{"title":"Dynamical evolution of the Uranian satellite system II. Crossing of the 5/3 Ariel–Umbriel mean motion resonance","authors":"","doi":"10.1016/j.icarus.2024.116254","DOIUrl":null,"url":null,"abstract":"<div><p>At present, the main satellites of Uranus are not involved in any low order mean motion resonance (MMR). However, owing to tides raised in the planet, Ariel and Umbriel most likely crossed the 5/3 MMR in the past. Previous studies on this resonance passage relied on limited time-consuming <span><math><mrow><mi>N</mi><mo>−</mo></mrow></math></span>body simulations or simplified models focusing solely on the effects of the eccentricity or the inclination. In this paper, we aim to provide a more comprehensive view on how the system evaded capture in the 5/3 MMR. For that purpose, we developed a secular resonant two-satellite model with low eccentricities and low inclinations, including tides using the weak friction model. By performing a large number of numerical simulations, we show that capture in the 5/3 MMR is certain if the initial eccentricities of Ariel, <span><math><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, and Umbriel, <span><math><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, are related through <span><math><mrow><msup><mrow><mrow><mo>(</mo><msubsup><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo><</mo><mn>0</mn><mo>.</mo><mn>007</mn></mrow></math></span>. Moreover, we observe that the eccentricity of Ariel is the key variable to evade the 5/3 MMR with a high probability. We determine that for <span><math><mrow><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>></mo><mn>0</mn><mo>.</mo><mn>015</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn></mrow></math></span>, the system avoids capture in at least 60% of the cases. We also show that, to replicate the currently observed system, the initial inclinations of Ariel and Umbriel must lay within <span><math><mrow><msub><mrow><mi>I</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≤</mo><mn>0</mn><mo>.</mo><mn>05</mn><mo>°</mo></mrow></math></span> and <span><math><mrow><mn>0</mn><mo>.</mo><mn>06</mn><mo>°</mo><mo>≤</mo><msub><mrow><mi>I</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≤</mo><mn>0</mn><mo>.</mo><mn>11</mn><mo>°</mo></mrow></math></span>, respectively. We checked these results using a complete <span><math><mrow><mi>N</mi><mo>−</mo></mrow></math></span>body model with the five main satellites and did not observe any significant differences.</p></div>","PeriodicalId":13199,"journal":{"name":"Icarus","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0019103524003142/pdfft?md5=ead07189642683424e1c775ea533b5cc&pid=1-s2.0-S0019103524003142-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Icarus","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019103524003142","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
At present, the main satellites of Uranus are not involved in any low order mean motion resonance (MMR). However, owing to tides raised in the planet, Ariel and Umbriel most likely crossed the 5/3 MMR in the past. Previous studies on this resonance passage relied on limited time-consuming body simulations or simplified models focusing solely on the effects of the eccentricity or the inclination. In this paper, we aim to provide a more comprehensive view on how the system evaded capture in the 5/3 MMR. For that purpose, we developed a secular resonant two-satellite model with low eccentricities and low inclinations, including tides using the weak friction model. By performing a large number of numerical simulations, we show that capture in the 5/3 MMR is certain if the initial eccentricities of Ariel, , and Umbriel, , are related through . Moreover, we observe that the eccentricity of Ariel is the key variable to evade the 5/3 MMR with a high probability. We determine that for and , the system avoids capture in at least 60% of the cases. We also show that, to replicate the currently observed system, the initial inclinations of Ariel and Umbriel must lay within and , respectively. We checked these results using a complete body model with the five main satellites and did not observe any significant differences.
期刊介绍:
Icarus is devoted to the publication of original contributions in the field of Solar System studies. Manuscripts reporting the results of new research - observational, experimental, or theoretical - concerning the astronomy, geology, meteorology, physics, chemistry, biology, and other scientific aspects of our Solar System or extrasolar systems are welcome. The journal generally does not publish papers devoted exclusively to the Sun, the Earth, celestial mechanics, meteoritics, or astrophysics. Icarus does not publish papers that provide "improved" versions of Bode''s law, or other numerical relations, without a sound physical basis. Icarus does not publish meeting announcements or general notices. Reviews, historical papers, and manuscripts describing spacecraft instrumentation may be considered, but only with prior approval of the editor. An entire issue of the journal is occasionally devoted to a single subject, usually arising from a conference on the same topic. The language of publication is English. American or British usage is accepted, but not a mixture of these.