The University of Southampton

SESA6076 Spacecraft Orbital Mechanics and Control

Module Overview

This module elaborates the fundamental concepts of spaceflight orbital mechanics and introduces trajectory design for planet centred and interplanetary missions. It starts with a review of the two-body problem covered in SESA3025 and introduces the design and characterisation of planet-centred orbits in presence of perturbations and transfer manoeuvres. The module investigates the modelling of orbital perturbation, Earth-bound and interplanetary trajectory design, gravity assist manoeuvres, rendezvous & docking. Also, techniques for analytical and numerical orbital propagation and preliminary orbit determination will be considered. An introduction to concepts of dynamical system theory applied to missions to and around the Libration points of the circular restricted three body problem will be given.

Aims and Objectives

Module Aims

* To provide an introduction to modern methods of preliminary mission analysis and trajectory design * To foster an intuitive and quantitative understanding of astrodynamics in presence of perturbations, maneuvers and deep space travel

Learning Outcomes

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

  • Mathematically describe the mechanics of orbital motion including perturbations
  • Calculate frozen orbits and inter-orbit transfers
  • Understand low-energy trajectories in the three-body problem
  • Design interplanetary trajectories
  • Perform a preliminary trajectory design for a space mission
Transferable and Generic Skills

Having successfully completed this module you will be able to:

  • Study and learn independently
  • Solve problems systematically
Subject Specific Practical Skills

Having successfully completed this module you will be able to:

  • Gain an awareness of trajectory design and optimisation for space mission design
  • Gain an awareness of dynamical system theory for space mission design


Introduction Chapter 1: This looks strangely familiar - Revision of General Concepts * Vector algebra * Kinematics and Dynamics * Planar and Spherical Trigonometry Chapter 2: Round and round and round it goes! - Keplerian Orbits and Orbit Representation * Restricted Two-Body Problem * Elliptic, Parabolic & Hyperbolic Motion * Kepler's Equation * Classical Orbital Elements & State Vector Chapter 3: Is it a plane? Is it a bird? - Preliminary Orbit Determination Chapter 4: In 20.000 km, turn right. - Orbital Manoeuvres * Coplanar Manoeuvres * Non-Coplanar Transfers Chapter 5: That's mildly disturbing - Orbital Perturbations * Non-Uniform Gravity Field * Third-Body Perturbation * Atmospheric Drag * Solar Radiation Pressure Chapter 6: Foretelling the future - Orbital Propagation Techniques * Analytical * Semi-analytical * Numerical Chapter 7: Waltzing Matilda - Relative Orbital Motion * Relative Orbital Motion * Linearisation & State Transition Matrix Chapter 8: To boldly go… - Interplanetary Trajectories * Lambert's Problem * Patched Conics * Gravity-assisted trajectories Chapter 9: Torn between two bodies - Restricted Three-Body Problem * N-Body Problem * Circular Restricted Three-Body Problem * Natural Dynamics around Libration Points Chapter 10: Spiralling towards the finish line - Low-Thrust Trajectories * Optimal Control Problem * Low-Thrust Orbit Transfers Summary and Revision

Learning and Teaching

Teaching and learning methods

Teaching methods will include 36 lectures. Learning activities include directed reading and problem solving.

Completion of assessment task3
Preparation for scheduled sessions18
Follow-up work18
Wider reading or practice65
Total study time150

Resources & Reading list

Matlab and Python. 

V. Chobotov (2002). Orbital Mechanics. 

R. H. Battin (1999). An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition. 

Oliver Montenbruck and Eberhart Gill (2011). Satellite Orbits: Models, Methods and Applications. 

D. A. Vallado (2007). Fundamentals of Astrodynamics and Applications (Space Technology Library). 

H. Curtis (2009). Orbital Mechanics for Engineering Students. 



MethodPercentage contribution
Examination  (120 minutes) 100%


MethodPercentage contribution
Examination  (120 minutes) 100%

Repeat Information

Repeat type: Internal & External

Linked modules

Pre-requisite modules: SESA2024 Astronautics and SESA3039 Advanced Astronautics or equivalent

Share this module Share this on Facebook Share this on Google+ Share this on Twitter Share this on Weibo

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.