Project Research Area: Applied and Computational Mathematics
Description
Space travel is a topic that is well known in overview by many members of the general public thanks to its popularity in popular science and fiction. However, the mathematics governing the motion of objects in space can be complicated, but also very interesting.
Students taking this project will investigate orbital mechanics of natural bodies and spacecraft within the solar system. This will include looking at the stability of orbits and the trajectories required to get between specific locations within the solar system. All students will be expected to write at least some code in the project.
Trajectories of famous long distance space probes. Copied from https://solarsystem.nasa.gov/resources/720/pioneer-trajectories/ Public domain NASA image.
Group Project
The group project will serve as an introduction to the field of orbital mechanics. By the end of the group project you will have learned:- How to apply the framework of the circularly restricted three body problem to simplify orbital calculations.
- How basics of the rocket equation
- The basics of the Hohman transfer and how to calculate the transit time and total Δv required for any arbitary Hohman transfer.
- How to caluclate the Lagrange points between any two bodies in a circularly restricted three body problem.
- Understand the key mathematical principles underlying orbital mechanics.
- Wrtie Python code to model simple orbital mechanics.
- Be able to analyse and interpret your results.
Mode of operation and evidence of learning
The project will revolve around reading material provided by the project supervisor and synthesising that reading into a detailed understanding of the mathematical topic. Students should also be able to devlop basic skills in finding their own reference resources. Students should be able to produce Python code modelling the systems they have learned about and compare the results of their Python code with theory.Individual Project
The individual project will build on the work done in the group projects. Students will be expected to show additional independence in indentfying and researching a suitable extension. Some possible areas to investigate include:- Looking at the stability of Lagrange Points.
- Looking at Lyapunov and Halo orbits around Lagrange Points.
- Looking at more detailed fuel and transit time efficency calculation.
- Looking at transfer orbits other than the Hohmann transfer.
- Looking at using the Kalman Filter (and/or other methods) to caluclate the motion of bodies such as asteroids.
Mode of operation and evidence of learning
Students should be able to identify appropriate research sources (such as academic papers and textbooks) themselves, and judge how appropriate they are to their project. They should be able to make simple extensions to the models they find in their reading, and then write advanced Python code for these models. They should be able to compare them to theory and (where appropriate) real world data.Essential prior modules
Computational Mathematics II (MATH2761) (or equivalent personal programming experience)
Corequisites
Dynamical Systems III (MATH3091) is not required, but students may find some of the material useful
Resources
- NASA: Basics of Space Flight - a good, mainly non-technical introcution to the topic
Contact
Feel free to contact me before selecting this project - in particular if you are not taking the suggested pre- and co-requisites. My email is m.t.matuszewski@durham.ac.uk.