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The University of Southampton

SESA6076 Spacecraft Orbital Mechanics

Module Overview

This module introduces students to the fundamental concepts of spaceflight orbital mechanics and then elaborates on trajectory design for planet centred and interplanetary missions. Starting from a review of Keplerian motion introduced in earlier modules, it covers the design and characterisation of planet-centred orbits in presence of perturbations and orbital transfer manoeuvres. The module investigates the modelling of orbital perturbation, Earth-bound and interplanetary trajectory design, gravity assist manoeuvres, and rendezvous & docking dynamics. Furthermore, techniques for analytical and numerical orbit propagation and orbit determination from observations will be considered. Finally, an introduction to concepts of modern dynamical system theory applied to missions to and around the libration points in the circular restricted three body problem will be presented.

Aims and Objectives

Learning Outcomes

Knowledge and Understanding

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

  •  provide a comprehensive knowledge and understanding of scientific principles and methodology underpinning modern Orbital Mechanics to enable appreciation of the scientific and engineering context, and to support understanding of relevant historical, current and future developments and technologies (SM1m)
  •  know and understand design processes and methodologies in mission design and analysis, and apply and adapt them in unfamiliar situations (D10)
  •  demonstrate awareness that engineering activities should promote sustainable development and apply quantitative techniques where appropriate (EL11)
  •  make general evaluations of risk issues in the context of mission design and analysis, including health & safety, environmental and commercial risk (EL13)
  •  know and understand the mathematical and statistical methods necessary to underpin Orbital Mechanics, and to enable you to apply a range of mathematical methods, tools, and notations proficiently and critically in the analysis and solution of space mission design problems (SM2m)
  •  demonstrate awareness of developing technologies related to Orbital Mechanics (SM4m)
  •  show a comprehensive knowledge and understanding of mathematical and computational models relevant to Orbital Mechanics and an appreciation of their limitations (SM5m)
  •  understand concepts relevant to Orbital Mechanics, some from outside engineering, and evaluate them critically and apply them effectively, including in engineering projects (SM6m, SM9m)
  •  understand the relevant scientific principles of Orbital Mechanics (SM7m)
  •  be aware of current problems and/or new insights most of which is at, or informed by, the forefront of mission design and analysis (SM8m)
  •  understand how Orbital Mechanics is applied in the context of mission development and spacecraft operations (P1m)
  •  know the characteristics of particular equipment, processes or products relevant to space mission design and analysis with extensive knowledge and understanding of a wide range of engineering materials and components (P2m)
  •  thoroughly understand current space mission design practice and its limitations, and some appreciation of likely new developments (P9m)
Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

  •  identify, classify and describe the performance of systems and components through the use of analytical methods and modelling techniques (EA2m)
  •  apply quantitative and computational methods, using alternative approaches and understanding their limitations, in order to solve space mission design and analysis problems and implement appropriate action (EA3m)
  •  use fundamental knowledge to investigate new and emerging technologies (EA5)
  •  extract and evaluate pertinent data and to apply engineering analysis techniques in the solution of unfamiliar problems (EA6m)
  •  apply and integrate knowledge and understanding of other engineering disciplines to support study of Orbital Mechanics and the ability to evaluate them critically and to apply them effectively (SM3m)
  •  plan self-learning and improve performance, as the foundation for lifelong learning/CPD (G2m)
  •  monitor and adjust a personal programme of work on an on-going basis (G3m)
  •  apply engineering techniques taking account of a range of commercial and industrial constraints (P10m)


Introduction Chapter 1: This looks strangely familiar – Revision of Mathematical 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 * Classical Orbital Elements & State Vector * Kepler’s Equation & Time Dependence Chapter 3: Is it a plane? Is it a bird? – Observations and Orbit Determination * Observation Techniques * Reference Frames and Time * 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 fly-by trajectories Chapter 9: Torn between two bodies – N-Body Problems * N-Body Problem * Circular Restricted Three-Body Problem * Natural Dynamics around Libration Points Summary and Revision

Learning and Teaching

Teaching and learning methods

Teaching methods will include 36 lectures using a mix of slides and blackboard derivations. Panopto recordings of the lectures along with the slide deck will be made available on Blackboard wherever possible. The lectures are complemented by 4 supervised 2h computer lab sessions as well as weekly office hours. Further learning activities include directed reading and individual problem solving.

Preparation for scheduled sessions24
Wider reading or practice10
Follow-up work24
Completion of assessment task24
Specialist Laboratory 8
Total study time150

Resources & Reading list

Matlab/Python and GMAT. Scientific computing environment and GMAT mission analysis tool (open source) will be used in the computer labs.



MethodPercentage contribution
Continuous Assessment 30%
Final Assessment  70%


MethodPercentage contribution
Set Task 100%


MethodPercentage contribution
Set Task 100%

Repeat Information

Repeat type: Internal & External

Linked modules

Pre-requisites: SESA2024 or equivalent This module is REQUIRED for the following: MSc Space Systems Engineering (3893-1) MPhys with Space Science BSc Physics with Space Science It is OPTIONAL for all of the following: MEng Aero & Astro MEng Aero & Astro with Placement Aerodynamics Aerodynamics with Placement Airvehicle Systems & Design Airvehicle Systems & Design with Placement Comp Eng & Design Comp Eng & Design with Placement Engineering Management Engineering Management with Placement Materials and Structures Materials and Structures with Placement Semester Abroad: Semester One Semester Abroad: Semester One with Placement Semester Abroad: Semester Two Semester Abroad: Semester Two with Placement Semester in Industry Semester in Industry with Placement Spacecraft Engineering Spacecraft Engineering with Placement


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

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