Fundamentals of Astrodynamics for Space Missile Defense

Fundamentals of Astrodynamics for Space Missile Defense


Image Courtesy of Lockheed Martin

Instructed by Bong Wie, Professor Emeritus of Aerospace Engineering at Iowa State University

  • This course introduces the fundamental problems of classical astrodynamics, such as the two-body problem, Kepler’s problem, Lambert’s problem, and orbit perturbations    
  • This course will include astrodynamical application examples to enhance the learning experience: ballistic missile and lunar trajectories; orbital transfer, intercept, and rendezvous guidance problems; orbit analysis and simulation of LEO and GEO satellites; hypersonic entry guidance and counter hypersonics
  • It will further explore the technically challenging problem of developing a space-based missile defense system (e.g. the Golden Dome).
  • All students will receive an AIAA Certificate of Completion at the end of the course

This course introduces the fundamental principles of classical astrodynamics and various astrodynamical application examples including ballistic missile trajectories, hypersonic entry guidance and space-based intercept missile guidance. It is intended for aerospace GNC engineers, space mission designers, spacecraft systems engineers, technical managers, and graduate students, who are interested in a comprehensive overview of classical astrodynamics as applied to space missile defense. 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 timely emerging topics such as hypersonic entry guidance and space-based missile guidance.

WHAT YOU WILL LEARN

  • The fundamentals of classical orbital dynamics and modern computational astrodynamics
  • The orbital transfer, intercept, and rendezvous guidance problems
  • A variety of astrodynamical guidance laws required for the successful development of a space-based interceptor missile system (e.g. the Golden Dome).

KEY COURSE TOPICS

  • Classical Two-Body Problem
  • Kepler’s Problem and Its Solution via Universal Variables
  • Lambert’s Problem and itsVarious Computational Solutions; Lambert Guidance
  • Perturbed Orbit Simulations of LEO and GEO Satellites
  • Clohessy-Wiltshir-Hill (CWH) Relative Equations of Motion
  • Missile GN&C Systems and Guidance Laws
  • Orbital Transfer, Intercept, and Rendezvous
  • Guidance Problems
  • Hypersonic Entry Guidance and Counter Hypersonics
  • Interceptor Missile Guidance in Space

WHO SHOULD ATTEND
This course is intended for aerospace GNC engineers and researchers, space mission designers, space systems engineers, technical managers, and graduate students, who want to enhance their basic understanding of orbital dynamics and astrodynamical guidance, especially as applied to the technically challenging problem of designing a space-based missile defense system (e.g. the Golden Dome). 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-based intercept missiles.

COURSE INFORMATION
Type of Course: Instructor-Led Short Course
Course Level: Fundamentals
Course Length: 2 days
AIAA CEU’s available: Yes

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

Outline

Class 1: Two-Body Problem

1.1       Constants of Two-Body Problem and Orbit Equation

1.2       Eccentric Anomaly and Kepler’s Equation

1.3       Orbit Determination and Prediction

1.4       Applications: Ballistic Missiles, Lunar Trajectories, etc.

 

Class 2: Kepler’s Problem

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)

 

 Class 3: Lambert’s Problem and Solutions

3.1       Lambert’s Problem; Lambert Guidance

3.2       Lambert Theorem

3.3       Classical Solution of Lambert’s Problem

3.4       Universal Variables Solution

3.5       Gauss/Battin Methods

3.6       Gooding’s Method

3.7       Sun’s Method

3.8        A New Exact Solution to Lambert’s Problem (A. Negrete and O. Abdelkhalik, 2024)

 

Class 4: Orbit Perturbations

4.1       Earth’s Oblateness Effect

4.2       Orbit Analysis and Simulation of LEO and GEO Satellites

4.3       Clohessy-Wiltshir-Hill (CWH) Relative Equations of Motion

 

Class 5: Missile Guidance and Control 

5.1       Introduction to Missile GN&C Systems

5.2       PN Guidance and Its variants

5.3       Predictive/Explicit Guidance

5.4       Optimal Feedback Guidance

5.5       ZEM/ZEV Feedback Guidance and Its Variants

5.6       Impact Time Control (ITC) Guidance

5.7       Impact Time and Angle Control (ITAC) Guidance

 

Class 6: Orbital Transfer, Intercept, and Rendezvous Guidance

6.1       Orbital Maneuver via Two-Impulse Hohmann Transfer

6.2       Circular CWH Equations of Motion

6.3         Orbital Guidance and Control Examples

6.4       Elliptical CWH Equations of Motion

 

Class 7: Hypersonic Entry Guidance and Counter Hypersonics

7.1       Introduction to Hypersonic Entry Guidance

7.2       Case Study Examples

7.3       Entry Guidance for Avoiding No-Fly Zones

7.4       Introduction to Counter Hypersonics

 

Class 8: Space-Based Interceptor Missile Guidance     

8.1       Introduction to the ‘Golden Dome’ Missile Defense Shield

8.2       Introduction to Space Missile Guidance

8.3       Low-Thrust Orbital Transfer via ZEM/ZEV Feedback Guidance

8.4       Orbital Intercept/Rendezvous via Differential Geometry Guidance

8.5       Orbital Intercept/Rendezvous via ZEM/ZEV Feedback Guidance

8.6       Course Summary

Materials
Instructors

Bong Wie is Professor Emeritus 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. In early 2010s, he was 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). During late 2010s, his research focused on further developing the ZEM/ZEV feedback guidance strategies for robotic/human Mars precision powered descent & landing with hazard avoidance and retargeting. He is currently exploring technically challenging, guidance and control problems of hypersonic reentry vehicles and an advanced guidance problem of missiles with precision impact time and angle control (ITAC) requirements. For 2018-2023, he was co-Editor of Astrodynamics, an international journal established in 2018. The following on-demand short courses by Dr. Wie are available from AIAA:

 

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