应用天文研究组知识库

为了进一步提高地月激光测距精度,新部署单体大孔径的激光角反射器是下一代月球角反射器的主要选择,由于单口径角反射器相比阵列式反射器面积要小,反射器指向要求更高。针对这一问题,本文在不含二面角误差的理想角反射器前提下,通过数值模拟的方法分析了角反射器的有效衍射区域随激光光束入射条件的变化规律。在忽略大气影响的简化条件下模拟了地面3个激光测月台站对新布置角反射器的观测情况,通过LevenbergMarquardt方法优化了角反射器的指向。结果表明,选择合适的指向可以将反射器有效衍射面积提高到80%以上,同时得到低纬度地面台站比高纬度台站更有利于观测的结论,提示我国应当充分利用已建成的两个低纬度激光测月台站,以期在未来地月激光测距和地月科学研究中发挥更大的作用。

Objective: Lunar laser ranging has made outstanding contributions to maintaining the earth-moon reference frame, understanding the earth-moon system, and testing general relativity theory. However, due to the influence of the moon’s apparent libration, the array corner retroreflector installed on the moon 50years ago could not determine the corner retroreflector that reflected the photons, which would introduce cm-level errors. To overcome this problem, the newly deployed single large-aperture laser corner retroreflector is the leading choice for the next generation of lunar corner cube retroreflectors(CCR). Since the single-aperture corner retroreflector has a smaller reflection area than the array type, the CCR has higher requirements for directing. In this study, we analyze the effective diffraction region of the next-generation CCR and the relationship with the laser beam incident conditions employing numerical simulation. Ignoring the influence of atmospheric and dihedral errors, the observation situation of the newly-arranged CCR by three ground stations is simulated. The CCR pointing is optimized using the Levenberg-Marquardt method. We hope that our basic strategy and findings can be helpful in the deployment of the new CCR on the lunar surface in the near future. Methods: In this study, a mathematical model with an effective diffraction region(EDR)is developed first for a retroreflector based on its geometrical structure and vector form of reflection-refraction law. Through numerical simulation, the regularity of change for EDR is analyzed. Then, we select three typical areas as the locations of the new CCR in the future, i. e. , the Chang’E-3landing area, Mare Nectaris area, and Shacklten Crater area. In terms of ground stations, three places such as GRASSE, APOLLO, and YNAO, are selected for observation. The minimal angle between the normal direction of the CCR and laser emitted by the ground station is taken as the optimizing objective. The optimization process is performed using the Levenberg-Marquardt method. In addition, the observation condition characteristics of the three ground stations are analyzed. Results and Discussions: Assuming the arrangement of the lunar reflector points to the earth’s center at date J2000. 0, the angle changes between the three specific areas selected in this study and the laser beams emitted by the ground stations are shown in Figs. 5--7. Because the distance between the earth and the moon is much larger than their radii, the angles between different lunar regions and stations on the earth are almost the same. They also have the same period, ～2190. 4days. The moon’s anomaly mainly determines this period. Mean anomaly(F)and the latitude parameter(l)are superimposed(l-F); that is, the apparent libration is the main reason for the angle change. In this paper, the Levenberg-Marquardt method is used to optimize the normal direction of the corner reflector surface. Taking the Shacklten Crater area as an example, the optimized angle is shown in Fig. 8. The maximum angle is reduced to～10°, and the corner retroreflector’s effective utilization can exceed 80％. Similar results can be obtained by calculating the normal direction of the reflective surface of the Chang’E-3landing area and the Mare Nectaris area. The disturbance period of the angle change is caused by 2l-2F, affected by the apparent libration. To further study the observational characteristics of the angular reflection of the lunar surface at different stations, we consider the effective diffraction area (the angular reflection aperture area is set to 1)cumulated monthly (27days). The observation area is the same, related to the earth-moon distance as the main influencing factor. However, for the same placement area, the lower latitude APOLLO and YNAO laser lunar station have better observation effects than the high-latitude GRASSE station. This shows that building stations in low-latitude regions of the earth can improve the efficiency of lunar laser ranging observations. Conclusions: In this study, the numerical simulation method is used to systematically analyze the changes of the effective diffraction area of the next-generation single lunar corner reflector under different laser beam incident conditions. The influence of different lunar corner retroreflector orientations on ground observations is comprehensively discussed. The Levenberg-Marquardt method is used to optimize the corner retroreflector orientations in three typical regions by simulating the real observation time. The results show that the moon’s apparent libration is the main influencing factor affecting the effective diffraction area. This effect can only be reduced by optimizing the orientation, and there is no way to eliminate it. Meanwhile, the observation efficiency of low-latitude laser lunar stations is significantly higher than that of high-latitude stations. In addition, China is located in the eastern part of Asia, forming an excellent complementary effect with the stations in European countries and the United States. The results suggest that we should fully utilize the favorable conditions at the two low-latitude stations, the 1. 2mlaser lunar ranging station of Yunnan Observatories, Chinese Academy of Sciences and the Zhuhai Tianqin laser lunar ranging station, to make significant contributions in future lunar exploration and laser ranging experiments