Analysis of the Effect of Earth’s Equatorial Ellipticity on the Existence and Stability of the Lagrangian Points in the Earth–Moon–Sun System
We have investigated existence of Lagrangian points and analyzed stability in the Earth–Moon–Sun system including the effect of Earth’s equatorial ellipticity parameter . First we have expressed the equations of motion of the Moon in the spherical coordinate system using the potential of the Earth....
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| Veröffentlicht in: | Astronomy reports 2023-12, Vol.67 (12), p.1489-1498 |
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| creator | Kumar, Mukesh Yadav, Sushil |
| description | We have investigated existence of Lagrangian points and analyzed stability in the Earth–Moon–Sun system including the effect of Earth’s equatorial ellipticity parameter
. First we have expressed the equations of motion of the Moon in the spherical coordinate system using the potential of the Earth. We observed that there exist collinear and non-collinear Lagrangian points for different values of Earth’s equatorial ellipticity
. We also analyzed the effect of
on the stability of Lagrangian points including the effect of
. We observed that all the Lagrangian points are unstable for different values of
. Finally, we have drawn and analyzed zero velocity curves by taking different values of Jacobi constants. |
| doi_str_mv | 10.1134/S1063772923340036 |
| format | Article |
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. First we have expressed the equations of motion of the Moon in the spherical coordinate system using the potential of the Earth. We observed that there exist collinear and non-collinear Lagrangian points for different values of Earth’s equatorial ellipticity
. We also analyzed the effect of
on the stability of Lagrangian points including the effect of
. We observed that all the Lagrangian points are unstable for different values of
. Finally, we have drawn and analyzed zero velocity curves by taking different values of Jacobi constants.</description><identifier>ISSN: 1063-7729</identifier><identifier>EISSN: 1562-6881</identifier><identifier>DOI: 10.1134/S1063772923340036</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Astronomy ; Coordinate systems ; Earth ; Ellipticity ; Equations of motion ; Lagrangian equilibrium points ; Moon ; Observations and Techniques ; Physics ; Physics and Astronomy ; Spherical coordinates ; Stability analysis</subject><ispartof>Astronomy reports, 2023-12, Vol.67 (12), p.1489-1498</ispartof><rights>Pleiades Publishing, Ltd. 2023. ISSN 1063-7729, Astronomy Reports, 2023, Vol. 67, No. 12, pp. 1489–1498. © Pleiades Publishing, Ltd., 2023.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-758296619ebcbc9d106339a49acf42e7c920e4ccce2eb4f8e351707f28e656703</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S1063772923340036$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1063772923340036$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Kumar, Mukesh</creatorcontrib><creatorcontrib>Yadav, Sushil</creatorcontrib><title>Analysis of the Effect of Earth’s Equatorial Ellipticity on the Existence and Stability of the Lagrangian Points in the Earth–Moon–Sun System</title><title>Astronomy reports</title><addtitle>Astron. Rep</addtitle><description>We have investigated existence of Lagrangian points and analyzed stability in the Earth–Moon–Sun system including the effect of Earth’s equatorial ellipticity parameter
. First we have expressed the equations of motion of the Moon in the spherical coordinate system using the potential of the Earth. We observed that there exist collinear and non-collinear Lagrangian points for different values of Earth’s equatorial ellipticity
. We also analyzed the effect of
on the stability of Lagrangian points including the effect of
. We observed that all the Lagrangian points are unstable for different values of
. Finally, we have drawn and analyzed zero velocity curves by taking different values of Jacobi constants.</description><subject>Astronomy</subject><subject>Coordinate systems</subject><subject>Earth</subject><subject>Ellipticity</subject><subject>Equations of motion</subject><subject>Lagrangian equilibrium points</subject><subject>Moon</subject><subject>Observations and Techniques</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Spherical coordinates</subject><subject>Stability analysis</subject><issn>1063-7729</issn><issn>1562-6881</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kM1KxDAUhYMoOI4-gLuA62p-2jRdDkP9gRGF6rqkmXQmQyeZSVKwO99hVr6eT2JrBRfi6t7LOd-BewC4xOgaYxrfFBgxmqYkI5TGCFF2BCY4YSRinOPjfu_laNBPwZn3G4Qw5pRNwGFmRNN57aGtYVgrmNe1kmG4cuHC-vP9w8N834pgnRYNzJtG74KWOnTQmpF40z4oIxUUZgmLICrdfMtj4EKsnDArLQx8ttoED_UPN-YfHq01_ShaA4uuT9qeg5NaNF5d_MwpeL3NX-b30eLp7mE-W0SSMB6iNOEkYwxnqpKVzJbDizQTcSZkHROVyowgFUspFVFVXHNFE5yitCZcsYSliE7B1Zi7c3bfKh_KjW1d34cvSUZxmsQxZ70Ljy7prPdO1eXO6a1wXYlROXRf_um-Z8jI-N5rVsr9Jv8PfQEP6InK</recordid><startdate>20231201</startdate><enddate>20231201</enddate><creator>Kumar, Mukesh</creator><creator>Yadav, Sushil</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TG</scope><scope>8FD</scope><scope>H8D</scope><scope>KL.</scope><scope>L7M</scope></search><sort><creationdate>20231201</creationdate><title>Analysis of the Effect of Earth’s Equatorial Ellipticity on the Existence and Stability of the Lagrangian Points in the Earth–Moon–Sun System</title><author>Kumar, Mukesh ; Yadav, Sushil</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-758296619ebcbc9d106339a49acf42e7c920e4ccce2eb4f8e351707f28e656703</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Astronomy</topic><topic>Coordinate systems</topic><topic>Earth</topic><topic>Ellipticity</topic><topic>Equations of motion</topic><topic>Lagrangian equilibrium points</topic><topic>Moon</topic><topic>Observations and Techniques</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Spherical coordinates</topic><topic>Stability analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kumar, Mukesh</creatorcontrib><creatorcontrib>Yadav, Sushil</creatorcontrib><collection>CrossRef</collection><collection>Meteorological & Geoastrophysical Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Meteorological & Geoastrophysical Abstracts - Academic</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Astronomy reports</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kumar, Mukesh</au><au>Yadav, Sushil</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analysis of the Effect of Earth’s Equatorial Ellipticity on the Existence and Stability of the Lagrangian Points in the Earth–Moon–Sun System</atitle><jtitle>Astronomy reports</jtitle><stitle>Astron. Rep</stitle><date>2023-12-01</date><risdate>2023</risdate><volume>67</volume><issue>12</issue><spage>1489</spage><epage>1498</epage><pages>1489-1498</pages><issn>1063-7729</issn><eissn>1562-6881</eissn><abstract>We have investigated existence of Lagrangian points and analyzed stability in the Earth–Moon–Sun system including the effect of Earth’s equatorial ellipticity parameter
. First we have expressed the equations of motion of the Moon in the spherical coordinate system using the potential of the Earth. We observed that there exist collinear and non-collinear Lagrangian points for different values of Earth’s equatorial ellipticity
. We also analyzed the effect of
on the stability of Lagrangian points including the effect of
. We observed that all the Lagrangian points are unstable for different values of
. Finally, we have drawn and analyzed zero velocity curves by taking different values of Jacobi constants.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1063772923340036</doi><tpages>10</tpages></addata></record> |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Astronomy Coordinate systems Earth Ellipticity Equations of motion Lagrangian equilibrium points Moon Observations and Techniques Physics Physics and Astronomy Spherical coordinates Stability analysis |
| title | Analysis of the Effect of Earth’s Equatorial Ellipticity on the Existence and Stability of the Lagrangian Points in the Earth–Moon–Sun System |
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