发表机构
Institute of Planetary Geodesy - Lohrmann Observatory, Technical University of Dresden（德累斯顿工业大学行星大地测量研究所-洛尔曼天文台）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对源与观测者距太阳系天体有限距离的情况，在1PN和1.5PN近似下推导光线偏转的简化表达式，可用于亚微角秒精度的天体测量。
AI 中文摘要
本文研究了在源和观测者距静止的太阳系天体为有限距离的情况下，光线信号穿过该太阳系天体引力场时的偏转效应。假设观测者位于地球附近，例如日地系统的拉格朗日点L2处，而天体光源的空间位置是任意的。天体外部的引力场由其完整的随时间变化的质量多极矩和自旋多极矩描述，因此这些引力天体可以具有任意形状、内部结构和旋转运动。在后牛顿（PN）方案的1PN和1.5PN近似下，确定了观测者位置处光线轨迹的单位切向量。得到了该单位切向量的简化表达式，其中忽略了所有在源、天体和观测者的所有天体测量构型下对光线偏转的总贡献小于10纳弧秒的项。研究表明，对于轴对称天体，光线的单位切向量以及光线偏转可由切比雪夫多项式表示。这一特性使得可以确定天体引力场中光线偏转效应，直至质量多极矩和自旋多极矩的任意阶次。研究还表明，当源和观测者位于距天体无限远的空间位置时，对应的总光线偏转角是光线偏转效应的上限。这些研究旨在实现亚微角秒精度级别的天体测量测量。
英文摘要
The effect of deflection of a light signal that propagates through the gravitational field of a solar system body at rest is considered in the case that the source and the observer are at a finite distance from the body. The observer is assumed to be located somewhere nearby the Earth, for instance at Lagrange point L2 of the Sun-Earth system, while the spatial position of the celestial light source is arbitrary. The gravitational fields in the exterior of the bodies are described by the full set of time-dependent mass-multipoles and spin-multipoles of these bodies. So the gravitating bodies can be of arbitrary shape, inner structure and rotational motion. The unit tangent vector of the light trajectory at the position of the observer is determined in the 1PN and 1.5PN approximation of the post-Newtonian (PN) scheme. A simplified expression for the unit tangent vector is obtained, where all terms are neglected that together contribute less than 10 nano-arcseconds in light deflection for all astrometric configurations between source, body and observer. It is shown that in the case of an axi-symmetric body the unit tangent vector of the light ray as well as the light deflection are given in terms of Chebyshev polynomials. This fact allows for determining the effect of light deflection in the gravitational fields of the bodies up to any order of the mass-multipoles and spin-multipoles. It is shown that the total light deflection, that is the angle of light deflection where source and observer are located at infinite spatial distance from the body, represents an upper limit of the effect of light deflection. These investigations are aiming at astrometric measurements on the sub-micro-arcsecond level of accuracy.
Comments40 pages, 2 figures, corrections made in Eqs.(139 - (141) and in Eq.(I15)
Journal refPhysical Review D 114 (2026) 044045
