73202 - Spacecraft Orbital Dynamics and Control

Learning outcomes

The student learns in details the dynamics of the centre of mass of an artificial satellite, both in the case of motion around a planet or for interplanetary trajectories. Also, the strategies and control laws for orbital maintenance, rendezvous, injection into an interplanetary trajectory and around a target planet are explained, as well as techniques for trajectory design using classical impulsive or low-thrust manoeuvres.

Course contents

Elements of Keplerian orbital mechanics

Equations of astrodynamics

Lagrange and Gauss planetary equations

Effect of the main orbital perturbations

- Earth flattening (J2)

- Ellipticity of the Equator (J22)

- Hints on North-South asymmetry (J3)

- Atmospheric Drag, hints on atmospheric models

- Solar radiation pressure

- Third body effect

Station keeping maneuvers

- Geostationary satellites (North-South)

- Geostationary satellites (East-West)

Interplanetary trajectories

- Impulsive and continuous thrust transfers

- Patched conic approach and sphere of influence

- Earth-to-Mars transfer

- Gravity assist and aero-breaking

Rendez-vous

- Macroscopic rendezvous

- Lambert problem (definition and applications)

- Pork-chop plots

- Euler-Hill equations

- Microscopic rendez-vous

Circular restricted three body problem

- Jacobi constant

- Lagrangian points and their stability

- Analytical construction of periodic/quasi-periodic orbits

- Single-shooting differential correction methods

- Hints on stable/unstable manifolds and low-energy transfers

Readings/Bibliography

Course notes distributed by the lecturer.

Further readings:

1. David A. Vallado, “Fundamentals of Astrodynamics and Applications” (Fourth Edition), ISBN: 978-11881883180, Microcosm Press, (2013)
2. Stephen Kemble, "Interplanetary Mission Analysis and Design", ISBN: 3-540-29913-0 (2006)
3. Parker, Jeffrey S., and Rodney L. Anderson. Low-energy lunar trajectory design. Vol. 12. John Wiley & Sons (2014).
4. Richard H. Battin, “An introduction to the mathematics and methods of astrodynamics” ISBN 1-56347-342-9, AIAA education series (1999)
5. A. E. Roy, “Orbital Motion”, ISBN-13: 978-0750310154, CRC Press (2004)
6. Oliver Montenbruck ; Eberhard Gill, “Satellite orbits : models, methods, and applications”, ISBN 978-3-540-67280-7, Springer-Verlag (2000)
   

Teaching methods

During the lecture hours, the topics are presented, all the introduced formulas are explicitly demonstrated, and the methods for solving the mathematical and engineering problems addressed during the exercise sessions are explained.

Some topics are explored in greater depth through practical exercises using Python.

Given the type of activity and the teaching methods adopted, attendance of this course requires all students to have previously completed Modules 1 and 2 of the safety training for study environments, in e-learning mode.

Assessment methods

The exam consists of three questions through which, in addition to assessing basic knowledge of the topics covered in class, the student's ability to solve new problems—or at least to outline an appropriate problem-solving strategy—will be evaluated. The assessment of this ability carries significant weight in determining the final grade. The student must pass at least two out of the three questions posed by the instructor in order to pass the exam. The ability to solve particularly complex engineering and mathematical problems, along with evidence of an in-depth level of study, are important factors in the possible awarding of honors (cum laude).

Teaching tools

Stardand tools include blackboard, LCD projector, and PC.

Office hours

See the website of Riccardo Lasagni Manghi