AIM: A course in point-mass gravitational dynamics in the context of the Solar System, stellar, galactic, and extragalactic environments.
LEVEL:
First year graduate (see prereqs below)
or 4th year honours with the permission of the instructor.
TEXTBOOKS:
- Solar System Dynamics (Burns and Gladman, chapters provided free of charge)
Required:
- Galactic Dynamics. Binney and Tremaine (Princeton University Press). MUST BE 2ND EDITON
Other potentially-useful references (not required):
- Galactic Astronomy. Binney and Merrifield (Princeton University Press)
- Solar System Dynamics. Dermott and Murray.
PREREQUISITES:
- Undergraduate classical mechanics at honours physics level. You
should have seen Hamilton's equations of motion.
- Differential equations at honours physics level (PDEs).
- Elementary knowledge of a scientific programming language. Some
numerical exploration will be required.
HOURS PER WEEK: Two 1.33 hr meetings per week.
3 CREDITS : Coursework will consist of assigned readings, discussion, assignments as well as midterm and final examimations.
Evaluation:
Midterm: 20%
Final: 30%
Homework: 40%
Participation: 10%
Unit: CELESTIAL MECHANICS
- Overview of solar system structure
- The 2-body problem
- The restricted 3-body problem
- Numerical techniques
- The N-body problem and dynamical chaos
- Resonances, perturbation equations
- The stability of the solar system
- Extrasolar Planets
* The level of the above topics is as covered in the commonly available:
Orbital Motion, 3rd Edition. A.E. Roy
Fundmentals of Celestial Mechanics, J.M.A. Danby
Solar System Dynamics, C.D. Murray and S.F. Dermott
* The remaining topics are on the scope of the coverage of that topic in:
Galactic Dynamics, 2nd edition. J. Binney and S. Tremaine
Most of the material is in Chapters 1-3, 7 and 8
Unit: GALACTIC/STELLAR DYNAMICS
- The structure of the galaxy
- Galactic kinematics
- Evidence for dark matter
- Dynamical friction
- Dynamics of star clusters
Unit: EXTRAGALACTIC DYNAMICS
- Galactic potentials and orbits
- Dynamics of clusters of galaxies
- Environmental effects
Date Readings HW due Jan 9 No readings due none due (HW1 assigned, due Jan 16) Jan 11 Ch 1, Ch 2 to end 2.2 no HW due, HW2 assigned Jan 16 2.3-2.7 HW1, HW2(Ch2 Q7 clarified) Jan 18 2.8, 2.9 HW3 (Ch 2, Q15)) Jan 23 2.10, 2.11, delayed HW 3 due Jan 25 3.1, 3.2 HW4 due (Kepler solver) Jan 30 rest of chapter 3 HW5 (planet position and Q8 Ch 3) Feb 1 None HW6 (sent via email). Feb 6 Chpt 4 to end of 4.3 HW7:Ch4 Q3. Note Q11 due Feb 8, a-d can be done already ) Feb 8 4.6, 4.7 HW8 : All of Ch4 Q11 (part e included) Feb 13 5.1 (emailed) HW 6,7,8 to be turned in. Feb 15 Remainder of Ch 5 HW9 will be due Feb 27 Feb 27 Chapter 6 HW9: Ch 5 Q4 + Q14, Ch 6 Q 5(b)+(c) Feb 29 Midterm exam -- Mar 5 8.1-8.5,skip Eqs 8.18-8.22 HW10 is to show (8.27) to 2nd order (only) Mar 7 8.6-8.8 HW11 Ch 8, Q11 Mar 12 Chpt 9 to Eq (9.10), 9.6 HW12 Ch 9, Q1 Sections now refer to Binney and Tremaine 2nd edition Mar 14 Chpt 1 to end p.20, 1.14 to end 1.1.6 No HW. Mar 19 Chpt 2 to end 2.2 (see email for skips!) HW13 : Chpt 2, Q1 Mar 21 2.3 and 2.4 no HW due. HW14 will be Chpt 2, Q7 Mar 26 2.7,Ch3 to end 3.1c, skip boxes HW14 due. Mar 28 3.1.1 to (3.57), 3.2-footnote 6 no HW due. Apr 2 3.3 to end p. 175 HW15 (oops, readings initially said p185) Apr 4 3.3 to end p. 184 HW16 (error: says 15 on printed) Apr 9 1.2, Chpt 4 to end of 4.1 HW17 Apr 11 4.8.3 to end p361, Ch7 to end 7.1, 7.5.3, 7.5.4, 8.3.1 No HW April 17 Final exam 12:15-14:45 In HENNINGS 309