Intro
Preface
Introduction
Orbital Dynamics in the Solar System
Two Dynamical Systems in the Orbital Dynamics
Mathematical Models for Satellite Motion: The Perturbed Two-Body Problem [1-8]
The Two-Body Problem and Kepler Orbit
The Method of Solving the Perturbed Two-Body Problem
The Perturbed Restricted Three-Body Problem in the Motion of Deep-Space Prober
The Restricted Three-Body Problem for Circular and Elliptical Motions [9-12]
Models for the Restricted N-body Problem and the Perturbed Restricted Three-Body Problem [13, 14]

The Restricted Problem of (n + k)-Bodies [15, 16]
General Restricted Three-Body Problem
References
Contents
About the Author
1 Selections and Transformations of Coordinate Systems
1.1 Time Systems and Julian Day [1, 2]
1.1.1 Selection of Standard Time
1.1.2 Time Reference Systems
1.1.3 Julian Day
1.2 Space Coordinate Systems [2-6]
1.3 Earth's Coordinate Systems [2, 6-10]
1.3.1 The Realization of the Dynamical Reference System and J2000.0 Mean Equatorial Reference System
1.3.2 The Intermediate Equator and Three Related Datum Points

1.3.3 Three Geocentric Coordinate Systems
1.3.4 Transformation of the Earth-Fixed Coordinate System O-XYZ and the Geocentric Celestial Coordinate System O-xyz
1.3.5 Relationship Between the IAU 1980 Model and the IAU 2000 Model
1.3.6 The Complicity in the Selection of Coordinate System Due to the Wobble of Earth's Equator
1.3.7 Coordinate Systems Related to Satellite Measurements, Attitudes, and Orbital Errors
1.4 The Moon's Coordinate Systems
1.4.1 Definitions of the Three Selenocentric Coordinate Systems [6]
1.4.2 The Moon's Physical Libration

1.4.3 Transformations Between the Three Selenocentric Coordinate Systems
1.5 Planets' Coordinate Systems
1.5.1 Definitions of Three Mars-Centric Coordinate Systems
1.5.2 Mars's Precession Matrix
1.5.3 Transformation of the Mars-Centric Equatorial Coordinate System and the Mars-Fixed Coordinate System
1.5.4 Transformation of the Geocentric Coordinate System and the Mars-Centric Coordinate System
1.5.5 An Explanation of the Application of the IAU 2000 Orientation Models of Celestial Bodies
References
2 The Complete Solution for the Two-Body Problem

2.1 Six Integrals of the Two-Body Problem
2.1.1 The Angular Momentum Integral (the Areal Integral)
2.1.2 The Orbital Integral in the Motion Plane and the Vis Viva Formula
2.1.3 The Sixth Motion Integral: Kepler's Equation
2.2 Basic Formulas of the Elliptical Orbital Motion
2.2.1 Geometric Relationships of the Orbital Elements in the Elliptical Motion
2.2.2 Expressions of the Position Vector ""0245r and Velocity
2.2.3 Partial Derivatives of Some Variables with Respect to Orbital Elements
2.2.4 Derivatives of M, E, and F with Respect to Time t