More New and Used

from Private Sellers

# Orbital Mechanics

**by**Prussing, John E.; Conway, Bruce A.

2nd

### 9780199837700

0199837708

Hardcover

12/12/2012

Oxford University Press, USA

## Questions About This Book?

Why should I rent this book?

Renting is easy, fast, and cheap! Renting from eCampus.com can save you hundreds of dollars compared to the cost of new or used books each semester. At the end of the semester, simply ship the book back to us with a free UPS shipping label! No need to worry about selling it back.

How do rental returns work?

Returning books is as easy as possible. As your rental due date approaches, we will email you several courtesy reminders. When you are ready to return, you can print a free UPS shipping label from our website at any time. Then, just return the book to your UPS driver or any staffed UPS location. You can even use the same box we shipped it in!

What version or edition is this?

This is the 2nd edition with a publication date of 12/12/2012.

What is included with this book?

- The
**New**copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc. - The
**Used**copy of this book is not guaranteed to include any supplemental materials. Typically, only the book itself is included. - The
**Rental**copy of this book is not guaranteed to include any supplemental materials. You may receive a brand new copy, but typically, only the book itself.

## Summary

One of the major challenges of modern space mission design is the orbital mechanics -- determining how to get a spacecraft to its destination using a limited amount of propellant. Recent missions such as Voyager and Galileo required gravity assist maneuvers at several planets to accomplishtheir objectives. Today's students of aerospace engineering face the challenge of calculating these types of complex spacecraft trajectories. This classroom-tested textbook takes its title from an elective course which has been taught to senior undergraduates and first-year graduate students forthe past 22 years. The subject of orbital mechanics is developed starting from the first principles, using Newton's laws of motion and the law of gravitation to prove Kepler's empirical laws of planetary motion. Unlike many texts the authors also use first principles to derive other importantresults including Kepler's equation, Lambert's time-of-flight equation, the rocket equation, the Hill-Clohessy-Wiltshire equations of relative motion, Gauss' equations for the variation of the elements, and the Gauss and Laplace methods of orbit determination. The subject of orbit transfer receivesspecial attention. Optimal orbit transfers such as the Hohmann transfer, minimum-fuel transfers using more than two impulses, and non-coplanar orbital transfer are discussed. Patched-conic interplanetary trajectories including gravity-assist maneuvers are the subject of an entire chapter and areparticularly relevant to modern space missions.

## Author Biography

**John E. Prussing**is Professor Emeritus of Aerospace Engineering at the University of Illinois at Urbana-Champaign.

**Bruce A. Conway**is Professor of Aerospace Engineering at the University of Illinois at Urbana-Champaign.

## Table of Contents

*Each Chapter ends with References and Problems.*

**Chapter 1: The**

*n***-Body Problem**

1.1 Introduction

1.2 Equations of Motion for the

*n*-Body Problem

1.3 Justification of the Two-Body Model

1.4 The Two-Body Problem

1.5 The Elliptic Orbit

1.6 Parabolic, Hyperbolic, and Rectilinear Orbits

1.7 Energy of the Orbit

**Chapter 2: Position in Orbit as a Function of Time**

2.1 Introduction

2.2 Position and Time in an Elliptic Orbit

2.3 Solution for the Eccentric Anomaly

2.4 The

*f*and

*g*Functions and Series

2.5 Position versus Time in Hyperbolic and Parabolic Orbits: Universal Variables

**Chapter 3: The Orbit in Space**

3.1 Introduction

3.2 The Orbital Elements

3.3 Determining the Orbital Elements from r and v

3.4 Velocity Hodographs

**Chapter 4: The Three-Body Problem**

4.1 Introduction

4.2 Stationary Solutions of the Three-Body Problem

4.3 The Circular Restricted Problem

4.4 Surfaces of Zero Velocity

4.5 Stability of the Equilibrium Points

4.6 Periodic Orbits in the Restricted Case

4.7 Invariant Manifolds

4.8 Special Solutions

**Chapter 5: Lambert's Problem**

5.1 Introduction

5.2 Transfer Orbits Between Specified Points

5.3 Lambert's Theorem

5.4 Properties of the Solutions to Lambert's Equation

5.5 The Terminal Velocity Vectors

5.6 Applications of Lambert's Equation

5.7 Multiple-Revolution Lambert Solutions

**Chapter 6: Rocket Dynamics**

6.1 Introduction

6.2 The Rocket Equation

6.3 Solution of the Rocket Equation in Field-Free Space

6.4 Solution of the Rocket Equation with External Forces

6.5 Rocket Payloads and Staging

6.6 Optimal Staging

**Chapter 7: Impulsive Orbit Transfer**

7.1 Introduction

7.2 The Impulsive Thrust Approximation

7.3 Two-Impulse Transfer Between Circular Orbits

7.4 The Hohmann Transfer

7.5 Coplanar Extensions of the Hohmann Transfer

7.6 Noncoplanar Extensions of the Hohmann Transfer

7.7 Conditions for Interception and Rendezvous

**Chapter 8: Continuous-Thrust Transfer**

8.1 Introduction

8.2 Equation of Motion

8.3 Propellant Consumption

8.4 Quasi-Circular Orbit Transfer

8.5 The Effects of Nonconstant Mass

8.6 Optimal Quasi-Circular Orbit Transfer

8.7 Constant-Radial-Thrust Acceleration

8.8 Shifted Circular Orbits

**Chapter 9: Interplanetary Mission Analysis**

9.1 Introduction

9.2 Sphere of Influence

9.3 Patched Conic Method

9.4 Velocity Change from Circular to Hyperbolic Orbit

9.5 Planetary Flyby (Gravity-Assist) Trajectories

9.6 Gravity-Assist Applications

**Chapter 10: Linear Orbit Theory**

10.1 Introduction

10.2 Linearization of the Equations of Motion

10.3 The Hill-Clohessy-Wiltshire (CW) Equations

10.4 The Solution of the CW Equations

10.5 Linear Impulsive Rendezvous

10.6 State Transition Matrix for a General Conic Orbit

**Chapter 11: Perturbation**

11.1 Introduction

11.2 The Perturbation Equations

11.3 Effect of Atmospheric Drag

11.4 Effect of Earth Oblateness

11.5 Effects of Solar-Lunar Attraction

11.6 Effect on the Orbit of the Moon

**Chapter 12: Canonical Systems and the Lagrange Equations**

12.1 Introduction

12.2 Hamilton's Equations

12.3 Canonical Transformations

12.4 Necessary and Sufficient Conditions for a Canonical Transformation

12.5 Generating Functions

12.6 Jacobi's Theorem

12.7 Canonical Equations for the Two-Body Problem

12.8 The Delaunay Variables

12.9 Average Effects of Earth Oblateness Using Delaunay Variables

12.10 Lagrange Equations

**Chapter 13: Perturbations Due to Nonspherical Terms in the Earth's Potential**

13.1 Introduction

13.2 Effect of the Zonal Harmonic Terms

13.3 Short-Period Variations

13.4 Long-Period Variations

13.5 Variations at

*O*(

*J*2/2)

13.6 The Potential in Terms of Conventional Elements

13.7 Variations Due to the Tesseral Harmonics

13.8 Resonance of a Near-Geostationary Orbit

**Chapter 14: Orbit Determination**

14.1 Introduction

14.2 Angles-Only Orbit Determination

14.3 Laplacian Initial Orbit Determination

14.4 Gaussian Initial Orbit Determination

14.5 Orbit Determination from Two Position Vectors

14.6 Differential Correction

Appendix 1: Astronomical Constants

Appendix 2: Physical Characteristics of the Planets

Appendix 3: Elements of the Planetary Orbits

Index