Approaches to Solving Galactic Dynamics Problems

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SUMMARY

The discussion centers on solving problems related to Galactic Dynamics, specifically addressing homework questions involving Poisson's equation, Jeans' equation, and classical Newtonian mechanics. The participants express uncertainty in defining relaxation time mathematically and solving for trajectory r(t) in question 3b. Additionally, they seek clarification on deriving a density distribution from Jeans' equation, which is not covered in lectures. The conversation highlights the need for external resources and deeper understanding of these equations to tackle the assigned problems effectively.

PREREQUISITES
  • Understanding of Poisson's equation in astrophysics
  • Familiarity with Jeans' equation and its applications
  • Knowledge of classical Newtonian mechanics
  • Basic mathematical skills for solving differential equations
NEXT STEPS
  • Study the derivation and applications of Poisson's equation in astrophysical contexts
  • Learn how to apply Jeans' equation to derive density distributions in stellar systems
  • Explore methods for solving differential equations related to trajectories in gravitational fields
  • Review classical mechanics principles to clarify the influence of potential on massless particles
USEFUL FOR

This discussion is beneficial for students and researchers in astrophysics, particularly those tackling problems in Galactic Dynamics, as well as educators seeking to enhance their teaching materials on related topics.

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Homework Statement


http://www.mso.anu.edu.au/~kcf/ATA/ATA_assignment.pdf
Question One
Question 3b
Question 4b2. Homework Equations /Attempt at a solution
For the first one I am not even sure how to approach this, i understand/have poissons equation, general laws of motion and an idea of what relaxation time should be but I am not sure how to mathematically define it.

For 3b i get http://members.iinet.net.au/~housewrk/3rd/3b.jpg with L const and I am not sure how to go about solving that for the trajectory r(t)

For 4b I had to hunt around for Jeans' equation (not given in lectures, sort of a read outside the course thing) and using the info in the question used the reduced form of http://members.iinet.net.au/~housewrk/3rd/4b.jpg and again not sure how to get a density distribution out of that, as this form seems to treat it on a single particle basis. To be perfectly honest i thought it was a trick question as if theyre massless why should they be influenced by the potential? (we're only considering classical Newtonian mechanics in this course, not GR stuff)Any help (pointing out my stupid mistakes included, if youre nice) would be greatly appriciated =D

Thanks
-G
 
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