The University of Southampton

SESA6076 Spacecraft Orbital Mechanics and Control

Module Overview

This module explains the fundamental concepts of spaceflight orbital mechanics and trajectory design for planet centred and interplanetary mission. It leads on from a review of the two-body problem covered in part II and introduces to the design and characterisation of planet-centred orbits in presence of perturbation and transfer manoeuvres. The module investigates various techniques for interplanetary trajectory design, gravity assists manoeuvres, rendezvous and docking. Dynamical system theory methods are used to design mission to the Libration points of the Sun-Earth and Moon-Earth system. Preliminary concepts for optimisation of low-thrust and impulsive trajectories will be introduced, together with techniques for orbit maintenance.

Aims and Objectives

Module Aims

The development of the spacecraft trajectory design, starting from the study of the natural dynamics to the orbit design and maintenance.

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

  • To gain a good understanding of the basic principles of dynamical system theory applied to astrodynamics and trajectory optimisation.
Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

  • Understand the mechanics of orbits in an accurate force model
  • Calculate frozen orbits and inter-orbit transfers
  • Design trajectories in the three-body problem
  • Design interplanetary trajectories
  • Write appropriately the trajectory optimisation problem
  • 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:

  • Study and learn independently
  • Solve problems systematically
  • Gain an awareness of trajectory design and optimisation for space mission design
  • Gain an awareness of dynamical system theory for space mission design


Introduction (1 lecture) Chapter 1– (3 lectures) Mathematical methods and dynamics review. Chapter 2- Numerical integration of ODE system (1 lecture) ODE and numerical integration of differential equations. Chapter 3 – Keplerian orbits and orbit representation (4 lectures) Restricted two-body problem, Kepler equation, Ephemerides, Position and velocity as function of time, Angular momentum, Energy, Orbital elements and state vector, Coordinate transformation, Spherical geometry, Ground tracks. Chapter 4 – Orbit perturbations: modelling and applications (3 lectures) Frozen orbits, Lagrange and Gauss equations, Disturbing function, Solar radiation pressure, Third-body perturbation, Atmospheric drag, Non-spherical gravity field, Semi-analytical techniques for orbit propagation. Chapter 5 – Orbital manoeuvres (3 lectures) Review Hohmann transfer, Bi-elliptical transfer, Out-of-plane manoeuvre, Inter-orbit transfers. Chapter 6 –Interplanetary trajectories (5 lectures) Lambert problem, Fly-bys, Launch windowsoptimisation, Sphere of influence, Patched conics, Ephemerides, Tisserand plane, Gravity-assist and aerodynamics assisted gravity assist. Chapter 7 – Restricted Three-Body Problem (4 lectures) N-body problem, Three-body problem, Restricted-three body problem, Lagrange points, Jacobi constant, Periodic orbits, Manifold dynamics for missions at Libration point orbits. Chapter 8 – Relative motion in orbit (2 lecture) Docking and relative motion, Clohessy-Wiltshire equations, Linearisation, Formation flying. Chapter 9 – Low-thrust trajectories (3 lectures) Optimal control problem, Low thrust orbit transfers. Chapter 10 – Station keeping control (3 lectures) Optimal feedback control. Exercise class (4 lectures spread during the course).

Special Features


Learning and Teaching

Teaching and learning methods

Teaching methods will include 36 lectures. Learning activities include directed reading, problem solving. Matlab programming of related problem will be suggested to students and revised during tutoring classes.

Preparation for scheduled sessions63
Wider reading or practice30
Total study time150

Resources & Reading list

V. Chobotov (2002). Orbital Mechanics. 

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

Matlab and Python. 

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

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


Assessment Strategy



MethodPercentage contribution
Exam  (120 minutes) 100%


MethodPercentage contribution
Exam  (120 minutes) 100%

Repeat Information

Repeat type: Internal & External

Linked modules


To study this module, you will need to have studied the following module(s):

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