绝对重力仪中的有限光速修正
Correction due to finite speed of light in absolute gravimeters
摘要：
有限光速改正是绝对重力测量中最不一致的改正之一。不同作者报告的公式产生的校正分散高达8 $μ$ Gal，没有明显的原因。这个问题，虽然以前注意到，从来没有被研究过，现在的纠正，而不是严格证明假设。在本文中，我们试图修改的主题。像其他作者一样，我们使用基于信号延迟和多普勒效应的物理模型，然而，在实施模型时，我们还引入了两个与移动和静止反射器相关的时间尺度，推导出一组规则来在尺度之间切换，并建立从时间延迟或距离进展获得的轨迹失真的等效性。所得到的结果使我们能够产生准确的校正公式，为不同类型的仪器，并解释了其他作者所获得的结果的差异。我们发现，在不考虑信号延迟的情况下，由多普勒效应引起的修正量只占总修正量的$\frac23$。不一致的另一个主要来源是默认使用简化的轨迹模型。
英文摘要：
Correction due to finite speed of light is among the most inconsistent ones in absolute gravimetry. Formulas reported by different authors yield corrections scattered up to 8 $μ$Gal with no obvious reasons. The problem, though noted before, has never been studied, and nowadays the correction is rather postulated than rigorously proven. In this paper we make an attempt to revise the subject. Like other authors, we use physical models based on signal delays and the Doppler effect, however, in implementing the models we additionally introduce two scales of time associated with moving and resting reflectors, derive a set of rules to switch between the scales, and establish the equivalence of trajectory distortions as obtained from either time delay or distance progression. The obtained results enabled us to produce accurate correction formulas for different types of instruments, and to explain the differences in the results obtained by other authors. We found that the correction derived from the Doppler effect is accountable only for $\frac23$ of the total correction due to finite speed of light, if no signal delays are considered. Another major source of inconsistency was found in the tacit use of simplified trajectory models.
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