Spacecraft Trajectory Design via Quasi-periodic Invariant Tori

This project aims at identifying and characterizing novel transfer opportunities within non-integrable astrodynamics problems using quasi-periodic trajectories and their manifolds.

Start date
1 October 2021
Standard project duration is 4 years.
Application deadline
Funding information
  • UK fees covered.
  • Stipend in line with UKRI rate (£15,609 p.a. for 2021/22). £1000 p.a.
  • Researcher Training Support Grant.
  • Personal Computer (provided by the department.


With the development of miniaturized technologies and reliable off-the-shelf components, spacecraft missions are becoming more affordable and ambitious. Nowadays, shoe-box sized satellites known as CubeSats can venture into deep space at a fraction of the cost of the infamous Apollo program. This novel mission design paradigm propels academic research into sophisticated trajectories that can best take advantage of the chaotic space environment. A new trend emerging in orbital mechanics is the exploitation of quasi-periodic tori that can best describe and characterize the dynamics of non-autonomous systems such as the Sun-Earth and Earth-Moon three-body problems. This project aims at implementing modern numerical procedures for calculating quasi-periodic trajectories and their manifolds, thereby researching into novel transfer opportunities to send low-cost satellite missions towards the Moon and beyond. The ideal candidate should be familiar with MATLAB and/or similar programming languages; be comfortable with key astrodynamics concepts such as classic orbit elements; open to undertake further training in dynamical systems theory and numerical continuation methods.

The project will be supervised by Dr Nicola Baresi, lead of the Space Trajectory Analysis Group and lecturer in Orbital Mechanics at Surrey Space Centre. Dr Baresi has been involved in a variety of spacecraft projects, including Surrey’s VMMO and the Japanese EQUULEUS and MMX. Recent publications that are relevant for this studentship are:

  • Baresi et al., “Fully numerical methods for calculating quasi-periodic invariant tori in Astrodynamics”, Journal of the Astronautical Sciences, 2018;
  • Baresi et al, “A high-order Taylor polynomial approach for continuing trajectories in restricted three-body problems”, Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, 2020;
  • Baresi et al., “Trajectory Design and Maintenance of the Martian Moons eXploration Mission Around Phobos”, Journal of Guidance, Control, and Dynamics, 2021;

More info on Dr Baresi’s research activities can be found on the University website.

Eligibility criteria

Candidates must hold:

  • A minimum of a 2:1 UK honours degree or a recognised equivalent international qualification in a relevant discipline.
  • A 2:2 degree and a distinction at masters level.

This studentship is only available to UK students. 

IELTS requirements: IELTS Academic: 6.5 or above (or equivalent) with 6.0 in each individual category.

How to apply

Candidates must apply via the PhD in Space Engineering programme page. 

Please clearly state the studentship title and supervisor on your application.

Selected candidates will be interviewed within two weeks of the applications deadline

Application deadline

Contact details

Nicola Baresi
30 BA 01
Telephone: +44 (0)1483 688272

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