Spherical Harmonic Analysis of Gravitational Curvatures and Its Implications for Future Satellite Missions
Spherical Harmonic Analysis of Gravitational Curvatures and Its Implications for Future Satellite Missions
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DOI：
10.1007/s10712-016-9368-0
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发表时间：
2016-03
影响因子：
4.6
通讯作者：
M. Šprlák;P. Novák;M. Pitoňák
中科院分区：
文献类型：
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作者：
M. Šprlák;P. Novák;M. Pitoňák
在这项研究中，我们假设的引力曲率张量，即张量的三阶方向导数的地球引力位，是可观察的卫星高度。这样的张量由十个不同的分量组成，即重力曲率，它们可以组合成垂直-垂直-垂直、垂直-垂直-水平、垂直-水平-水平和水平-水平-水平重力曲率。首先，我们研究了引力曲率的谱性质。其次，我们推导了四种引力曲率球谐分析的新求积公式，并给出了相应的解析误差模型。第三，研究了用差分加速度计观测引力曲率的仪器的要求。结果表明，测量三阶方向导数的重力位提出了非常高的要求，部署的加速度计的精度超出了现有的传感器的限制。例如，对于与GOCE使命类似的轨道参数和性能，观测三阶方向导数需要噪声级为Hz的加速度计。
In this study we assume that a gravitational curvature tensor, i.e. a tensor of third-order directional derivatives of the Earth’s gravitational potential, is observable at satellite altitudes. Such a tensor is composed of ten different components, i.e. gravitational curvatures, which may be combined into vertical–vertical–vertical, vertical–vertical–horizontal, vertical–horizontal–horizontal and horizontal–horizontal-horizontal gravitational curvatures. Firstly, we study spectral properties of the gravitational curvatures. Secondly, we derive new quadrature formulas for the spherical harmonic analysis of the four gravitational curvatures and provide their corresponding analytical error models. Thirdly, requirements for an instrument that would eventually observe gravitational curvatures by differential accelerometry are investigated. The results reveal that measuring third-order directional derivatives of the gravitational potential imposes very high requirements on the accuracy of deployed accelerometers which are beyond the limits of currently available sensors. For example, for orbital parameters and performance similar to those of the GOCE mission, observing third-order directional derivatives requires accelerometers with the noise level ofHz.