论文标题
重力探针B可以测量的还剩下的东西吗？
Is there still something left that Gravity Probe B can measure?
论文作者
论文摘要
我们对一般相对论的长期旋转陀螺仪的一般相对论的长期旋转进液对轨道陀螺仪的一般相对论长期的旋转序列进行了完整的分析和数值处理，这是由于其主要的四倍矩$ j_2 $ $ j_2 $ $ j_2 $，而无需限制陀螺仪的镜头配置和对称的范围} $ bolds $ bolds $ bold的范围。中央身体。我们将结果应用于过去的太空重力探针B（GP-B）任务，通过找到其旋转偏斜$δ$的世俗速率，可能大于$ \ lyssim 30-40 \，\ mathrm {milliarcseconds \ per \ per \ per \ per year \ per， $ f_0 $。我们的分析计算和同时集成了自旋4向量和陀螺仪运动方程的平行传输方程，这证实了这一发现。对于GP-B，测量旋转降低率的平均误差为$σ^\ mathrm {gp-b} _ {\dotδ} = 18.3 \，\ Mathrm {mas \，yr}^{ - 1} $。我们还计算了由主要的角动量$ \ boldsymbol j $引起的重力旋转进动的一般分析表达式。鉴于它们的普遍性，我们的结果也可以扩展到其他感兴趣的天文学和天体物理场景，例如，旋转的银河系超级质量黑洞，靠近父颗星星的恒星，托有紧凑型明星核心的系外行星。
We perform a full analytical and numerical treatment, to the first post-Newtonian (1pN) order, of the general relativistic long-term spin precession of an orbiting gyroscope due to the mass quadrupole moment $J_2$ of its primary without any restriction on either the gyro's orbital configuration and the orientation in space of the symmetry axis $\boldsymbol{\hat{k}}$ of the central body. We apply our results to the past spaceborne Gravity Probe B (GP-B) mission by finding a secular rate of its spin's declination $δ$ which may be as large as $\lesssim 30-40\,\mathrm{milliarcseconds\,per\,year\,(\mathrm{mas\,yr}^{-1}})$, depending on the initial orbital phase $f_0$. Both our analytical calculation and our simultaneous integration of the equations for the parallel transport of the spin 4-vector and of the geodesic equations of motion of the gyroscope confirm such a finding. For GP-B, the reported mean error in measuring the spin's declination rate amounts to $σ^\mathrm{GP-B}_{\dotδ}=18.3\,\mathrm{mas\,yr}^{-1}$. We also calculate the general analytical expressions of the gravitomagnetic spin precession induced by the primary's angular momentum $\boldsymbol J$. In view of their generality, our results can be extended also to other astronomical and astrophysical scenarios of interest like, e.g., stars orbiting galactic supermassive black holes, exoplanets close to their parent stars, tight binaries hosting compact stellar corpses.
