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Computational study of tidal evolution of a planet-moon system

School of Science and Engineering

About the Project

We are all familiar with the effects of tides on Earth, which cause the ocean surface to rise and fall day and night. These tides are caused by the gravitational interactions between the Sun and the Earth as well as between the Moon and the Earth, and the effects vary depending on the relative positions of the Sun and the Moon. Just like the Earth feels the tidal effect, the Moon also experiences the effects of tides, which cause the Moon’s orbit to expand slowly.

Such tidal effects are important in understanding orbital evolution of planets close to the central star as well as moons around a planet. The efficiency of tidal energy dissipation is often parameterised by a dimensionless tidal quality factor Q (e.g. Goldreich & Soter 1966), but the factor depends on a spectrum of tidal forcing frequencies and thus is poorly determined. The simpler way of treating the tidal dissipation is to use a constant time lag assumption, which results from the weak friction model that gives exact tidal evolution equations (Hut 1981). However, it is unknown to what extent this model could be applied.

In the proposed project, we develop a new model to better understand the tidal evolution. We approximate a planetary body with a number of spheres and study its tidal evolution directly by numerical simulations, without relying on any particular tidal model. For the numerical simulations, we use PKDGRAV which is a parallel N-body gravity tree code (Stadel 2001) that has been adopted for particle collisions (Richardson et al. 2000, 2009, 2011). The code takes account of a soft-sphere option that handles long-lasting contacts (Schwartz et al. 2012), which is appropriate to describe a dense system like a planet and a moon. The goal of the project is to constrain a set of parameters which reproduces tidal evolution of moons around planets in the Solar System.

For informal enquiries about the project, contact Dr Soko Matsumura ()
For general enquiries about the University of Dundee, contact

Applicants must have obtained, or expect to obtain, a first or 2.1 UK honours degree, or equivalent for degrees obtained outside the UK in a relevant discipline.

English language requirement: IELTS (Academic) score must be at least 6.5 (with not less than 5.5 in each of the four components). Other, equivalent qualifications will be accepted. Full details of the University’s English language requirements are available online: http://www.dundee.ac.uk/guides/english-language-requirements.


Step 1: Email Dr Soko Matsumura () to (1) send a copy of your CV and (2) discuss your potential application and any practicalities (e.g. suitable start date).

Step 2: After discussion with Dr Matsumura, formal applications can be made via UCAS Postgraduate. When applying, please follow the instructions below:

Apply for the Doctor of Philosophy (PhD) degree in Physics: https://digital.ucas.com/coursedisplay/courses/07a14f7d-0d23-c83c-bae0-4dc4e2f7045f. Select the start date and study mode (full-time/part-time) agreed with the lead supervisor.

In the ‘provider questions’ section of the application form:
- Write the project title and ‘FindAPhD.com’ in the ‘if your application is in response to an advertisement’ box;
- Write the lead supervisor’s name and give brief details of your previous contact with them in the ‘previous contact with the University of Dundee’ box.

In the ‘personal statement’ section of the application form, outline your suitability for the project selected.

Funding Notes

There is no funding attached to this project. The successful applicant will be expected to provide the funding for tuition fees and living expenses, via external sponsorship or self-funding.


Goldreich, P., & Soter, S. 1966, Icar, 5, 375

Hut, P. 1981, A&A, 99, 126

Richardson D. C., Quinn T., Stadel J., Lake G., 2000, Icarus, 143, 45

Richardson D. C., Michel P., Walsh K. J., Flynn K. W., 2009, Planet. Space Sci., 57, 183

Richardson D. C., Walsh K. J., Murdoch N., Michel P., 2011, Icarus, 212, 427

Stadel J. G., 2001, PhD thesis, Univ. Washington

Schwartz S. R., Richardson D. C., Michel P., 2012, Granular Matter, 14, 363

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