Project III 2023-24
MATH 3382

Space Travel and Spacecraft Trajectories

Maciej Matuszewski

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 spacecraft within the solar system, in particular the trajectories required to get between specific locations within the solar system. There will be options to focus primarily on analytical calculations, or take more numerical direction. Students may wish to extend the project into areas such a trajectories which optimise fuel usage. The effects of general relativity will not be considered in this project.

Diagram showing the trajectories of the Pioneer 10, Pioneer 11, Voyager 1, and Voyager 2 space probes, viewed down from the north ecliptic pole (a standard top-down view). The orbits of the planets are highlighted, as are the dates each point in the trajectory was reached. Pioneer 10 passed the orbit of Pluto in 1988, Pioneer 11 in 1991, Voyager 1 in 1988, and Voyager 2 in 1991.

Trajectories of famous long distance space probes. Copied from https://solarsystem.nasa.gov/resources/720/pioneer-trajectories/ Public domain NASA image.

Prerequisites

Analysis in Many Variables II (MATH2031)

Mathematical Modelling II (MATH2637) required if you wish your project to look at numerical models

Corequisites

Dynamical Systems III (MATH3091) is not required, but students may find some of the material useful

Resources

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.