# Orbital Mechanics for Engineering Students

## 2nd Edition

**Authors:**Howard Curtis

**eBook ISBN:**9780080887845

**Paperback ISBN:**9781493301140

**Hardcover ISBN:**9780123747785

**eBook ISBN:**9780080970486

**Imprint:**Butterworth-Heinemann

**Published Date:**26th October 2009

**Page Count:**744

**View all volumes in this series:**Aerospace Engineering

## Table of Contents

Preface

Acknowledgments

Chapter 1 Dynamics of point masses

1.1 Introduction

1.2 Vectors

1.3 Kinematics

1.4 Mass, force and Newton’s law of gravitation

1.5 Newton’s law of motion

1.6 Time derivatives of moving vectors

1.7 Relative motion

1.8 Numerical integration

1.8.1 Runge-Kutta methods

1.8.2 Heun’s Predictor-Corrector method

1.8.3 Runge-Kutta with variable step size

Problems

List of Key Terms

Chapter 2 The two-body problem

2.1 Introduction

2.2 Equations of motion in an inertial frame

2.3 Equations of relative motion

2.4 Angular momentum and the orbit formulas

2.5 The energy law

2.6 Circular orbits (e = 0)

2.7 Elliptical orbits (0 < e < 1)

2.8 Parabolic trajectories (e = 1)

2.9 Hyperbolic trajectories (e > 1)

2.10 Perifocal frame

2.11 The lagrange coefficients

2.12 Restricted three-body problem

2.12.1 Lagrange points

2.12.2 Jacobi constant

Problems

List of Key Terms

Chapter 3 Orbital position as a function of time

3.1 Introduction

3.2 Time since periapsis

3.3 Circular orbits (e = 0)

3.4 Elliptical orbits (e < 1)

3.5 Parabolic trajectories (e = 1)

3.6 Hyperbolic trajectories (e < 1)

3.7 Universal variables

Problems

List of Key Terms

Chapter 4 Orbits in three dimensions

4.1 Introduction

4.2 Geocentric right ascension-declination frame

4.3 State vector and the geocentric equatorial frame

4.4 Orbital elements and the state vector

4.5 Coordinate transformation

4.6 Transformation between geocentric equatorial and perifocal frames

4.7 Effects of the Earth’s oblateness

4.8 Ground tracks

Problems

List of Key Terms

Chapter 5 Preliminary orbit determination

5.1 Introduction

5.2 Gibbs method of orbit determination from three position vectors

5.3 Lambert’s problem

5.4 Sidereal time

5.5 Topocentric coordinate system

5.6 Topocentric equatorial coordinate system

5.7 Topocentric horizon coordinate system

5.8 Orbit determination from angle and range measurements

5.9 Angles only preliminary orbit determination

5.10 Gauss method of preliminary orbit determination

Problems

List of Key Terms

Chapter 6 Orbital maneuvers

6.1 Introduction

6.2 Impulsive maneuvers

6.3 Hohmann transfer

6.4 Bi-elliptic Hohmann transfer

6.5 Phasing maneuvers

6.6 Non-Hohmann transfers with a common apse line

6.7 Apse line rotation

6.8 Chase maneuvers

6.9 Plane change maneuvers

6.10 Nonimpulsive orbital maneuvers

Problems

List of Key Terms

Chapter 7 Relative motion and rendezvous

7.1 Introduction

7.2 Relative motion in orbit

7.3 Linearization of the equations of relative motion in orbit

7.4 Clohessy-Wiltshire equations

7.5 Two-impulse rendezvous maneuvers

7.6 Relative motion in close-proximity circular orbits

Problems

List of Key Terms

Chapter 8 Interplanetary trajectories

8.1 Introduction

8.2 Interplanetary Hohmann transfers

8.3 Rendezvous Opportunities

8.4 Sphere of influence

8.5 Method of patched conics

8.6 Planetary departure

8.7 Sensitivity analysis

8.8 Planetary rendezvous

8.9 Planetary flyby

8.10 Planetary ephemeris

8.11 Non-Hohmann interplanetary trajectories

Problems

List of Key Terms

Chapter 9 Rigid-body dynamics

9.1 Introduction

9.2 Kinematics

9.3 Equations of translational motion

9.4 Equations of rotational motion

9.5 Moments of inertia

9.5.1 Parallel axis theorem

9.6 Euler’s equations

9.7 Kinetic energy

9.8 The spinning top

9.9 Euler angles

9.10 Yaw, pitch and roll angles

9.11 Quaternions

Problems

List of Key Terms

Chapter 10 Satellite attitude dynamics

10.1 Introduction

10.2 Torque-free motion

10.3 Stability of torque-free motion

10.4 Dual-spin spacecraft

10.5 Nutation damper

10.6 Coning maneuver

10.7 Attitude control thrusters

10.8 Yo-yo despin mechanism

10.8.1 Radial release

10.9 Gyroscopic attitude control

10.10 Gravity gradient stabilization

Problems

List of Key Terms

Chapter 11 Rocket vehicle dynamics

11.1 Introduction

11.2 Equations of motion

11.3 The thrust equation

11.4 Rocket performance

11.5 Restricted staging in field-free space

11.6 Optimal staging

11.6.1 Lagrange multiplier

Problems

List of Key Terms

Appendix A Physical data

Appendix B A road map

Appendix C Numerical intergration of the n-body equations of motion

Appendix D MATLAB® algorithms

Appendix E Gravitational potential energy of a sphere

References

Index

## Description

*Orbital Mechanics for Engineering Students, Second Edition*, provides an introduction to the basic concepts of space mechanics. These include vector kinematics in three dimensions; Newton’s laws of motion and gravitation; relative motion; the vector-based solution of the classical two-body problem; derivation of Kepler’s equations; orbits in three dimensions; preliminary orbit determination; and orbital maneuvers. The book also covers relative motion and the two-impulse rendezvous problem; interplanetary mission design using patched conics; rigid-body dynamics used to characterize the attitude of a space vehicle; satellite attitude dynamics; and the characteristics and design of multi-stage launch vehicles.

Each chapter begins with an outline of key concepts and concludes with problems that are based on the material covered. This text is written for undergraduates who are studying orbital mechanics for the first time and have completed courses in physics, dynamics, and mathematics, including differential equations and applied linear algebra. Graduate students, researchers, and experienced practitioners will also find useful review materials in the book.

## Key Features

- NEW: Reorganized and improved discusions of coordinate systems, new discussion on perturbations and quarternions
- NEW: Increased coverage of attitude dynamics, including new Matlab algorithms and examples in chapter 10
- New examples and homework problems

## Readership

Undergraduate students in aerospace, astronautical, mechanical engineering and engineering physics. Related professional aerospace and space engineering fields.

## Details

- No. of pages:
- 744

- Language:
- English

- Copyright:
- © Butterworth-Heinemann 2010

- Published:
- 26th October 2009

- Imprint:
- Butterworth-Heinemann

- eBook ISBN:
- 9780080887845

- Paperback ISBN:
- 9781493301140

- Hardcover ISBN:
- 9780123747785

- eBook ISBN:
- 9780080970486

## Ratings and Reviews

## About the Authors

### Howard Curtis Author

Professor Curtis is former professor and department chair of Aerospace Engineering at Embry-Riddle Aeronautical University. He is a licensed professional engineer and is the author of two textbooks (Orbital Mechanics 3e, Elsevier 2013, and Fundamentals of Aircraft Structural Analysis, McGraw Hill 1997). His research specialties include continuum mechanics, structures, dynamics, and orbital mechanics.

### Affiliations and Expertise

Professor Emeritus, Aerospace Engineering, Embry-Riddle Aeronautical University, Florida, USA