identifier><identifier>DOI: 10.1016/j.asr.2015.10.030</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>Clouds ; Density ; Dust ; Dynamical systems ; Dynamics ; Libration points ; Mathematical models ; Oblateness ; Power-law density profile ; Restricted three-body problem ; Stability</subject><ispartof>Advances in space research, 2016-01, Vol.57 (1), p.189-201</ispartof><rights>2015 COSPAR</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c433t-4c0387be4bf518aaf6fe2b1b09370ef9f00d0d12188f791c9bad911ecd4094413</citedby><cites>FETCH-LOGICAL-c433t-4c0387be4bf518aaf6fe2b1b09370ef9f00d0d12188f791c9bad911ecd4094413</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.asr.2015.10.030$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Falaye, B.J.</creatorcontrib><creatorcontrib>Dong, Shi-Hai</creatorcontrib><creatorcontrib>Oyewumi, K.J.</creatorcontrib><creatorcontrib>Falaiye, O.A.</creatorcontrib><creatorcontrib>Joshua, E.S.</creatorcontrib><creatorcontrib>Omojola, J.</creatorcontrib><creatorcontrib>Abimbola, O.J.</creatorcontrib><creatorcontrib>Kalu, O.</creatorcontrib><creatorcontrib>Ikhdair, S.M.</creatorcontrib><title>Triangular libration points in the R3BP under combined effects of oblateness, radiation and power-law profile</title><title>Advances in space research</title><description>We study the effects of oblateness up to J4 of the primaries and power-law density profile (PDP) on the linear stability of libration location of an infinitesimal mass within the framework of restricted three body problem (R3BP), by using a more realistic model in which a disc with PDP is rotating around the common center of the system mass with perturbed mean motion. The existence and stability of triangular equilibrium points have been explored. It has been shown that triangular equilibrium points are stable for 0<μ<μc and unstable for μc⩽μ≤1/2, where μc denotes the critical mass parameter. We find that, the oblateness up to J2 of the primaries and the radiation reduces the stability range while the oblateness up to J4 of the primaries increases the size of stability both in the context where PDP is considered and ignored. The PDP has an effect of about ≈0.01 reduction on the application of μc to Earth–Moon and Jupiter–Moons systems. We find that the comprehensive effects of the perturbations have a stabilizing proclivity. However, the oblateness up to J2 of the primaries and the radiation of the primaries have tendency for instability, while coefficients up to J4 of the primaries have stability predisposition. In the limiting case c=0, and also by setting appropriate parameter(s) to zero, our results are in excellent agreement with the ones obtained previously. Libration points play a very important role in space mission and as a consequence, our results have a practical application in space dynamics and related areas. The model may be applied to study the navigation and stationkeeping operations of spacecraft (infinitesimal mass) around the Jupiter (more massive) -Callisto (less massive) system, where PDP accounts for the circumsolar ring of asteroidal dust, which has a cloud of dust permanently in its wake.</description><subject>Clouds</subject><subject>Density</subject><subject>Dust</subject><subject>Dynamical systems</subject><subject>Dynamics</subject><subject>Libration points</subject><subject>Mathematical models</subject><subject>Oblateness</subject><subject>Power-law density profile</subject><subject>Restricted three-body problem</subject><subject>Stability</subject><issn>0273-1177</issn><issn>1879-1948</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNqNkUFvEzEQhS1EJULLD-DmIwc2zKw3sS1OpWpLpUqgqpwtrz0GRxs7tTet-Pd1Gs6op9GM3vtGM4-xjwhLBFx_2SxtLcsecNX6JQh4wxaopO5QD-otW0AvRYco5Tv2vtYNAPZSwoJt70u06fd-soVPcSx2jjnxXY5prjwmPv8hfie-_eT75Klwl7djTOQ5hUCuSXLgeZzsTIlq_cyL9fGIsMk3zBOVbrJPfFdyiBOdsZNgp0of_tVT9uvq8v7ie3f74_rm4vy2c4MQczc4EEqONIxhhcrasA7UjziCFhIo6ADgwWOPSgWp0enReo1Izg-ghwHFKft05La9D3uqs9nG6miabKK8rwalWvegtRKvkK5UP2j5QsWj1JVca6FgdiVubflrEMwhBbMxLQVzSOEwaik0z9ejh9q5j5GKqS5ScuRjaQ80Psf_uJ8BQ2aQVg</recordid><startdate>20160101</startdate><enddate>20160101</enddate><creator>Falaye, B.J.</creator><creator>Dong, Shi-Hai</creator><creator>Oyewumi, K.J.</creator><creator>Falaiye, O.A.</creator><creator>Joshua, E.S.</creator><creator>Omojola, J.</creator><creator>Abimbola, O.J.</creator><creator>Kalu, O.</creator><creator>Ikhdair, S.M.</creator><general>Elsevier Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TG</scope><scope>7U7</scope><scope>C1K</scope><scope>KL.</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20160101</creationdate><title>Triangular libration points in the R3BP under combined effects of oblateness, radiation and power-law profile</title><author>Falaye, B.J. ; Dong, Shi-Hai ; Oyewumi, K.J. ; Falaiye, O.A. ; Joshua, E.S. ; Omojola, J. ; Abimbola, O.J. ; Kalu, O. ; Ikhdair, S.M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c433t-4c0387be4bf518aaf6fe2b1b09370ef9f00d0d12188f791c9bad911ecd4094413</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Clouds</topic><topic>Density</topic><topic>Dust</topic><topic>Dynamical systems</topic><topic>Dynamics</topic><topic>Libration points</topic><topic>Mathematical models</topic><topic>Oblateness</topic><topic>Power-law density profile</topic><topic>Restricted three-body problem</topic><topic>Stability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Falaye, B.J.</creatorcontrib><creatorcontrib>Dong, Shi-Hai</creatorcontrib><creatorcontrib>Oyewumi, K.J.</creatorcontrib><creatorcontrib>Falaiye, O.A.</creatorcontrib><creatorcontrib>Joshua, E.S.</creatorcontrib><creatorcontrib>Omojola, J.</creatorcontrib><creatorcontrib>Abimbola, O.J.</creatorcontrib><creatorcontrib>Kalu, O.</creatorcontrib><creatorcontrib>Ikhdair, S.M.</creatorcontrib><collection>CrossRef</collection><collection>Meteorological & Geoastrophysical Abstracts</collection><collection>Toxicology Abstracts</collection><collection>Environmental Sciences and Pollution Management</collection><collection>Meteorological & Geoastrophysical Abstracts - Academic</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Advances in space research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Falaye, B.J.</au><au>Dong, Shi-Hai</au><au>Oyewumi, K.J.</au><au>Falaiye, O.A.</au><au>Joshua, E.S.</au><au>Omojola, J.</au><au>Abimbola, O.J.</au><au>Kalu, O.</au><au>Ikhdair, S.M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Triangular libration points in the R3BP under combined effects of oblateness, radiation and power-law profile</atitle><jtitle>Advances in space research</jtitle><date>2016-01-01</date><risdate>2016</risdate><volume>57</volume><issue>1</issue><spage>189</spage><epage>201</epage><pages>189-201</pages><issn>0273-1177</issn><eissn>1879-1948</eissn><abstract>We study the effects of oblateness up to J4 of the primaries and power-law density profile (PDP) on the linear stability of libration location of an infinitesimal mass within the framework of restricted three body problem (R3BP), by using a more realistic model in which a disc with PDP is rotating around the common center of the system mass with perturbed mean motion. The existence and stability of triangular equilibrium points have been explored. It has been shown that triangular equilibrium points are stable for 0<μ<μc and unstable for μc⩽μ≤1/2, where μc denotes the critical mass parameter. We find that, the oblateness up to J2 of the primaries and the radiation reduces the stability range while the oblateness up to J4 of the primaries increases the size of stability both in the context where PDP is considered and ignored. The PDP has an effect of about ≈0.01 reduction on the application of μc to Earth–Moon and Jupiter–Moons systems. We find that the comprehensive effects of the perturbations have a stabilizing proclivity. However, the oblateness up to J2 of the primaries and the radiation of the primaries have tendency for instability, while coefficients up to J4 of the primaries have stability predisposition. In the limiting case c=0, and also by setting appropriate parameter(s) to zero, our results are in excellent agreement with the ones obtained previously. Libration points play a very important role in space mission and as a consequence, our results have a practical application in space dynamics and related areas. The model may be applied to study the navigation and stationkeeping operations of spacecraft (infinitesimal mass) around the Jupiter (more massive) -Callisto (less massive) system, where PDP accounts for the circumsolar ring of asteroidal dust, which has a cloud of dust permanently in its wake.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.asr.2015.10.030</doi><tpages>13</tpages></addata></record> |
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| subjects | Clouds Density Dust Dynamical systems Dynamics Libration points Mathematical models Oblateness Power-law density profile Restricted three-body problem Stability |
| title | Triangular libration points in the R3BP under combined effects of oblateness, radiation and power-law profile |
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