重力探测器B还能测量到什么吗？
Is there still something left that Gravity Probe B can measure?
摘要：
我们进行了全面的分析和数值处理，第一后牛顿（1 pN）的顺序，广义相对论长期自旋进动的轨道陀螺仪由于质量四极矩$J_2$的主要没有任何限制的陀螺仪的轨道配置和在空间中的对称轴$\boldsymbol{\hat{k}}$的中心体的取向。我们将我们的结果应用到过去的星载重力探测器B（GP-B）的任务，通过寻找其自旋的deconstructionPDMATHABMO的长期率可能是大的$\lesssim 30-40\,\mathrm{milliarcseconds\,per\,year\,(\mathrm{mas\,yr}^{-1}})$，取决于初始轨道相位$f_0$。我们的分析计算和我们的同步积分方程的平行运输的自旋4-矢量和测地线方程的陀螺仪的运动证实了这样的发现。对于GP-B，测量尾旋下降率的平均误差为$σ^\mathrm{GP-B}_{\dotδ}=18.3\,\mathrm{mas\,yr}^{-1}$。我们还计算了由质点角动量$\boldsymbol J$引起的重磁自旋进动的一般解析表达式。考虑到它们的普遍性，我们的结果也可以扩展到其他天文和天体物理场景，例如，围绕银河系超大质量黑洞运行的恒星，靠近其母星的系外行星，拥有紧凑恒星尸体的紧密双星。
英文摘要：
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.
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