Orbital Mechanics S1 (SPACE)
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. describe mathematically the oirientation of orbits in 3D space.
4. understand the main perturbations acting on Earth satellites and apply equations for predicting perturbed Keplerian motion.
5. determine orbits from observations of position and velocity and plan transfer trajectories.
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 studying two and n-body problems. 2 body problems will be considered and analytical solutions will be derived and applied for transfers, orbital manoeuvres and orbital timing. Orbital elements will be introduced to describe the size, shape, and orientation of an orbit. Methods for determining orbits from observations and calculating interplanetary trajectories (Gibbs', Lambert). Effects of perturbations on trajectories will be quantified through variational equations. The main perturbations affecting satellite orbits will be considered. Spacecraft relative motion, based on the linearization of the gravitational field about a (typically circular reference plane) will be considered and applied for rendezvous manoeuvres and extended to consider spacecraft stability due to gravitational gradients.
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 tutorial sessions.
You will have additional opportunities to self-assess your learning via tutorial problem sheets.
You will be summatively assessed by an in-class assessment and a written closed-book examination at the end of the module.
If module is failed, the typical reassessment offered will be exam only.
| Assessment type
|
Assessment description
|
Weighting
|
Pass mark
|
| Examination
|
Closed-book written examination
|
85%
|
50%
|
| Examination
|
In-class computer assessment
|
15%
|
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.
Reading list
Module leaders
Dr Errikos Levis