Orbital Mechanics

Module aims

This module presents the application of orbital mechanics and rigid body dynamics to a wide range of problems in non-atmospheric flight, along with analytical and numerical solutions to a wide range of problems in path planning and path optimisation such as fuel- or time-optimal trajectories. Spacecraft relative motion, stability and control are also analysed.

Learning outcomes

On successfully completing this module, you should be able to:
1. derive the equations of motion for a 2 body problem, including velocity calculations and means of undertaking orbital transfers and manoeuvres.
2. apply the orbital timing equations to relate orbital position with time.
3. Show the main perturbations acting on Earth satellites and describe the dynamics of the 3-body problem.
4. Solve Lambert's problem for orbital transfers.
5. Determine orbits from observations of range, range-rate, and angles.
6. describe and extend the relative motion of one satellite to another to inform the stability of a satellite in its orbit.

7. formulate the equations of relative motion (angular and translational) to consider and control a spacecraft’s state relative to a reference plane and for the purposes of determining the stability of a spacecraft. 

Module syllabus

Topics will include the following,
1) Equations of motion
2) 2-body problem
3) Orbital manoeuvres
4) Orbital timing
5) Orbital frame of reference and orbital elements
6) Orbital determination
7) 3rd body and geopotential, atmospheric drag, etc. perturbations
8) Lamberts problem and interplanetary motion
9) Relative motion with gravity gradients
10) Gravity gradient based stability 

Teaching methods

The module will be delivered primarily through large-class lectures introducing the key concepts and methods, supported by a variety of delivery methods combining the traditional and the technological.  The content is presented predominantly via slides and notes, with the complement of the whiteboard and visualizer.

Learning will be reinforced through tutorial question sheets. 

Assessments

This module presents opportunities for both formative and summative assessment.  
You will be formatively assessed through progress tests and tutorial sessions. 
You will have additional opportunities to self-assess your learning via tutorial problem sheets. 
You will be summatively assessed by a written closed-book examination at the end of the module as well as through practical laboratory assessments and a written laboratory report.
 
Assessment type Assessment description Weighting Pass mark
Examination Closed-book written examination 75% 50%
Coursework Coursework assignment 25% 50%
 
You will receive feedback following the coursework submission.
You will receive feedback on examinations in the form of an examination feedback report on the performance of the entire cohort.
You will receive feedback on your performance whilst undertaking tutorial exercises, during which you will also receive instruction on the correct solution to tutorial problems.
Further individual feedback will be available to you on request via this module’s online feedback forum, through staff office hours and discussions with tutors. 
 

Module leaders

Dr Robert Hewson