相对论框架下月球自转的数值模拟
发布时间：2018-12-13 17:01
【摘要】：月球自古以来就是各个时代科学家主要的研究对象,通过对月球运动的研究,人们逐渐建立了太阳系中天体运动的模型。同时正是基于对月球的研究,牛顿建立万有引力定律(月球是重要验证)。历史上许多著名的科学家都对月球进行了很多的研究,也正是对于月球的研究,拉普拉斯等人建立了天体力学的一般理论。现在,随着激光测月技术的不断发展人们对月球的轨道运动和自转运动有了更深层次的了解。月球的自转运动尤其是月球运动中的一个重要的研究课题,由于月球自转运动和轨道运动的耦合非常弱,所以对于月球自转的研究有助于我们更好的研究月球的内部结构。Kiloner等人在2010年建立了相对论框架下刚体地球的自转理论。他们不仅完善了刚体的后牛顿的一般方程,还着重考虑了如何计算后牛顿力矩,相对论惯性矩,如何处理多个相对论参考系,不同的时间系统以及相应的物理量的尺度化问题。通过该理论,我们可以在严格的相对论框架下计算月球的自转,同时也能检验爱因斯坦的引力理论。本文首先概述了在一阶后牛顿精度下,用来描述引力N体问题的DamourSoffel-Xu(DSX)体系,包括全局参考系和局部参考系的定义和多极矩展开的思想,以及质心运动方程和自转运动方程。DSX已经被国际天文联合会接受为研究太阳系中天体运动相对论效应的基本理论。在第二部分我们介绍了在牛顿框架下前人是如何研究月球自转动力学的,包括三个欧拉角的定义,欧拉方程的建立。我们使用球谐函数(等价于对称无迹张量)对引力势进行了展开,讨论了有形状的两个天体之间的相互作用。最后给出了引力场中刚体自转的方程。在第四章,我们首先建立了一个运动学非旋转的月心天球参考系(SCRS),然后给出了月心时(TCS)和太阳系质心时(TCB)的变换关系,随后我们在SCRS参考系中写出了月球自转的后牛顿运动方程,并对它进行了数值积分。我们计算了包括后牛顿力矩,测地岁差和引力磁的总的相对论修正对月球自转的影响,发现了两个主周期18.6年和80.1年,此外我们也分析了由于月球引力场的四阶球谐系数和五阶球谐系数引起的自旋轴的进动,主要的进动周期分别为27.3天,2.9年,18.6年和80.1年。最后一章,我们对工作中存在的问题做了简要地分析,并指明了后面工作的方向。
[Abstract]:Since ancient times, the moon has been the main research object of scientists of all ages. Through the study of the motion of the moon, people have gradually established the model of the celestial body movement in the solar system. At the same time, based on the study of the moon, Newton established the law of gravity (the moon is an important test). In history, many famous scientists have done a lot of research on the moon, and it is the study of the moon that Laplace and others have established the general theory of celestial mechanics. Now, with the continuous development of laser lunar survey technology, people have a deeper understanding of lunar orbit motion and rotation motion. The rotation motion of the moon, especially the motion of the moon, is an important research subject, because the coupling between the rotation motion and the orbit motion of the moon is very weak. So the study of lunar rotation is helpful for us to study the interior structure of the moon better. Kiloner et al established the rotation theory of rigid body earth under the frame of relativistic theory in 2010. They not only perfect the general equation of post-Newton of rigid body, but also consider how to calculate post-Newtonian moment, relativistic moment of inertia, how to deal with multiple relativistic reference systems, different time systems and the scaling of corresponding physical quantities. Through this theory, we can calculate the rotation of the moon under the strict relativistic frame, and we can also test Einstein's theory of gravity. This paper first summarizes the DamourSoffel-Xu (DSX) system used to describe the gravitational N-body problem in the first order post-Newton precision, including the definition of the global reference system and the local reference system and the idea of multipole moment expansion. DSX has been accepted by the International Astronomical Union as the basic theory for studying the relativistic effects of the motion of celestial bodies in the solar system. In the second part, we introduce how the previous researchers studied the dynamics of lunar rotation under Newton's framework, including the definitions of three Euler angles and the establishment of Euler's equations. In this paper, the spherical harmonic function (equivalent to symmetric unscented Zhang Liang) is used to expand the gravitational potential, and the interaction between two celestial bodies with shape is discussed. Finally, the equation of rigid body rotation in gravitational field is given. In chapter 4, we first establish a kinematic non-rotating reference system of the celestial sphere of the moon, (SCRS), and then give the transformation relationship between the (TCS) at the lunar center and the (TCB) at the centroid of the solar system. Then we write out the post-Newtonian equation of motion for the lunar rotation in the SCRS reference system and numerically integrate it. We have calculated the effects of the general relativistic corrections including post-Newtonian moment, geodesic precession and gravitational magnetism on the lunar rotation, and found two main periods of 18.6 years and 80.1 years. In addition, we also analyze the precession of the spin axis caused by the fourth order spherical harmonic coefficient and the fifth order spherical harmonic coefficient of the lunar gravitational field. The main precession periods are 27.3 days, 2.9 days, 18.6 years and 80.1 years, respectively. In the last chapter, we make a brief analysis of the problems in the work and point out the direction of the later work.
【学位授予单位】：上海大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P184.41
本文编号：2376875
[Abstract]:Since ancient times, the moon has been the main research object of scientists of all ages. Through the study of the motion of the moon, people have gradually established the model of the celestial body movement in the solar system. At the same time, based on the study of the moon, Newton established the law of gravity (the moon is an important test). In history, many famous scientists have done a lot of research on the moon, and it is the study of the moon that Laplace and others have established the general theory of celestial mechanics. Now, with the continuous development of laser lunar survey technology, people have a deeper understanding of lunar orbit motion and rotation motion. The rotation motion of the moon, especially the motion of the moon, is an important research subject, because the coupling between the rotation motion and the orbit motion of the moon is very weak. So the study of lunar rotation is helpful for us to study the interior structure of the moon better. Kiloner et al established the rotation theory of rigid body earth under the frame of relativistic theory in 2010. They not only perfect the general equation of post-Newton of rigid body, but also consider how to calculate post-Newtonian moment, relativistic moment of inertia, how to deal with multiple relativistic reference systems, different time systems and the scaling of corresponding physical quantities. Through this theory, we can calculate the rotation of the moon under the strict relativistic frame, and we can also test Einstein's theory of gravity. This paper first summarizes the DamourSoffel-Xu (DSX) system used to describe the gravitational N-body problem in the first order post-Newton precision, including the definition of the global reference system and the local reference system and the idea of multipole moment expansion. DSX has been accepted by the International Astronomical Union as the basic theory for studying the relativistic effects of the motion of celestial bodies in the solar system. In the second part, we introduce how the previous researchers studied the dynamics of lunar rotation under Newton's framework, including the definitions of three Euler angles and the establishment of Euler's equations. In this paper, the spherical harmonic function (equivalent to symmetric unscented Zhang Liang) is used to expand the gravitational potential, and the interaction between two celestial bodies with shape is discussed. Finally, the equation of rigid body rotation in gravitational field is given. In chapter 4, we first establish a kinematic non-rotating reference system of the celestial sphere of the moon, (SCRS), and then give the transformation relationship between the (TCS) at the lunar center and the (TCB) at the centroid of the solar system. Then we write out the post-Newtonian equation of motion for the lunar rotation in the SCRS reference system and numerically integrate it. We have calculated the effects of the general relativistic corrections including post-Newtonian moment, geodesic precession and gravitational magnetism on the lunar rotation, and found two main periods of 18.6 years and 80.1 years. In addition, we also analyze the precession of the spin axis caused by the fourth order spherical harmonic coefficient and the fifth order spherical harmonic coefficient of the lunar gravitational field. The main precession periods are 27.3 days, 2.9 days, 18.6 years and 80.1 years, respectively. In the last chapter, we make a brief analysis of the problems in the work and point out the direction of the later work.
【学位授予单位】：上海大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P184.41
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