Numerical integration of a relativistic two-body problem via a multiple scales method

被引：48

作者：

Abouelmagd, Elbaz I. ^{[1
,2
,3
]}

Elshaboury, S. M. ^{[4
]}

Selim, H. H. ^{[1
]}

机构：

[1] Natl Res Inst Astron & Geophys, Celestial Mech Unit, Dept Astron, Cairo, Egypt

[2] King Abdulaziz Univ, Nonlinear Anal & Appl Math Res Grp NAAM, Dept Math, Jeddah 21413, Saudi Arabia

[3] Univ Jeddah, Dept Math, Fac Sci & Arts, Jeddah, Saudi Arabia

[4] Ain Shams Univ, Fac Sci, Dept Math, Cairo, Egypt

来源：

ASTROPHYSICS AND SPACE SCIENCE | 2016年 / 361卷 / 01期

关键词：

N-body problem; Perturbed two-body problem; Relativistic two-body problem; Multiple scales method; PPN parameterizations; TRIANGULAR POINTS; RADIATION; SATELLITE; STABILITY; DYNAMICS; MOTION; DRAG;

D O I：

10.1007/s10509-015-2625-8

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

We offer an analytical study on the dynamics of a two-body problem perturbed by small post-Newtonian relativistic term. We prove that, while the angular momentum is not conserved, the motion is planar. We also show that the energy is subject to small changes due to the relativistic effect. We also offer a periodic solution to this problem, obtained by a method based on the separation of time scales. We demonstrate that our solution is more general than the method developed in the book by Brumberg (Essential Relativistic Celestial Mechanics, Hilger, Bristol, 1991). The practical applicability of this model may be in studies of the long-term evolution of relativistic binaries (neutron stars or black holes).

引用

页数：10

共 22 条

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Abouelmagd, Elbaz I. ;

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2015, 20 (03) :1057-1069

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ASTROPHYSICS AND SPACE SCIENCE, 2014, 350 (02) :495-505

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Abouelmagd, Elbaz I. .

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Adler R., 1965, Introduction to General Relativity

[8]

[Anonymous], 2005, METHODS CELESTIAL ME

[9]

[Anonymous], 1991, Essential Relativistic Celestial Mechanics

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