I was going to put this up in the homework forum, but I feel the folks down here are more capable of helping me out.

I have to do an assignment, but I cannot go in for office hours to get help from my professor. Regretfully, I lost the sheet and forgot to grab another until just a few days ago and now I'm on my own. All I really need are the formulas.

Here goes:

1. I can do part a, but I am completely flabbergasted at part b.

2. Need formula

3. Need formula

4. I believe I can do this one, but don't I need the velocity of the coma cluster to solve it?

1b) Use the circular orbit acceleration formula: a=v^2/r. Now just think what supplies the acceleration?

2) Use the same formula as 1b. Keep in mind what supplies the acceleration. I believe we can assume spherical symmetry since the dark matter distribution (majority of the mass) is more or less spherical.

3) This is just simple trig. Draw an isosceles triangle with and angle of 28.5*.5 degrees as the angle. The opposite leg is the length you want to find. The bisector of that leg to your angle is 4 Mpc. Do some trig (split the triangle into 2 right triangles), and you should get the answer.

4) You don't need the velocity or the distance. Just find how long it takes the scale factor a to double. For uniform expansion, a governs the expansion of the whole universe. So when a doubles, the proper distances to every point doubles. Remember:

Thank you guys very much for your replies. This has really helped.

@ Astronuc: The force of gravity pulling the particle down and the force of movement to the side?

@ Matterwave: I'm really confused as to how one gets mass out of the equation you listed. It seems that there's a bit more to questions 1b and 2 than I thought.

I'm thinking I need to figure out how massive certain volumes-

I just realized v represented volume. Now I get it.