AI 中文总结
本文针对扭秤测量G时的大气牛顿噪声问题，开发了符合GUM的不确定度传播框架，推导了两种几何结构的传递函数，为未来扭秤测量的不确定度预算提供了实用方案。
AI 中文摘要
牛顿引力常数的测量仍受限于环境和仪器相关的系统误差，对这类误差的处理往往不如对仪器噪声的处理明确。其中，大气密度波动会产生无法屏蔽的重力梯度，这些梯度会直接耦合到扭秤的可观测量中，形成大气牛顿噪声。本文开发了一种符合GUM（测量不确定度表示指南）的框架，用于将这一贡献通过力矩估计器传播到扭秤测量的不确定度预算中。我们推导了两种基准几何结构的闭式空间传递函数：一种是双质量哑铃，可作为耦合上限参考；另一种是完全对称的十字形，可作为理想化的抑制极限，揭示了在抑制低阶环境耦合与保留信号响应之间的权衡。我们还将平稳相关输入与非平稳基线漂移分离，其中仅用Ornstein–Uhlenbeck过程作为前者的基准。大气压力基准表明，由此产生的背景贡献低于当前参考不确定度水平，但当系统误差底限达到百万分之一（ppm）量级时，该贡献可能变得相关。该框架为将特定站点的环境重力梯度纳入未来扭秤测量的不确定度预算提供了实用途径。
英文摘要
Measurements of Newton's gravitational constant remain limited by environmental and apparatus-dependent systematics whose treatment is often less explicit than that of instrumental noise. Among these, atmospheric density fluctuations generate unshieldable gravity gradients that couple directly to torsion-balance observables as atmospheric Newtonian noise. Here, we develop a GUM-consistent framework for propagating this contribution through the torque estimator into the uncertainty budget of torsion-balance measurements. We derive closed-form spatial transfer functions for two benchmark geometries: a two-mass dumbbell, which provides an upper-coupling reference, and a perfectly symmetric cross, which serves as an idealized rejection limit and exposes the trade-off between suppressing low-order environmental coupling and preserving signal response. We also separate stationary correlated inputs from non-stationary baseline drift, using the Ornstein--Uhlenbeck process only as a benchmark for the former. Atmospheric pressure benchmarks indicate that the resulting background contribution is below present reference uncertainty levels, but can become relevant as systematic floors approach the part-per-million regime. This framework provides a practical route for incorporating site-specific environmental gravity gradients into future torsion-balance uncertainty budgets.
Comments19 pages, 5 figures
