Fundamentals of Classical Astrodynamics and Applications

Lecture 1:  Two-Body Problem

1.1 Constants of Two-Body Problem

1.2 Orbit Equation

1.3 Kepler’s Equation

1.4 Classical Orbital Elements

Lecture 2:  Kepler’s Problem and Solutions

2.1 Kepler’s Orbit Prediction Problem

2.2 Lagrange’s f and g Functions

2.3 A Universal Variable Formulation of Time-of-Flight (TOF)

2.4 Solution of Kepler’s Problem via Universal Variables

Lecture 3:  Lambert’s Problem and Solutions I

3.1 Lambert’s Problem; Lambert Guidance

3.2 Lambert Theorem

3.3 A Classical Solution of Lambert’s Problem

3.4 Gauss/Battin Methods for Lambert’s Problem

Lecture 4:  Lambert’s Problem and Solutions II

4.1 Universal Variables Solution of Lambert’s Problem

4.2 Unified Form of TOF by Lancaster and Blanchard

4.3 Improved Solutions by Gooding and Sun

4.4 Asteroid Intercept Mission Design Examples

Lecture 5:  Angles-Only Initial Orbit Determination (IOD) Problem

5.1 Lagrange’s Formulation

5.2 Laplace’s Formulation

5.3 Gauss’ Formulation

5.4 Numerical Examples

Lecture 6:  Circular Restricted Three-Body (CR3B) Problem

6.1 CR3BP Formulation

6.2 Stability of Lagrange Points

6.3 Halo Orbits

6.4 Sub-L1 Lagrange Halo Orbit for a Solar Sail Mission

Lecture 7:  Orbit Perturbations

7.1 Gravitational Potential of an Irregular-Shaped Body

7.2 Perturbed Orbit Simulations of LEO and GEO Satellites

7.3 Close-Proximity Orbits around an Irregular-Shaped Asteroid

7.4 Vinti’s Spheroidal Method for J2, J3, and J4 Effects

Lecture 8:  Orbital Transfer, Intercept, and Rendezvous Guidance

8.1 Clohessy-Wiltshir-Hill (CWH) Equations of Motion

8.2 Elliptical CWH Equations

8.3 Orbital Transfer Guidance

8.4 Orbital Intercept and Rendezvous Guidance

Bong Wie is Professor of Aerospace Engineering at Iowa State University. He holds a B.S. in aerospace engineering from Seoul National University and a M.S. and Ph.D. in aeronautics and astronautics from Stanford University. In 2006 he received AIAA’s Mechanics and Control of Flight Award for his innovative research on advanced control of complex spacecraft such as solar sails, large flexible structures, and agile imaging satellites equipped with control moment gyros. He is the author of two AIAA textbooks: “Space Vehicle Dynamics and Control(2^nd Edition, 2008)” and “Space Vehicle Guidance, Control, and Astrodynamics (2015).” He has published 210 technical papers including 80 journal articles.He has three US patents on singularity-avoidance steering logic of control moment gyros. During the past 10 years, he has been actively involved in guidance, control, and astrodynamics research for deflecting or disrupting hazardous near-Earth objects (NEO). From 2011-2014, he was a NIAC (NASA Advanced Innovative Concepts) Fellow for developing an innovative solution to NASA’s NEO impact threat mitigation grand challenge and its flight validation mission design. His NIAC study effort has resulted in two distinct concepts for effectively disrupting hazardous asteroids with short warning time, called a hypervelocity asteroid intercept vehicle (HAIV) and a multiple kinetic-energy impactor vehicle (MKIV). His current research focuses on developing optimized two-phase ZEM/ZEV feedback guidance strategies for robotic/human Mars precision powered descent & landing with hazard avoidance and retargeting. He is also currently involved in a guidance and control research problem of Mars entry. He is co-Editor of Astrodynamics, an international journal newly established in 2018.