{"title":"Relative equilibria and periodic orbits in a Circular Planar (2+2)-Body Problem","authors":"Lennard F. Bakker, Nicholas J. Freeman","doi":"10.1007/s10569-023-10173-0","DOIUrl":"https://doi.org/10.1007/s10569-023-10173-0","url":null,"abstract":"<p>We present a planar four-body model, the Circular Planar (2+2)-Body Problem, for the motion of two asteroids (having small but positive masses) moving under the gravitational attraction of each other and under the gravitational attraction of two primaries (with masses much larger than the two smaller mass bodies) moving in uniform circular motion about their center of mass. We show the Circular Planar (2+2)-Body Problem has (at least) 6 relative equilibria and (at least) 10 one-parameter families of periodic orbits, two of which are of Hill-type. The existence of six relative equilibria and eight one-parameter families of periodic orbits is obtained by a reduction of the Circular Planar (2+2)-Body Problem in which the primaries have equal mass, the asteroids have equal mass, and the positions of the asteroids are symmetric with respect to the origin. The remaining two one-parameter families of periodic orbits, which are of comet-type, are obtained directly in the Circular Planar (2+2)-Body Problem.</p>","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138536278","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}
{"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}
{"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}
{"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}
{"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}
{"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}
A. Vananti, Moritz Meyer zu Westram, T. Schildknecht
{"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}