相對論框架下月球自轉(zhuǎn)的數(shù)值模擬
發(fā)布時(shí)間：2018-12-13 17:01
【摘要】：月球自古以來就是各個(gè)時(shí)代科學(xué)家主要的研究對象,通過對月球運(yùn)動的研究,人們逐漸建立了太陽系中天體運(yùn)動的模型。同時(shí)正是基于對月球的研究,牛頓建立萬有引力定律(月球是重要驗(yàn)證)。歷史上許多著名的科學(xué)家都對月球進(jìn)行了很多的研究,也正是對于月球的研究,拉普拉斯等人建立了天體力學(xué)的一般理論�，F(xiàn)在,隨著激光測月技術(shù)的不斷發(fā)展人們對月球的軌道運(yùn)動和自轉(zhuǎn)運(yùn)動有了更深層次的了解。月球的自轉(zhuǎn)運(yùn)動尤其是月球運(yùn)動中的一個(gè)重要的研究課題,由于月球自轉(zhuǎn)運(yùn)動和軌道運(yùn)動的耦合非常弱,所以對于月球自轉(zhuǎn)的研究有助于我們更好的研究月球的內(nèi)部結(jié)構(gòu)。Kiloner等人在2010年建立了相對論框架下剛體地球的自轉(zhuǎn)理論。他們不僅完善了剛體的后牛頓的一般方程,還著重考慮了如何計(jì)算后牛頓力矩,相對論慣性矩,如何處理多個(gè)相對論參考系,不同的時(shí)間系統(tǒng)以及相應(yīng)的物理量的尺度化問題。通過該理論,我們可以在嚴(yán)格的相對論框架下計(jì)算月球的自轉(zhuǎn),同時(shí)也能檢驗(yàn)愛因斯坦的引力理論。本文首先概述了在一階后牛頓精度下,用來描述引力N體問題的DamourSoffel-Xu(DSX)體系,包括全局參考系和局部參考系的定義和多極矩展開的思想,以及質(zhì)心運(yùn)動方程和自轉(zhuǎn)運(yùn)動方程。DSX已經(jīng)被國際天文聯(lián)合會接受為研究太陽系中天體運(yùn)動相對論效應(yīng)的基本理論。在第二部分我們介紹了在牛頓框架下前人是如何研究月球自轉(zhuǎn)動力學(xué)的,包括三個(gè)歐拉角的定義,歐拉方程的建立。我們使用球諧函數(shù)(等價(jià)于對稱無跡張量)對引力勢進(jìn)行了展開,討論了有形狀的兩個(gè)天體之間的相互作用。最后給出了引力場中剛體自轉(zhuǎn)的方程。在第四章,我們首先建立了一個(gè)運(yùn)動學(xué)非旋轉(zhuǎn)的月心天球參考系(SCRS),然后給出了月心時(shí)(TCS)和太陽系質(zhì)心時(shí)(TCB)的變換關(guān)系,隨后我們在SCRS參考系中寫出了月球自轉(zhuǎn)的后牛頓運(yùn)動方程,并對它進(jìn)行了數(shù)值積分。我們計(jì)算了包括后牛頓力矩,測地歲差和引力磁的總的相對論修正對月球自轉(zhuǎn)的影響,發(fā)現(xiàn)了兩個(gè)主周期18.6年和80.1年,此外我們也分析了由于月球引力場的四階球諧系數(shù)和五階球諧系數(shù)引起的自旋軸的進(jìn)動,主要的進(jìn)動周期分別為27.3天,2.9年,18.6年和80.1年。最后一章,我們對工作中存在的問題做了簡要地分析,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.
【學(xué)位授予單位】：上海大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：P184.41
本文編號：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.
【學(xué)位授予單位】：上海大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：P184.41
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