Pub Date : 2023-09-29DOI: 10.1007/s10569-023-10161-4
Giovanni F. Gronchi, Giulio Baù, Clara Grassi
Abstract We consider the Keplerian distance d in the case of two elliptic orbits, i.e., the distance between one point on the first ellipse and one point on the second one, assuming they have a common focus. The absolute minimum $$d_{textrm{min}}$$ dmin of this function, called MOID or orbit distance in the literature, is relevant to detect possible impacts between two objects following approximately these elliptic trajectories. We revisit and compare two different approaches to compute the critical points of $$d^2$$ d2 , where we squared the distance d to include crossing points among the critical ones. One approach uses trigonometric polynomials, and the other uses ordinary polynomials. A new way to test the reliability of the computation of $$d_{textrm{min}}$$ dmin is introduced, based on optimal estimates that can be found in the literature. The planar case is also discussed: in this case, we present an estimate for the maximal number of critical points of $$d^2$$ d2 , together with a conjecture supported by numerical tests.
摘要:我们考虑两个椭圆轨道的开普勒距离d，即第一个椭圆上一点与第二个椭圆上一点之间的距离，假设它们有一个共同的焦点。该函数的绝对最小值$$d_{textrm{min}}$$ d min，在文献中称为MOID或轨道距离，与检测两个物体之间可能的撞击有关，这些物体大致遵循这些椭圆轨迹。我们重新审视并比较了计算$$d^2$$ d 2临界点的两种不同方法，其中我们对距离d进行平方，以包括临界点之间的交叉点。一种方法使用三角多项式，另一种方法使用普通多项式。本文介绍了一种基于文献中最优估计来检验$$d_{textrm{min}}$$ d min计算可靠性的新方法。在平面情况下，我们给出了$$d^2$$ d2的最大临界点数的估计，并给出了数值试验支持的一个猜想。
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Pub Date : 2023-08-31DOI: 10.1007/s10569-023-10160-5
G. Caritá, S. Aljbaae, A. B. Prado, A. C. Signor, M. Morais, D. M. Sanchez
{"title":"Analysis of the natural orbits around Io","authors":"G. Caritá, S. Aljbaae, A. B. Prado, A. C. Signor, M. Morais, D. M. Sanchez","doi":"10.1007/s10569-023-10160-5","DOIUrl":"https://doi.org/10.1007/s10569-023-10160-5","url":null,"abstract":"","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72502190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.1007/s10569-023-10158-z
Sara Di Ruzza
{"title":"Correction: Chaotic coexistence of librational and rotational dynamics in the averaged planar three-body problem","authors":"Sara Di Ruzza","doi":"10.1007/s10569-023-10158-z","DOIUrl":"https://doi.org/10.1007/s10569-023-10158-z","url":null,"abstract":"","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"84 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78067546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-25DOI: 10.1007/s10569-023-10157-0
Di Wu, A. Rosengren
{"title":"An investigation on space debris of unknown origin using proper elements and neural networks","authors":"Di Wu, A. Rosengren","doi":"10.1007/s10569-023-10157-0","DOIUrl":"https://doi.org/10.1007/s10569-023-10157-0","url":null,"abstract":"","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75907437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-10DOI: 10.1007/s10569-023-10156-1
Morad Nazari, D. Canales, Brennan McCann, Eric Butcher, K. Howell
{"title":"Framework for the full N-body problem in SE(3) and its reduction to the circular restricted full three-body problem","authors":"Morad Nazari, D. Canales, Brennan McCann, Eric Butcher, K. Howell","doi":"10.1007/s10569-023-10156-1","DOIUrl":"https://doi.org/10.1007/s10569-023-10156-1","url":null,"abstract":"","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84013129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-30DOI: 10.1007/s10569-023-10155-2
Sara Di Ruzza
{"title":"Chaotic coexistence of librational and rotational dynamics in the averaged planar three-body problem","authors":"Sara Di Ruzza","doi":"10.1007/s10569-023-10155-2","DOIUrl":"https://doi.org/10.1007/s10569-023-10155-2","url":null,"abstract":"","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85579695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-20DOI: 10.1007/s10569-023-10151-6
W. Tian
{"title":"PETREL19: a new numerical solution of planetary and lunar ephemeris","authors":"W. Tian","doi":"10.1007/s10569-023-10151-6","DOIUrl":"https://doi.org/10.1007/s10569-023-10151-6","url":null,"abstract":"","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85224403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-19DOI: 10.1007/s10569-023-10152-5
M. Guzzo, E. Lega
{"title":"Theory and applications of fast Lyapunov indicators to model problems of celestial mechanics","authors":"M. Guzzo, E. Lega","doi":"10.1007/s10569-023-10152-5","DOIUrl":"https://doi.org/10.1007/s10569-023-10152-5","url":null,"abstract":"","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78464346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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