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Comparison and analysis on lunar rotation with lunar gravity field models

机译：月球重力场模型的月球旋转的比较与分析

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Understanding the structure of and dynamic processes in the deep interior of planets is crucial for understanding their origin and evolution. An effective way to constrain them is through observation of rotation and subsequent simulation. In this paper, a numerical model of the Moon’s rotation and orbital motion is developed based on previous studies and implemented independently. The Moon is modeled as an anelastic body with a liquid core. The equations of the rotation were nonlinear and the Euler angles are cross coupled. We solve them numerically via the Runge-Kutta-Fehlberg (RKF) and multi-steps Adams-Bashforth-Moulton (ABM) predictor-corrector numerical integration. We have found that adequate accuracy is maintained by taking twelve steps per day using eleventh differences in the integrating polynomial. The lunar orbital and rotational equations are strongly coupled, so we integrated the rotation and motion simultaneously. We refer to other planetary informations from the newest planetary and lunar ephemeris INPOP17a, which is reported had fitted the longest LLR (Lunar Laser Ranging) observation data. Using the model GL660B from GRAIL (Gravity Recovery and Interior Laboratory) mission, we firstly compare our numerical results with the INPOP17a to prove the reasonability of our model. After that we apply the lunar gravity model CEGM02 determined from Chang’E-1 mission and SGM100h from SELENE mission to our model, the difference between results from CEGM02 and GL660B are less than ? 0.20 ～ 0.15 $-0.20 sim0.15$ arc-second, and ? 0.25 ～ 0.20 $-0.25 sim0.20$ arc-second for GL660B and SGM100h. Compared to SGM100h, the results show that the low degree and order coefficients (less than 6 from this paper) of lunar gravity field were improved in CEGM02 as expected. It is the first time to demonstrate that these models can be applied to lunar rotation model. These results manifest that a development of the gravity field measure will help us to know the rotation motion more precisely.
机译：了解行星深度内部的结构和动态过程对于了解其起源和演化至关重要。通过观察旋转和随后的模拟来限制它们的有效方法。在本文中，基于先前的研究开发了月球旋转和轨道运动的数值模型，独立实施。月球以液体核心为一个凹凸式体型。旋转的等式是非线性的，并且欧拉角是交叉耦合的。我们通过Trage-Kutta-Fehlberg（RKF）和多步骤Adams-Bashforth-Moulton（ABM）预测器校正器数值集成来数字地解决了它们。我们发现，通过使用多项式的第十一差异每天服用12个步骤，维持足够的准确性。月球轨道和旋转方程强烈耦合，因此我们同时整合旋转和运动。我们指的是来自最新行星和月球故事会INPOP17A的其他行星信息，报告拟合了最长的LLR（月球激光测距）观察数据。使用GL660B型GL660B从Grail（重力恢复和内部实验室）使命中，我们首先将我们的数值结果与InPOP17A进行了比较，以证明我们模型的合理性。之后，我们将从Selene任务到我们的模型中的Chang'e-1任务和SGM100H确定的月球重力模型CEGM02，CEGM02和GL660B的结果之间的差异小于？ 0.20〜0.15 $ -0.20 SIM0.15 $弧秒，又？ 0.25〜0.20 $ -0.25 SIM0.20 $弧秒用于GL660B和SGM100H。与SGM100H相比，结果表明，由于预期的CEGM02，在CEGM02中改善了月球重力场的低度和订单系数（来自本文的纸张）的低度和订单系数。这是第一次证明这些模型可以应用于月球旋转模型。这些结果表明，重力场测量的发展将有助于我们更精确地了解旋转运动。

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