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

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• 作者：Elbaz I. Abouelmagd ; S. M. Elshaboury ; H. H. Selim
• 关键词：\(N\) ; body problem ; Perturbed two ; body problem ; Relativistic two ; body problem ; Multiple scales method ; PPN parameterizations
• 刊名：Astrophysics and Space Science
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：361
• 期：1
• 全文大小：883 KB
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• 作者单位：Elbaz I. Abouelmagd (1) (2) (3)
  S. M. Elshaboury (4)
  H. H. Selim (1)
  
  1. Celestial Mechanics Unit, Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan, Cairo, Egypt
  2. Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
  3. Department of Mathematics, Faculty of Science and Arts, University of Jeddah, Jeddah, Saudi Arabia
  4. Mathematics Department, Faculty of Science, Ain Shams University, Cairo, Egypt
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Astronomy
  
• 出版者：Springer Netherlands
• ISSN：1572-946X

文摘

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).