set6-06-sol

# set6-06-sol - Astro 346 Spring Semester 2006 Homework 6th...

This preview shows pages 1–2. Sign up to view the full content.

Astro 346, Spring Semester 2006 Homework, 6th set, solutions. Problem 1: The relaxation problem in galaxy cannibalism (10 P) In problem 9.11 the last expression is derived using the result of problem 9.10, namely that the stellar orbits are virialized. Then the average kinetic energy of stars is half their average potential energy, so V 2 = G M 2 R That assumption should not be made in problem 14.3, because we look at the interaction between two galaxies whose stars are not yet on virialized orbits. So, you should start with the second-to-last equation of problem 9.11, after correction that now we are not dealing with star-star interactions, but star vs. galaxy core ( m * vs. m ). t relax = V 3 4 π G 2 m m * n ln(2 R/r ) ( X ) Here r is the impact parameter (closest separation along trajectory) for strong deflection as determined in 9.11, so the logarithmic term can be modified to the form given in 14.3. 1 r = V 2 2 G m 2 R r = R V 2 G m Note that the cluster core radius was denoted with an upper case R in 9.11, but the galaxy core radius in 14.3 is written as lower case

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern