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引用次数: 0
摘要
摘要 为了提高轨道运动和前冲预测的准确性，引入了考虑广义相对论效应的 vis-viva 公式的修改。更新后的方程在牛顿条件下简化为传统的 vis-viva 方程，是比传统方程更精确的天体动力学工具。初步模拟结果表明，修改后的 vis-viva 公式具有应用于更复杂 n 体系统的潜力。这种方法假定了球面对称性；不过，在未来的研究中可以消除这一限制。这项研究是连接经典力学和相对论力学的关键一步，因此对天体动力学领域做出了重要贡献。
General relativistic approach to the vis-viva equation on Schwarzschild metric
Abstract
A modification to the vis-viva equation that accounts for general relativistic effects is introduced to enhance the accuracy of predictions of orbital motion and precession. The updated equation reduces to the traditional vis-viva equation under Newtonian conditions and is a more accurate tool for astrodynamics than the traditional equation. Preliminary simulation results demonstrate the application potential of the modified vis-viva equation for more complex n-body systems. Spherical symmetry is assumed in this approach; however, this limitation could be removed in future research. This study is a pivotal step toward bridging classical and relativistic mechanics and thus makes an important contribution to the field of celestial dynamics.
期刊介绍：
General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation.
It welcomes in particular original articles on the following topics of current research:
Analytical general relativity, including its interface with geometrical analysis
Numerical relativity
Theoretical and observational cosmology
Relativistic astrophysics
Gravitational waves: data analysis, astrophysical sources and detector science
Extensions of general relativity
Supergravity
Gravitational aspects of string theory and its extensions
Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations
Quantum field theory in curved spacetime
Non-commutative geometry and gravitation
Experimental gravity, in particular tests of general relativity
The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.
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