# Rotation curve

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

## Answers and Replies

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

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

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

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?

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

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.

so just replace the r with dr?

Try

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

thanks... ....

should i integrate this formula or not

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.

alryty.. thanks alot :D

wait a minute...

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

Go to bed.

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

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_)

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