Module code: PHYM059

Module provider


Module Leader

READ JI Prof (Physics)

Number of Credits


ECT Credits



FHEQ Level 7

JACs code


Module cap (Maximum number of students)


Module Availability

Semester 2

Overall student workload

Lecture Hours: 22

Tutorial Hours: 11

Laboratory Hours: 11

Assessment pattern

Assessment type Unit of assessment Weighting

Alternative Assessment


Prerequisites / Co-requisites

Introduction to Astronomy (year 2); Cosmology & Galaxy formation and Research Techniques in Astronomy are not required but would be advantageous.

Module overview

In this module, students will study the Universe from a dynamical perspective. In the first part of the course, they will study “collisional” stellar systems - from the dynamics of our Solar system and the supermassive black hole at the centre of our Galaxy, to the dynamical evolution of massive star clusters orbiting in the Milky Way. Students will then study “collisionless” systems, modelling the motion of stars and gas in galaxies. This will provide some of the key evidence for dark matter in the Universe. Finally, students will study the motion of gas in galaxies, looking at what this can tell us about star formation, galaxy formation, and the future history of our own Galaxy and its neighbours. We will bring students up to a level where they will be at the forefront of modern research in this field.

Module aims

To provide students with a deep understanding of classic dynamics applied to the cosmos and what this can teach us about the formation of our Solar system, galaxies, and the Universe as a whole.

Learning outcomes

Attributes Developed
On successful completion of this module, students will be familiar with Lagrangian and Hamiltonian dynamics and will understand why the Solar System is chaotic. They will understand the difference between collisional and collisionless stellar systems and will be able to perform basic mass modelling of the black hole at the centre of our Galaxy, and the stars and gas in Galaxies themselves. They will understand the principle evidence for dark matter in the Universe and they will be able to calculate the fate of our Galaxy as it collides with its nearest neighbour Andromeda several billion years from now. Finally, they will understand that much of the Universe can be treated as a “fluid” and they will be able to apply the Euler equations to study the motion of gas in galaxies. The coursework assignments will develop the students' programming and problem solving skills.

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Module content

-Introduction -

Astronomy as a unique science; observables, distance and time in astronomy; collisional versus collisionless stellar systems.


- Solving Gravity -

How to calculate the (classical) gravitational potential for systems of arbitrary complexity. We start with spherical or ‘oblate spheroidal’ systems in which Newton's theorems can be applied, before presenting general analytic solutions of the Poisson equation.


- Collisional systems -

We study the dynamics of collisional stellar systems, starting with our Solar system and the black hole at the centre of our Galaxy. We show that the Solar system is chaotic and discuss why it is in fact surprisingly stable. We calculate the mass of the dark object at the centre of the Galaxy and discuss similar data in other galaxies. Finally, we study the dynamics and thermodynamics of dense star clusters like the old Globular Clusters that orbit the Milky Way.


- Collisionless systems -

We discuss the dynamics of collisionless fluids like stars and dark matter in galaxies. We use the motion of these stars to derive the gravitational potential in galaxies and present key evidence for “dark matter” in the Universe. Finally, we discuss how dynamics can be used to unravel the past and predict the future of our Galaxy.


Methods of Teaching / Learning

33 hours of lectures (3h/week)


The final examination will be of 1.5hr duration, with two questions from three to be attempted.


In addition, there will be a coursework assignment where the students will write an orbit integrator. They will use this to model either the dynamics of a few stars in a small star cluster (a collisional system), or stars within a galaxy (a collisionless system).


Assessment Strategy

Reading list


Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.