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Information about the course:

PAP317 Advanced dynamics (Dynamiikan jatkokurssi)

Lecturers: Prof. Peter Johansson (Room D332)
                   Dr. Mikael Granvik (Room D312)

Course assistants:  Dr. Pauli Pihajoki (Room D325)
                                  M.Sc. Lauri Siltala (Room D308)


Lectures: Mondays 10.15-12.00  Room D115, Physicum
Problem sessions: Four times in total on Mondays 14.15-16.00 Room D115 Physicum on the following dates: 11.2 and 11.3 (period 3) and 1.4 and 29.4 (period 4)


First lecture on 14.1.2019 and last lecture on 29.4.2019

  • 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:
  1. B. Gladman & J. Burns: Planetary Dynamics, 2011 (draft of a book under preparation)
  2. J. Binney & S. Tremaine: Galactic Dynamics, Second Edition, Princeton University Press, 2008
  • Additional material can be found in  the following books
  1. J. M. A. Danby, Fundamentals of Celestial Mechanics, Second Edition, Willmann-Bell, Inc., 1992
  2. G. Bertin: Dynamics of Galaxies, Cambridge Univ Press, 2000.


The course project is about the dynamics of dwarf planet Pluto with these initial conditions.

Deadline: 30.04.2019. The maximum award is 30 exercise points.


Final exam:

  • The final exam will be held on Wednesday 8.5.2019 at 10-14 in Room D115, Physicum

Course syllabus:

Lecture 1: 14.1.2019: "Introduction to solar system dynamics"

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

Lecture 2: 21.1.2019: "2-body problem and applications"

  • TBD

Lecture 3: 28.1.2019: "Perturbation theory"

  • TBD

Lecture 4: 4.2.2019: "N-body problem and numerical integration"

  • TBD

Lecture 5: 11.2.2019: "3-body problem"

  • TBD

Lecture 6: 18.2.2019: "Disturbing function and secular dynamics"

  • TBD

Lecture 7: 25.2.2019: "Novel concepts in planetary-system dynamics"

  • Yarkovsky effect
  • Planetary migration

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Lecture 8: 11.3.2019: "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: 18.3.2019: "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: 25.3.2019: "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: 1.4.2019: "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: 8.4.2019: "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: 15.4.2019: "Relaxation processes and Kinetic theory" Binney & Tremaine: pages: 376-386, 554-573

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

Lecture 14: 29.4.2019: "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:

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