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 (prerequisite)

• Restricted two-body problem
• Equations of astrodynamics
  
• Integrals of motion and orbital parameters
• Full two-body problem

Perturbation methods

•  Special perturbation methods
• General perturbation methods
• Lagrange planetary equations
• Gauss planetary equations

Major perturbations for Earth satellites

• Earth gravity potential (spherical harmonics)
  
• J2 (oblateness) + Sun-synchronous and Molniya/Tundra orbits
  
• J22 (ellipticity of equator) + East-West station-keeping for GEO satellites
• J3 (North-South asymmetry)
• Atmospheric drag + hints on atmospheric models
• Solar radiation pressure
• Third body + North-South station-keeping for GEO satellites 

Orbital transfers

• Rocket equation and main propulsion systems
• Impulsive coplanar transfers (Hohmann vs Bi-elliptic)
• Impulsive non-coplanar transfers
• Low-thrust spiral climb/descent (analytical approximation)
• Introduction to low-thrust trajectory optimization
• Patched conic approach and sphere of influence
• Earth-to-Mars transfer
• Gravity assist

Intercept problem and rendezvous

•  Macroscopic rendezvous
• Lambert problem definition and applications (LAB excercise)
• Pork-chop plots
• Euler-Hill equations
• Microscopic rendezvous

Circular restricted three body problem

• Jacobi constant
• Lagrangian points and their stability (LAB excercise)
• Analytical construction of periodic/quasi-periodic orbits (LAB excercise)
• Single-shooting differential correction methods (LAB excercise)
• Hints on stable/unstable manifolds and low-energy transfers

Readings/Bibliography

Course material provided by the lecturer (Virtuale platform):

1. Hand-written lecture notes
2. Lecture notes in LaTex format
3. Power Point slides presented during lectures

Further readings:

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

Teaching methods

The course is delivered primarily through in-person lectures, during which the instructor introduces the mathematical and engineering problems outlined in the syllabus and presents the main methods for solving them.

The lectures combine step-by-step derivations of mathematical formulas on the blackboard with presentations using projected slides. In addition, selected topics are explored in greater depth through hands-on classroom exercises based on Jupyter Notebooks.

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

Examination Format

The examination is conducted orally and consists of three questions. Two questions are selected by the instructor, while the third is chosen by the student from a list of topics presented during the course.

For each question, students are given approximately 40 minutes to prepare an outline of their answer, including diagrams, mathematical formulas, and derivations (where applicable). At the end of this period, the answer is discussed with the instructor in order to assess the student's understanding of the topics covered.

Each answer is graded on a scale from 0 to 10, and the three scores contribute to the final grade.

The ability to solve particularly challenging mathematical and engineering problems, together with evidence of an exceptionally thorough understanding of the course material, is an important factor in the possible award of cum laude.

 

Exam Sessions

For organizational reasons related to the duration of the oral examination, each session is limited to a maximum of six students.

If the number of registrations exceeds this limit, an additional session will be scheduled for the following day or, if necessary, on the next available date.

 

Use of AI Tools

AI can be a useful tool to support individual study by providing deeper insights, summaries, and self-assessment activities. However, with regard to the assessment of learning, the use of AI is prohibited during in-person examinations. Any use of AI constitutes a violation of academic integrity.

 

Additional Information

Students with specific learning disorders (SLD) or temporary or permanent disabilities are encouraged to contact the University's dedicated support office well in advance (https://site.unibo.it/studenti-con-disabilita-e-dsa/en ). The office will propose any appropriate accommodations for the examination, which must be submitted to the instructor for approval at least 15 days before the examination date. The instructor will evaluate the proposed accommodations in light of the intended learning outcomes of the course.

Teaching tools

Stardand tools include blackboard, LCD projector, and PC.

Office hours

See the website of Riccardo Lasagni Manghi