###### Information about the course:

53918 Advanced dynamics (Dynamiikan jatkokurssi)

Lecturers: Associate Prof. Peter Johansson (Room D332)

Dr. Mikael Granvik (Room D312)

Course assistant: M.Sc. Antti Rantala (Room D308)

**Lectures: Thursdays 12.15-14.00 Room B121, Exactum (Note Lecture 13 will be on Tuesday 25.4 in the same room B121)****Problem sessions: Every two weeks on Thursdays 14.15-16.00 Room B119 Exactum on 26.1., 9.2. and Room B121 on 16.3., 6.4., 27.4. **

First lecture on 19.1.2017 and last lecture on 4.5.2017

- In total 14 lectures.
- The first 7 lectures will cover solar system dynamics and the final 7 lectures in the second part of the course will cover Galactic dynamics
- Problem sets with 20 problems (10 solar system dynamics and 10 galactic dynamics) will be handed out
- A course project on programming a numerical integrator will correspond to the equivalent of 10 problems.
- The minimum requirement for the problem sets and course project is 1/3 of the total points, surplus points will result in bonus points for the exam.

**Course material:**

- The course material will consist of handouts closely following the material in the following text books:

- B. Gladman & J. Burns:
*Planetary Dynamics*, 2011 (draft of a book under preparation) - J. Binney & S. Tremaine:
*Galactic Dynamics*, Second Edition, Princeton University Press, 2008

- Additional material can be found in the following books

- J. M. A. Danby,
*Fundamentals of Celestial Mechanics*, Second Edition, Willmann-Bell, Inc., 1992 - G. Bertin:
*Dynamics of Galaxies*, Cambridge Univ Press, 2000.

**The course project is about the dynamics of dwarf planet Pluto: project.pdf**

**Download the initial conditions file here: input_precise.dat**

**Deadline: 30.04.2017. The maximum award is 30 exercise points. **

**Final exam:**

**The final exam will be held on Thursday 11.5.2017 at 10-14 in Room D106, Physicum**

**Course syllabus:**

**Lecture 1: 19.1.2017: "Introduction to solar system dynamics"**

- Structure and dynamical evolution of the solar system
- Short recap of the 2-body problem

**Lecture 2: 26.1.2017: "2-body problem and applications"**

- TBD

**Lecture 3: 2.2.2017: "Perturbation theory"**

- TBD

**Lecture 4: 9.2.2017: "N-body problem and numerical integration"**

- TBD

**Lecture 5: 16.2.2017: "3-body problem"**

- TBD

**Lecture 6: TBD.2.2017: "Disturbing function and secular dynamics"**

- TBD

**Lecture 7: 2.3.2017: "Novel concepts in planetary-system dynamics"**

- Yarkovsky effect
- Planetary migration

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**Lecture 8: 16.3.2017: "Introduction to galactic dynamics and potential theory" Binney & Tremaine: pages: 1-5, 33-37, 55-77**

- Introduction to stellar systems
- Time scales: Relaxation timescale & Dynamical timescale
- Potential theory, Basic definitions and concepts
- Potentials of Spherical systems
- Potentials of Flattened systems

**Lecture 9: 23.3.2017: "N-body codes and orbit theory" Binney & Tremaine: pages: 122-137, 142-158**

- Direct summation
- Tree codes
- Particle-mesh codes
- Orbits in Spherical potentials

**Lecture 10: 30.3.2017: "Orbit theory continued and numerical orbit integration" Binney & Tremaine: pages: 159-170, 196-211**

- Orbits in axisymmetric potentials
- Symplectic integrators
- Leapfrog integrators
- Regularisation

**Lecture 11: 6.4.2017: "Equilibria and Stability of Collisionless Systems" Binney & Tremaine: pages: 274-283, 287-292, 338-347)**

- The collisionless Boltzmann Equation
- Distribution functions for spherical systems
- Particle-based and orbit-based models

**Lecture 12: 20.4.2017: "The Jeans and virial equations and stellar kinematics as mass detector" Binney & Tremaine: pages: 347-372**

- The Jeans Equations
- The Tensor and Scalar Virial theorems
- Detecting black holes
- Extended mass distributions of elliptical galaxies

**Lecture 13: 25.4.2017: "Kinetic theory" Binney & Tremaine: pages: 554-573**

- Relaxation processes.
- General kinetic results.
- The thermodynamics of self-gravitating systems.

**Lecture 14: 4.5.2017: "Mergers of galaxies and galaxy formation" Binney & Tremaine: pages: 639-655, 674-678, 695-710**

- Dynamical friction and its application.
- Tidal radii and tidal forces.
- Galaxy mergers and the structure of merger remnants.
- Galaxy formation and galaxies in a cosmological setting.

**Problem sets: **

**3rd period:**

**4th period:**

**Final results and course grading: **

**Results from the problem sets:****Final grades:**