Numerical Simulation Of The Moon’s Rotation In A Rigorous Relativistic Framework

Moon has been an important research object for scientists since ancient time. People construct the geometrical model of the universe through the studying of the Moon. Based on the motion of the Moon, Newton find the law of Universal Gravitation. There are also other famous scientists including Laplace research the Moon and construct the general theory of celestial mechanics. Now, with the improvement of the technology of lunar laser ranging, we can know more about the Moon, such as the high accuracy data of the orbital and rotational motion of the Moon. The physical libration of the Moon is an important research subject in the motion of the Moon, because of the weakly couple of the orbital and rotational motion of the Moon, we can only study the libration of the Moon to know its internal physical properties.Recently, Klioner et al have established a rigid Earth’s rotation theory in the framework of general relativity. They not only complete the post-Newtonian rotational equations of the rigid body, but also consider how to compute the post-newtonian torque, relativistic inertial torque. They also discuss how to deal with different relativistic reference systems,time transformation, and relativistic scaling due to the conversion of those relativistic systems. We can use this theory to calculate the rotation of the Moon in a rigorous relativistic framework and also to test the Einstein’s gravity theory.In this Thesis, we firstly introduce the Damour-Soffel-Xu framework which treat the general-relativistic celestial mechanic of systems of N arbitrarily composed bodies in the first post-Newtonian accuracy. Their theory include the definition of the global and local reference systems, the ideal of multiple expansion, the equations of the motion of the center of the mass and the rotational equations of motion. This theory have also been accepted by International Astronomical Union which regard it as the fundamental theory to study the relativistic effects in the solar systems. In the second part of Thesis, we explain how to deal with the rotation of the Moon in the Newtonian framework including the definition of three Euler angles and Euler equations which describe the rotation of rigid body. Due to the symmetry of gravitational potential, we expand it in terms of Spherical Harmonics(or symmetric and trace-free Cartsian tensors). finally, we discuss how to write the Euler equations in the gravitational field, especially the figure-figure interaction between the rigid body. In chapter 4, we construct a kinematically non-rotating reference system named the Selenocentric Celestial Reference System(SCRS) and give the time transformation between the Selenocentric Coordinate Time(TCS) and Barycentric Coordinate Time(TCB). The post-Newtonian equations of the Moon’s rotation are written in the SCRS,and they are integrated numerically. We calculate the correction to the rotation of the Moon due to total relativistic torque which includes post-Newtonian and gravitomagnetic torques, as well as geodetic precession. We find two dominant periods ofassociated with this correction: 18.6 years and 80.1 years. In addition, the precession of the rotating axes caused by fourth-degree and fifth-degree harmonics of the Moon is also analyzed, and we have found that the main periods of this precession are 27.3 days, 2.9 years, 18.6 years and80.1 years. Chapter 5 contains the conclusion and gives the research direction in the future.