Fundamentals of Classical Astrodynamics and Applications

This 2-3 Day course focuses on the fundamental problems and applications of classical astrodynamics.


This course presents the fundamental principles of classical astrodynamics and applications. It is intended for GNC engineers, spacecraft systems engineers, space mission designers, technical managers, and graduate students, who are interested in a comprehensive introduction to the classical astrodynamics problems, such as the two-body problem, Kepler’s problem, Lambert’s problem, angles-only initial orbit determination problem, circular restricted three-body problem, and orbit perturbations. This course is based on the instructor’s two AIAA textbooks: “Space Vehicle Dynamics and Control (2nd edition, 2008)” and Space Vehicle Guidance, Control, and Astrodynamics (2015),”with additional new materials on emerging astrodynamical topics. This course will complement AIAA’s other on-demand course: “Fundamentals of Space Vehicle Guidance, Control, and Astrodynamics.”

What You Will Learn

· The fundamentals of classical orbital dynamics and modern computational astrodynamics

· The basic principles of orbital transfer, intercept, and rendezvous guidance problems

· Various astrodynamical methods required for the successful development of advanced space systems and complex space missions

Key Course Topics

· Classical Two-Body Problem

· Kepler’s Problem and Its Solution via Universal Variables

· Lambert’s Problem and its Various Computational Solutions; Lambert Guidance

· Angles-Only Initial Orbit Determination (IOD) Problem and Numerical Examples

· Circular Restricted Three-Body Problem (CR3BP); Lagrange Points; Halo Orbits

· Circular and Elliptical Clohessy-Wiltshir-Hill (CWH) Relative Equations of Motion

· Orbital Transfer, Intercept, and Rendezvous Guidance Problems

· Vinti’s Analytical/Computational Method for J2, J3, and J4 Effects

· Perturbed Orbit Simulation of LEO and GEO Satellites

· Close-Proximity Orbit Simulation around an Irregular-Shaped Asteroid

· See detailed outline below

Who Should Attend

This course is intended for GNC/AOCS engineers and researchers, space mission designers, space systems engineers, and graduate students, who want to enhance their basic understanding of classical astrodynamics. This introductory course focuses on the basic physical concepts and mathematical tools required for the analysis and design of advanced space missions and GNC systems of space vehicles.

Course Information:
Type of Course: Instructor-Led Short Course
Course Level: Intermediate/Advanced
Course Length: 2 or 3 days
AIAA CEU's available: Yes

This course is also available as an on-demand course. Register here.


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(2nd 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.


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