Families of Asymmetric Periodic Orbits in the Restricted Three-body Problem

被引:0
作者
K. E. Papadakis
机构
[1] University of Patras,Department of Engineering Sciences
来源
Earth, Moon, and Planets | 2008年 / 103卷
关键词
Asymmetric orbit; Critical orbit; Homoclinic orbit; Levi-Civita regularization; Periodic orbit; Restricted three-body problem;
D O I
暂无
中图分类号
学科分类号
摘要
This paper studies the asymmetric solutions of the restricted planar problem of three bodies, two of which are finite, moving in circular orbits around their center of masses, while the third is infinitesimal. We explore, numerically, the families of asymmetric simple-periodic orbits which bifurcate from the basic families of symmetric periodic solutions f, g, h, i, l and m, as well as the asymmetric ones associated with the families c, a and b which emanate from the collinear equilibrium points L1, L2 and L3 correspondingly. The evolution of these asymmetric families covering the entire range of the mass parameter of the problem is presented. We found that some symmetric families have only one bifurcating asymmetric family, others have infinity number of asymmetric families associated with them and others have not branching asymmetric families at all, as the mass parameter varies. The network of the symmetric families and the branching asymmetric families from them when the primaries are equal, when the left primary body is three times bigger than the right one and for the Earth–Moon case, is presented. Minimum and maximum values of the mass parameter of the series of critical symmetric periodic orbits are given. In order to avoid the singularity due to binary collisions between the third body and one of the primaries, we regularize the equations of motion of the problem using the Levi-Civita transformations.
引用
收藏
页码:25 / 42
页数:17
相关论文
共 50 条
[21]   Generalized periodic orbits in some restricted three-body problems [J].
Ortega, Rafael ;
Zhao, Lei .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2021, 72 (01)
[22]   Generalized periodic orbits in some restricted three-body problems [J].
Rafael Ortega ;
Lei Zhao .
Zeitschrift für angewandte Mathematik und Physik, 2021, 72
[23]   Asymptotic Orbits at the Triangular Equilibria in the Photogravitational Restricted Three-Body Problem [J].
K. E. Papadakis .
Astrophysics and Space Science, 2006, 305 :57-66
[24]   Asymptotic orbits at the triangular equilibria in the photogravitational restricted three-body problem [J].
Papadakis, K. E. .
ASTROPHYSICS AND SPACE SCIENCE, 2006, 305 (01) :57-66
[25]   Search for periodic orbits in the general three-body problem [J].
Iasko, P. P. ;
Orlov, V. V. .
ASTRONOMY REPORTS, 2014, 58 (11) :869-879
[26]   Search for periodic orbits in the general three-body problem [J].
P. P. Iasko ;
V. V. Orlov .
Astronomy Reports, 2014, 58 :869-879
[27]   On the period of the periodic orbits of the restricted three body problem [J].
Perdomo, Oscar .
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2017, 129 (1-2) :89-104
[28]   Horseshoe periodic orbits in the restricted three body problem [J].
Llibre, J ;
Ollé, M .
NEW ADVANCES IN CELESTIAL MECHANICS AND HAMILTONIAN SYSTEMS, 2004, :137-152
[29]   On the period of the periodic orbits of the restricted three body problem [J].
Oscar Perdomo .
Celestial Mechanics and Dynamical Astronomy, 2017, 129 :89-104
[30]   Determination of the doubly symmetric periodic orbits in the restricted three-body problem and Hill's lunar problem [J].
Xu, Xingbo .
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2023, 135 (02)