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 the modelling of orbital perturbation, techniques for analytical and numerical orbital propagation, Earth-bounded and interplanetary trajectory design, gravity assist manoeuvres, rendezvous & docking as well as preliminary orbit determination. Also, preliminary concepts of dynamical system theory will be used to investigate missions to and around Libration points of the Sun-Earth and Moon-Earth system, as well as notions of low-thrust and impulsive trajectory optimisation, together with techniques for orbit maintenance.

Aims and Objectives

Module Aims

Understand and apply concepts and techniques of spacecraft trajectory design, starting from the study of the natural dynamics to the orbit design and maintenance. The student will also gain an understanding of the basic principles of preliminary orbit determination, spacecraft trajectory propagation, dynamical system theory applied to astrodynamics and trajectory optimisation.

Learning Outcomes

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
  • 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 & Revision of General Concepts - Notation - Coordinate Systems - Vector Representation - Rotation Matrices and Euler Angles - Kinematics and Dynamics - Planar and Spherical Trigonometry - Implicit Equations & Root Finding - Special Functions Keplerian Orbits and Orbit Representation - Restricted Two-Body Problem - Keplerian Motion - Elliptic, Parabolic & Hyperbolic Motion - Position & Velocity as a Function of Time - Kepler’s Equation - Universal Variables - Classical Orbital Elements & State Vector - Coordinate Transformations Preliminary Orbit Determination - Coordinate Systems - Angles-Only Observations - Three Position Vectors and Time - Two Position Vectors and Time: Lambert’s Problem Orbital Manoeuvres - Coplanar Manoeuvres: - Hohmann Transfer - Bi-elliptical Transfer - Phasing Manoeuvres - Non-Homann Transfers - Non-Coplanar Transfers: - Inclination-Only Changes - Changes in the Right Ascension of the Ascending Node - Changes to the Inclination and the Ascending Node Orbital Perturbations - Non-Uniform Gravity Field - Third-Body Perturbation - Atmospheric Drag - Solar Radiation Pressure - Other Perturbations Orbital Propagation Techniques - General Perturbation Techniques - Special Perturbation Techniques - High Fidelity Orbit Propagation Relative Motion and Rendezvous - Relative Orbital Motion - Linearisation - Clohessy-Wiltshire Equations - State Transition Matrix - Rendezvous - Formation Flying Interplanetary Trajectories - Lambert’s Problem - Fly-by’s - Sphere of Influence - Patched Conics - Tisserand Plane - Gravity-assisted trajectories Restricted Three-Body Problem - N-Body Problem - Three-Body Problem - Restricted Three-Body Problem - Lagrange Points - Jacobi Constant - Periodic Orbits - Manifol Dynamics around Libration Points Low-Thrust Trajectories - Optimal Control Problem - Low-Thrust Orbit Transfers

Special Features


Learning and Teaching

Teaching and learning methods

Teaching methods will include 36 lectures. Learning activities include directed reading, problem solving, and computer lab sessions.

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

Resources & Reading list

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

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

V. Chobotov (2002). Orbital Mechanics. 

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

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

Matlab and Python. 


Assessment Strategy



MethodPercentage contribution
Exam  (120 minutes) 100%


MethodPercentage contribution
Exam  (120 minutes) 100%

Repeat Information

Repeat type: Internal & External

Linked modules

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


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

SESA3039Advanced Astronautics
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