Optimal Space Trajectories

Studies in Astronautics, Volume 1: Optimal Space Trajectories focuses on the concept of optimal transfer and the problem of optimal space trajectories. It examines the relative performances of the various propulsion systems (classical and electrical propulsions) and their optimization (optimal mass breakdown), along with parametric and functional optimizations and optimal transfers in an arbitrary, uniform, and central gravitational field. Organized into 13 chapters, this volume begins with an overview of optimal transfer and the modeling of propulsion systems. It then discusses the Hohmann transfer, the Hoelker and Silber bi-elliptical transfer, and the deficiencies of parametric optimization. The book explains the canonical transformation, optimization of the thrust law using the Maximum Principle, and optimal orbit corrections. The time-free orbital transfers and time-fixed orbital transfers and rendezvous are also discussed. Moreover, this volume explains the classical high-thrust and electric low-thrust propulsion systems and rendezvous between two planets. This book is written primarily for engineers who specialize in aerospace mechanics and want to pursue a career in the space industry or space research. It also introduces students to the different aspects of the problem of optimal space trajectories.

Foreword

Preface

Acknowledgements

Recommendations for Selective Reading

Nomenclature

0 Introduction

0.1 The problem of optimal space trajectories

0.2 Scheme of the study

0.3 Optimal transfer definition

1 Modeling and Optimization of Propulsion Systems

1.1 Modeling of propulsion systems

1.2 Optimization of propulsion systems

2 Parametric Optimization : The Hohmann Transfer

2.1 Parametric optimization

2.2 The Hohmann transfer

2.3 The Hoelker and Silber transfer

2.4 Limitations of parametric optimization

3 Functional Optimization : The Contensou-Pontryagin Maximum Principle

3.1 Calculus of variations

3.2 The Contensou-Pontryagin Maximum Principle

3.3 Canonical transformations

3.4 Equations for the variations

3.5 Perturbing Hamiltonian

3.6 Average Hamiltonian

4 Optimal Transfers in a General Gravitational Field

4.1 Optimization of the thrust law

4.2 Integrals

4.3 End conditions

5 Optimal Transfers in a Uniform Gravitational Field

5.1 Optimal thrust law

5.2 Interception

5.3 Rendezvous

5.4 Optimal energy build-up

6 Optimal Transfer in a Central Gravitational Field : General Considerations

6.1 The central-field assumption

6.2 Use of Cartesian coordinates

6.3 Use of orbital coordinates

7 Optimal Orbit Corrections : General Considerations

7.1 Linearization

7.2 Solution of the linearized problem

7.3 General results. Uncoupling

7.4 Conclusion

8 Optimal Orbit Corrections : Examples of Transfers

8.1 Optimal infinitesimal modification of the semi-major axis

8.2 Optimal infinitesimal rotation of the plane of orbit

8.3 Optimal transfers between close, coplanar, circular orbits

8.4 Optimal, multi-impulse transfers between close, near-circular orbits

9 Optimal Orbit Corrections : Examples of Rendezvous

9.1 Mean rendezvous

9.2 Multi-impulse, very long duration rendezvous between close, near-circular, non-coplanar orbits

9.3 Multi-impulse, long-duration rendezvous between close,

coplanar, near-circular orbits

10 Time-Free Orbital Transfers : General Considerations

10.1 Introduction and assumptions

10.2 Separation between elliptic and hyperbolic phases

10.3 Optimal acquisition of the parabolic level

10.4 Ellipse ellipse transfer

10.5 Hyperbola -> hyperbola transfer

11 Time-Free Orbital Transfers : Results

11.1 Classification of orbits

11.2 Transfer between parabolae

11.3 Transfers from or towards the parabolic level

11.4 Transfers between hyperbolae

11.5 Transfer between elliptic orbits

12 Time-Fixed Orbital Transfers and Rendezvous

12.1 High-thrust propulsion systems

12.2 Low-thrust propulsion systems

13 Interplanetary Rendezvous

13.1 Classical propulsion (IFT system)

13.2 Electric propulsion

13.3 Comparison of propulsion systems

Author Index

Subject Index