Homework Help: Rotation curve

1. Mar 13, 2007

b_o3

Hello everyone... can someone help me with this problem please:

The rotation curve V(r) for a mass distribution characterizes the rotational velocity of a test particle in orbit in its gravitational field as a function of radius from its center. Suppose you have a spherically symmetric mass distribution with the mass density p(r)=p0(r0/r)^3/2, where r0 and p0 are constants, derive the expression for M(r), the total mass interior to r. From this derive the rotation curve function. Suppose the mass distribution is trunctuated at some radius R0, what do you expect the rotation curve to look like (i.e as a function of r) at r>R0

any help would be appreciated, thanks :D

2. Mar 13, 2007

Mentz114

We need to see some attempt at a solution. What is the mass of a sphere with radius r and density p ?

3. Mar 13, 2007

b_o3

M= density*( (4/3)pi * r^3

4. Mar 13, 2007

Mentz114

If you put the density expression p(r) into your equation, you've nearly solved the first part.

5. Mar 14, 2007

b_o3

oh thanks, so i got M(r)= p0(r0/r)^3/2*4/3pi*r^3... now im supposed to derive the rotation curve function... isnt that just the circumference?

6. Mar 14, 2007

b_o3

can u help me out with deriving the rotation curve function... from that formula

7. Mar 14, 2007

Mentz114

To get the required expression for M(r) you must now work out the mass of a thin shell of thickness dr, then integrate that expresion wrt to r from 0 to r.
You need calculus now.

8. Mar 14, 2007

b_o3

so just replace the r with dr?

9. Mar 14, 2007

Mentz114

Try

mass of shell = M(r+dr)-M(r)

10. Mar 14, 2007

b_o3

thanks... ....

11. Mar 14, 2007

b_o3

should i integrate this formula or not

12. Mar 14, 2007

Mentz114

Yes, integrate it between 0 and r. This will give the final expression for M(r).

I have to go offline now, so it's over to you.

13. Mar 14, 2007

b_o3

alryty.. thanks alot :D

14. Mar 14, 2007

b_o3

wait a minute...

15. Mar 14, 2007

b_o3

can u PLZZZZ show me how to do the integration.. its just not working :S ... myt have something to do with my being up all nyt Oo

16. Mar 14, 2007

Mentz114

Go to bed.

17. Mar 14, 2007

b_o3

no... :(?.........

18. Mar 14, 2007

b_o3

lol yea... i need this done today tho
seriously cant u just give me the integrated formula i cant get it :S (i dnt take calculus_)

19. Mar 14, 2007

b_o3

COME On SAVE me ! ive just got this one problem left