Secular frequencies of 3-D exoplanetary systems View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2008-03

AUTHORS

Anne-Sophie Libert, Jacques Henrard

ABSTRACT

Using a 12th order expansion of the perturbative potential in powers of the eccentricities and the inclinations, we study the secular effects of two non-coplanar planets which are not in mean–motion resonance. By means of Lie transformations (which introduce an action–angle formulation of the Hamiltonian), we find the four fundamental frequencies of the 3-D secular three-body problem and compute the long-term time evolutions of the Keplerian elements. To find the relations between these elements, the main combinations of the fundamental frequencies common to these evolutions are identified by frequency analysis. This study is performed for two different reference frames: a general one and the Laplace plane. We underline the known limitations of the linear Laplace–Lagrange theory and point out the great sensitivity of the 3-D secular three-body problem to its initial values. This analytical approach is applied to the exoplanetary system Andromedae in order to search whether the eccentricities evolutions and the apsidal configuration (libration of ) observed in the coplanar case are maintained for increasing initial values of the mutual inclination of the two orbital planes. More... »

PAGES

209-229

References to SciGraph publications

Journal

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10569-007-9113-6

DOI

http://dx.doi.org/10.1007/s10569-007-9113-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1023844365


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1402", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Applied Economics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/14", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Economics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Namur", 
          "id": "https://www.grid.ac/institutes/grid.6520.1", 
          "name": [
            "University of Namur, 8, Rempart de la Vierge, 5000, Namur, Belgium"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Libert", 
        "givenName": "Anne-Sophie", 
        "id": "sg:person.014744513045.32", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014744513045.32"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Namur", 
          "id": "https://www.grid.ac/institutes/grid.6520.1", 
          "name": [
            "University of Namur, 8, Rempart de la Vierge, 5000, Namur, Belgium"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Henrard", 
        "givenName": "Jacques", 
        "id": "sg:person.012411554565.81", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012411554565.81"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/j.icarus.2006.02.007", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001507567"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.icarus.2007.05.007", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002313820"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01245757", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004542622", 
          "https://doi.org/10.1007/bf01245757"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/asna.18430200602", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005058457"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1086/317829", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010236450"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10569-007-9097-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012686154", 
          "https://doi.org/10.1007/s10569-007-9097-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10569-007-9097-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012686154", 
          "https://doi.org/10.1007/s10569-007-9097-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01234556", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023877304", 
          "https://doi.org/10.1007/bf01234556"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01230629", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028918192", 
          "https://doi.org/10.1007/bf01230629"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01230629", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028918192", 
          "https://doi.org/10.1007/bf01230629"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.icarus.2005.11.015", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037936414"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-010-2611-6_26", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040699962", 
          "https://doi.org/10.1007/978-94-010-2611-6_26"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1086/322115", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043486837"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0167-2789(93)90210-r", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050082884"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0167-2789(93)90210-r", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050082884"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1051/0004-6361:20064941", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1056936744"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1051/0004-6361:20065767", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1056937402"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.3057799", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057902622"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1086/115978", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058454557"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1086/491584", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058776227"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1086/491584", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058776227"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2008-03", 
    "datePublishedReg": "2008-03-01", 
    "description": "Using a 12th order expansion of the perturbative potential in powers of the eccentricities and the inclinations, we study the secular effects of two non-coplanar planets which are not in mean\u2013motion resonance. By means of Lie transformations (which introduce an action\u2013angle formulation of the Hamiltonian), we find the four fundamental frequencies of the 3-D secular three-body problem and compute the long-term time evolutions of the Keplerian elements. To find the relations between these elements, the main combinations of the fundamental frequencies common to these evolutions are identified by frequency analysis. This study is performed for two different reference frames: a general one and the Laplace plane. We underline the known limitations of the linear Laplace\u2013Lagrange theory and point out the great sensitivity of the 3-D secular three-body problem to its initial values. This analytical approach is applied to the exoplanetary system Andromedae in order to search whether the eccentricities evolutions and the apsidal configuration (libration of ) observed in the coplanar case are maintained for increasing initial values of the mutual inclination of the two orbital planes.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s10569-007-9113-6", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136436", 
        "issn": [
          "0008-8714", 
          "0923-2958"
        ], 
        "name": "Celestial Mechanics and Dynamical Astronomy", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "100"
      }
    ], 
    "name": "Secular frequencies of 3-D exoplanetary systems", 
    "pagination": "209-229", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "7199063a0feb603f555b42ccb7edc73cfa7803a4514dbb92cb45c2b831a6f4dd"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10569-007-9113-6"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1023844365"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10569-007-9113-6", 
      "https://app.dimensions.ai/details/publication/pub.1023844365"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T14:32", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000373_0000000373/records_13102_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs10569-007-9113-6"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10569-007-9113-6'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10569-007-9113-6'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10569-007-9113-6'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10569-007-9113-6'


 

This table displays all metadata directly associated to this object as RDF triples.

124 TRIPLES      21 PREDICATES      44 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10569-007-9113-6 schema:about anzsrc-for:14
2 anzsrc-for:1402
3 schema:author Nc414457313124d209aaf134af1aa2dd5
4 schema:citation sg:pub.10.1007/978-94-010-2611-6_26
5 sg:pub.10.1007/bf01230629
6 sg:pub.10.1007/bf01234556
7 sg:pub.10.1007/bf01245757
8 sg:pub.10.1007/s10569-007-9097-2
9 https://doi.org/10.1002/asna.18430200602
10 https://doi.org/10.1016/0167-2789(93)90210-r
11 https://doi.org/10.1016/j.icarus.2005.11.015
12 https://doi.org/10.1016/j.icarus.2006.02.007
13 https://doi.org/10.1016/j.icarus.2007.05.007
14 https://doi.org/10.1051/0004-6361:20064941
15 https://doi.org/10.1051/0004-6361:20065767
16 https://doi.org/10.1063/1.3057799
17 https://doi.org/10.1086/115978
18 https://doi.org/10.1086/317829
19 https://doi.org/10.1086/322115
20 https://doi.org/10.1086/491584
21 schema:datePublished 2008-03
22 schema:datePublishedReg 2008-03-01
23 schema:description Using a 12th order expansion of the perturbative potential in powers of the eccentricities and the inclinations, we study the secular effects of two non-coplanar planets which are not in mean–motion resonance. By means of Lie transformations (which introduce an action–angle formulation of the Hamiltonian), we find the four fundamental frequencies of the 3-D secular three-body problem and compute the long-term time evolutions of the Keplerian elements. To find the relations between these elements, the main combinations of the fundamental frequencies common to these evolutions are identified by frequency analysis. This study is performed for two different reference frames: a general one and the Laplace plane. We underline the known limitations of the linear Laplace–Lagrange theory and point out the great sensitivity of the 3-D secular three-body problem to its initial values. This analytical approach is applied to the exoplanetary system Andromedae in order to search whether the eccentricities evolutions and the apsidal configuration (libration of ) observed in the coplanar case are maintained for increasing initial values of the mutual inclination of the two orbital planes.
24 schema:genre research_article
25 schema:inLanguage en
26 schema:isAccessibleForFree false
27 schema:isPartOf N147b1a45aeed460aa4add1c1d0be8ccc
28 N59d296d3b8414b4eb8981f0e2966bdbd
29 sg:journal.1136436
30 schema:name Secular frequencies of 3-D exoplanetary systems
31 schema:pagination 209-229
32 schema:productId N8466544ac0c24becbf588f7b3ef33381
33 N87e9f4c73e9144cf8a86600ac6a84a09
34 N99af77ed54e64faa91a2bd865da1a801
35 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023844365
36 https://doi.org/10.1007/s10569-007-9113-6
37 schema:sdDatePublished 2019-04-11T14:32
38 schema:sdLicense https://scigraph.springernature.com/explorer/license/
39 schema:sdPublisher N5d31fe4f032b4092af99c38c102f6d66
40 schema:url http://link.springer.com/10.1007%2Fs10569-007-9113-6
41 sgo:license sg:explorer/license/
42 sgo:sdDataset articles
43 rdf:type schema:ScholarlyArticle
44 N147b1a45aeed460aa4add1c1d0be8ccc schema:issueNumber 3
45 rdf:type schema:PublicationIssue
46 N59d296d3b8414b4eb8981f0e2966bdbd schema:volumeNumber 100
47 rdf:type schema:PublicationVolume
48 N5d31fe4f032b4092af99c38c102f6d66 schema:name Springer Nature - SN SciGraph project
49 rdf:type schema:Organization
50 N8466544ac0c24becbf588f7b3ef33381 schema:name readcube_id
51 schema:value 7199063a0feb603f555b42ccb7edc73cfa7803a4514dbb92cb45c2b831a6f4dd
52 rdf:type schema:PropertyValue
53 N87e9f4c73e9144cf8a86600ac6a84a09 schema:name dimensions_id
54 schema:value pub.1023844365
55 rdf:type schema:PropertyValue
56 N99af77ed54e64faa91a2bd865da1a801 schema:name doi
57 schema:value 10.1007/s10569-007-9113-6
58 rdf:type schema:PropertyValue
59 Nc414457313124d209aaf134af1aa2dd5 rdf:first sg:person.014744513045.32
60 rdf:rest Ne7469241f4484a1ba9c89d092d127e08
61 Ne7469241f4484a1ba9c89d092d127e08 rdf:first sg:person.012411554565.81
62 rdf:rest rdf:nil
63 anzsrc-for:14 schema:inDefinedTermSet anzsrc-for:
64 schema:name Economics
65 rdf:type schema:DefinedTerm
66 anzsrc-for:1402 schema:inDefinedTermSet anzsrc-for:
67 schema:name Applied Economics
68 rdf:type schema:DefinedTerm
69 sg:journal.1136436 schema:issn 0008-8714
70 0923-2958
71 schema:name Celestial Mechanics and Dynamical Astronomy
72 rdf:type schema:Periodical
73 sg:person.012411554565.81 schema:affiliation https://www.grid.ac/institutes/grid.6520.1
74 schema:familyName Henrard
75 schema:givenName Jacques
76 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012411554565.81
77 rdf:type schema:Person
78 sg:person.014744513045.32 schema:affiliation https://www.grid.ac/institutes/grid.6520.1
79 schema:familyName Libert
80 schema:givenName Anne-Sophie
81 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014744513045.32
82 rdf:type schema:Person
83 sg:pub.10.1007/978-94-010-2611-6_26 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040699962
84 https://doi.org/10.1007/978-94-010-2611-6_26
85 rdf:type schema:CreativeWork
86 sg:pub.10.1007/bf01230629 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028918192
87 https://doi.org/10.1007/bf01230629
88 rdf:type schema:CreativeWork
89 sg:pub.10.1007/bf01234556 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023877304
90 https://doi.org/10.1007/bf01234556
91 rdf:type schema:CreativeWork
92 sg:pub.10.1007/bf01245757 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004542622
93 https://doi.org/10.1007/bf01245757
94 rdf:type schema:CreativeWork
95 sg:pub.10.1007/s10569-007-9097-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012686154
96 https://doi.org/10.1007/s10569-007-9097-2
97 rdf:type schema:CreativeWork
98 https://doi.org/10.1002/asna.18430200602 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005058457
99 rdf:type schema:CreativeWork
100 https://doi.org/10.1016/0167-2789(93)90210-r schema:sameAs https://app.dimensions.ai/details/publication/pub.1050082884
101 rdf:type schema:CreativeWork
102 https://doi.org/10.1016/j.icarus.2005.11.015 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037936414
103 rdf:type schema:CreativeWork
104 https://doi.org/10.1016/j.icarus.2006.02.007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001507567
105 rdf:type schema:CreativeWork
106 https://doi.org/10.1016/j.icarus.2007.05.007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002313820
107 rdf:type schema:CreativeWork
108 https://doi.org/10.1051/0004-6361:20064941 schema:sameAs https://app.dimensions.ai/details/publication/pub.1056936744
109 rdf:type schema:CreativeWork
110 https://doi.org/10.1051/0004-6361:20065767 schema:sameAs https://app.dimensions.ai/details/publication/pub.1056937402
111 rdf:type schema:CreativeWork
112 https://doi.org/10.1063/1.3057799 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057902622
113 rdf:type schema:CreativeWork
114 https://doi.org/10.1086/115978 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058454557
115 rdf:type schema:CreativeWork
116 https://doi.org/10.1086/317829 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010236450
117 rdf:type schema:CreativeWork
118 https://doi.org/10.1086/322115 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043486837
119 rdf:type schema:CreativeWork
120 https://doi.org/10.1086/491584 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058776227
121 rdf:type schema:CreativeWork
122 https://www.grid.ac/institutes/grid.6520.1 schema:alternateName University of Namur
123 schema:name University of Namur, 8, Rempart de la Vierge, 5000, Namur, Belgium
124 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...