GUIDELINES AND STUDY TIPS FOR QUIZ 1 ON MAR 30/2010


1. Please bring a calculator  No books or notes are allowed.

2. For the quiz, expect a mix of long and short questions. The
  questions will test conceptual understanding, a few will
  require you to work though simple algebra 

3. The quiz can include material covered in class up to the last 
  lecture on orbits (Th Mar 12), as well as related material 
  in the books. An expanded  class syllabus is on 
    http://www.as.utexas.edu/~sj/a381c-sp10/a381c-sp10-outline.txt 
   
Below are some study tips from the syllabus. Note, however, that
these tips are not exhaustive and  the quiz may  include some items 
that are not listed below:

For section (II) Important Timescales
a) you should know the significance of the  timescales, how to use 
  them, and know typical numbers for different stellar systems 
  galaxies, stellar clusters, etc

For section (III) Newtonian Dynamics and Potential Theory 
a) For spherical potential, you should know the expressions for
  Potential Phi  (e.g., Eq 9 on lecture of Tu Feb 9),  the 
  Gravitational force F, circular speed Vc, Escape speed Ve, 
  and total  Potential energy W

b) For spherical potential, if given density rho(r), you should
   know the 3 methods to get potential Phi(r), as discussed in 
   the solution for homework problem 2.3 :
    - Use Force times Distance to get work done
    - Integrate Poisson's Equation
    - Use the summation of shells at r'<r and r'=r to infinity

c) What are the relevance and practical applicability of different types
  of spherical rho(r) density profiles, e.g., Keplerian, Isochrone, Power
  laws with different indices,  NFW profile 

d) What are the relevance and practical applicability of different types
  of axisymmetric rho(R,z) density profiles, e.g., Logarithmic, Kuzmin?

e) Review the applications for spherical and axisymmetric potential 
  e.g., estimating lower limit on size of DM halo; the equation for 
  dynamical  heating of a thin locally isothermal disk; getting the
  M/L ratio for matter in the disk plane.
 

For section(IV) Stellar Orbits  

a) For different types of non-rotating potentials, such as 
    - spherically symmetric potential Phi(r) 
    - axisymmetric potential  Phi(R,z) 
    - 2D non-axisymmetric potential  Phi(R,phi)= Phi(x,y)
know
  - the surfaces of section and isolating integrals of motion (e.g., 
    E, Lz, L, approximate  version of L, Ex, Ex') 
  - the basic shape/nature of the main orbits (e.g., closed ellipse vs
    open rosettes for  Phi(r), quasi-planar loop orbits for  Phi(R,z), 
    near-circular orbits close to z=o plane for Phi(R,z), Lissajous 
    figures, box orbits  and loop orbits for  Phi(x,y))
 
b) For Phi(r):  you should know the basic equations of motion and
   expressions for  E, L

c) For Phi(R,z), and near-circular orbits close to z=0 plane: you 
  should know expressions for E and Lz as well as the epicyclic
  frequency kappa in terms   of Omega or Vc (e.g., equations 6d and
  6e given in class on Th  Mar 4/2010).
 
d) For  2D non-axisymmetric rotating potential : you should know

 - the equation of motion  in the rotating frame 
      d^2x/dt^2 = -Grad(phi)  + Fictitious forces including Coriolis,
                                 Centrifugal
 - the Jacobi Integral  (conserved quantity)
-  the Lagrange points