In this study, equilibrium points and periodic orbits in the potential field of asteroids are investigated. We present the linearized equations of motion relative to the equilibrium points and characteristic equations. We find that the distribution of characteristic multipliers of periodic orbits around the equilibrium point and the distribution of eigenvalues of the equilibrium point correspond to each other. The distribution of eigenvalues of the equilibrium point confirms the topology and the stability of periodic orbits around the equilibrium point.
Context. The recent estimates of the 3D shape of the M/Xe-type triple asteroid system (216) Kleopatra indicated a density of 5 g.cm$^{-3}$. Such a high density implies a high metal content and a low porosity which is not easy to reconcile with its peculiar dumbbell shape. Aims. Given the unprecedented angular resolution of the VLT/SPHERE/ZIMPOL camera, we aim to constrain the mass and the shape of Kleopatra with high accuracy, hence its density. Methods. We combined our new VLT/SPHERE observations of Kleopatra recorded in 2017 and 2018 with archival data, as well as lightcurve, occultation, an…
The orbit of the outer satellite Alexhelios of (216) Kleopatra is already constrained by adaptive-optics astrometry, obtained with the VLT/SPHERE instrument. However, there is also a preceding occultation event in 1980 attributed to this satellite. Hereinafter, we try to link all observations, spanning 1980--2018. We find the nominal orbit exhibits an unexplained shift by $+60^\circ$ in the true longitude. Using both periodogram analysis and an $\ell = 10$ multipole model suitable for the motion of mutually interacting moons about the irregular body, we confirmed that it is not possible to adj…
In this work, we study the continuation of a periodic orbit on a relatively large scale and discover the existence of convergence under certain conditions, which has profound significance in research on asteroids and can provide a total geometric perspective to understanding the evolution of the dynamic characteristics from a global perspective. Based on the polyhedron model, convergence is derived via a series of theoretical analyses and derivations, which shows that a periodic orbit will evolve into a nearly circular orbit with a normal periodic ratio (e.g., 2:1, 3:2, and 4:3) and almost zer…
A generalized dipole-segment model for the gravitational field of elongated bodies
CFisUC, Departamento de Física, Universidade de Coimbra（科英布拉大学物理系）；CICGE, DGAOT, FCUP（波尔图大学）；PostGrad Program in Systems Engineering (PPGES) - University of Pernambuco (UPE)（伯南布哥大学系统工程专业研究生项目）；Department of Mathematics, School of Engineering and Sciences - São Paulo State University (FEG/UNESP)（圣保罗州立大学工程与科学学院数学系）；Instituto Universitario de Matemáticas y Aplicaciones - Universidad de Zaragoza（萨拉戈萨大学数学与应用研究院）；School of Aerospace and Mechanical Engineering The University of Oklahoma（俄克拉荷马大学航空航天与机械工程学院）；National Institute for Space Research (INPE)（国家空间研究所）
Few solar system asteroids and comets are found in high eccentricity orbits ($e > 0.9$) but in the primordial planetesimal disks and in exoplanet systems around dying stars such objects are believed to be common. For 2006 HY51, the main belt asteroid with the highest known eccentricity 0.9684, we investigate the probable rotational states today using our computer-efficient chaotic process simulation method. Starting with random initial conditions, we find that this asteroid is inevitably captured into stable spin-orbit resonances typically within tens to a hundred Myr. The resonances are confi…
Celestial bodies approximated with rigid triaxial ellipsoids in a two-body system can rotate chaotically due to the time-varying gravitational torque from the central mass. At small orbital eccentricity values, rotation is short-term orderly and predictable within the commensurate spin-orbit resonances, while at eccentricity approaching unity, chaos completely takes over. Here, we present the full 3D rotational equations of motion around all three principle axes for triaxial minor planets and two independent methods of numerical solution based on Euler rotations and quaternion algebra. The dom…
稳定运动的虚构特洛伊小行星天王星的等边平衡点周围的区域进行了调查，相对于小行星的轨道倾角，以确定该地区的大小和它们的形状。对于这项任务，我们使用的结果广泛的数值积分的轨道网格的初始条件周围的点L4和L5，并分析了稳定性的个人轨道。我们的基本动力学模型是外太阳系（木星、土星、天王星和海王星）。我们集成了运动方程的虚构特洛伊附近的稳定平衡点的选定轨道的年龄太阳系的50亿年。一个实验已经进行了切割通过拉格朗日点的固定值的倾角，而半长轴是不同的。稳定区相对于初始半长轴的延伸范围在19.05 < a < 19.3 AU之间，但取决于初始倾角。在另一次运行中，小行星轨道的倾角在0 < i < 60的范围内变化，半长轴是固定的。结果发现，只有四个稳定轨道的“窗口”幸存下来：这些是初始倾角0 < i < 7，9 < i < 13，31 < i < 36和38 < i < 50的轨道。我们假设至少有一些特洛伊围绕天王星拉格朗日点的稳定窗口在小，也高倾角的存在。
