Pub Date : 2023-11-06DOI: 10.1007/s10569-023-10168-x
Siddarth Kaki, Maruthi R. Akella
A semi-analytical solution for circular-to-circular planar orbit transfers is presented. In particular, the problem is addressed with a judiciously chosen maneuver sequence consisting of radial thrust, velocity normal thrust, and coast arcs. The radial thrust segments admit fully-analytical solutions, while the velocity normal thrust portion only admits a semi-analytical solution. For a given constant-acceleration thrust value, the range of radii to which the orbit can be changed is presented with two different schemes. Orbit escape is also demonstrated with successive applications of the first scheme. However, all the presented solutions are suboptimal in terms of time and fuel use.
{"title":"Coplanar circular-to-circular orbit transfer guidance with constant-thrust acceleration","authors":"Siddarth Kaki, Maruthi R. Akella","doi":"10.1007/s10569-023-10168-x","DOIUrl":"https://doi.org/10.1007/s10569-023-10168-x","url":null,"abstract":"<p>A semi-analytical solution for circular-to-circular planar orbit transfers is presented. In particular, the problem is addressed with a judiciously chosen maneuver sequence consisting of radial thrust, velocity normal thrust, and coast arcs. The radial thrust segments admit fully-analytical solutions, while the velocity normal thrust portion only admits a semi-analytical solution. For a given constant-acceleration thrust value, the range of radii to which the orbit can be changed is presented with two different schemes. Orbit escape is also demonstrated with successive applications of the first scheme. However, all the presented solutions are suboptimal in terms of time and fuel use.\u0000</p>","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138536261","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 : 2023-11-06DOI: 10.1007/s10569-023-10166-z
Colin R. McInnes
Abstract The general three-body problem is investigated with the addition of a fixed external force applied to one of the masses. It is firstly demonstrated that the centre-of-mass of the three-body system accelerates. Then, it is demonstrated that only a single, unstable, collinear equilibrium solution exits in the accelerating frame. While unstable, it is also demonstrated that this single equilibrium configuration is in principle controllable using additional control accelerations distributed between the masses. Potential applications of such an accelerated collinear equilibrium configuration are discussed for the active manoeuvring of chains of small asteroids for space resource utilisation.
{"title":"Equilibria in an accelerated three-body problem","authors":"Colin R. McInnes","doi":"10.1007/s10569-023-10166-z","DOIUrl":"https://doi.org/10.1007/s10569-023-10166-z","url":null,"abstract":"Abstract The general three-body problem is investigated with the addition of a fixed external force applied to one of the masses. It is firstly demonstrated that the centre-of-mass of the three-body system accelerates. Then, it is demonstrated that only a single, unstable, collinear equilibrium solution exits in the accelerating frame. While unstable, it is also demonstrated that this single equilibrium configuration is in principle controllable using additional control accelerations distributed between the masses. Potential applications of such an accelerated collinear equilibrium configuration are discussed for the active manoeuvring of chains of small asteroids for space resource utilisation.","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"43 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135633938","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 : 2023-10-18DOI: 10.1007/s10569-023-10167-y
Hanrui Pang, Siming Liu, Rong Liu
{"title":"Orbits of charged particles with an azimuthal initial velocity in a dipole magnetic field","authors":"Hanrui Pang, Siming Liu, Rong Liu","doi":"10.1007/s10569-023-10167-y","DOIUrl":"https://doi.org/10.1007/s10569-023-10167-y","url":null,"abstract":"","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135888629","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 : 2023-10-17DOI: 10.1007/s10569-023-10164-1
Gavin M. Brown, Daniel J. Scheeres
{"title":"Analyzing the structure of periodic orbit families that exist around asteroid (101955) Bennu","authors":"Gavin M. Brown, Daniel J. Scheeres","doi":"10.1007/s10569-023-10164-1","DOIUrl":"https://doi.org/10.1007/s10569-023-10164-1","url":null,"abstract":"","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136032880","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 : 2023-10-01DOI: 10.1007/s10569-023-10150-7
Rita Mastroianni, Ugo Locatelli
{"title":"Correction: Secular orbital dynamics of the innermost exoplanet of the $$upsilon $$-Andromedæ system","authors":"Rita Mastroianni, Ugo Locatelli","doi":"10.1007/s10569-023-10150-7","DOIUrl":"https://doi.org/10.1007/s10569-023-10150-7","url":null,"abstract":"","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135606060","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 : 2023-10-01DOI: 10.1007/s10569-023-10165-0
A. Vananti, Moritz Meyer zu Westram, T. Schildknecht
Abstract In the characterization of the space debris environment, the computation of the orbit of the debris objects is usually conducted by considering the association of short sequences of observations called tracklets. In case the orbits can be already determined with sufficient accuracy from single tracklets, it is necessary to define a criterion to decide if two calculated orbits correspond to the same object. One possibility is to introduce a definition of distance between orbits and to consider a threshold below which the two orbits are considered to be originating from the same object. The concept of distance is quite general and leaves room to different definitions. There are different ways to describe and to parameterize the space of the possible orbits. In this article, new metrics are proposed which extend distance definitions suggested in previous works. In these metrics in addition to orbital plane and orbital shape, also the position of the object along the orbit is taken into account. The obtained distances are scaled according to the orbit covariance. This has the advantage that the distance between orbits with different accuracy can be evaluated. The proposed metrics are then compared with existing common metrics to assess their applicability.
{"title":"Metrics on space of closed orbits for near-Earth objects identification","authors":"A. Vananti, Moritz Meyer zu Westram, T. Schildknecht","doi":"10.1007/s10569-023-10165-0","DOIUrl":"https://doi.org/10.1007/s10569-023-10165-0","url":null,"abstract":"Abstract In the characterization of the space debris environment, the computation of the orbit of the debris objects is usually conducted by considering the association of short sequences of observations called tracklets. In case the orbits can be already determined with sufficient accuracy from single tracklets, it is necessary to define a criterion to decide if two calculated orbits correspond to the same object. One possibility is to introduce a definition of distance between orbits and to consider a threshold below which the two orbits are considered to be originating from the same object. The concept of distance is quite general and leaves room to different definitions. There are different ways to describe and to parameterize the space of the possible orbits. In this article, new metrics are proposed which extend distance definitions suggested in previous works. In these metrics in addition to orbital plane and orbital shape, also the position of the object along the orbit is taken into account. The obtained distances are scaled according to the orbit covariance. This has the advantage that the distance between orbits with different accuracy can be evaluated. The proposed metrics are then compared with existing common metrics to assess their applicability.","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135761396","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 : 2023-09-29DOI: 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。
{"title":"Revisiting the computation of the critical points of the Keplerian distance","authors":"Giovanni F. Gronchi, Giulio Baù, Clara Grassi","doi":"10.1007/s10569-023-10161-4","DOIUrl":"https://doi.org/10.1007/s10569-023-10161-4","url":null,"abstract":"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 $$d_{textrm{min}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>d</mml:mi> <mml:mtext>min</mml:mtext> </mml:msub> </mml:math> 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 $$d^2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>d</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> , 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 $$d_{textrm{min}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>d</mml:mi> <mml:mtext>min</mml:mtext> </mml:msub> </mml:math> 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 $$d^2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>d</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> , together with a conjecture supported by numerical tests.","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135200114","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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