# Homework Help: Orbital velocity and rotational velocity

1. Mar 19, 2012

### mun

Hi

Is "orbital velocity" supposed to be the same as "rotational velocity"? it seems that a "rotation curve" is supposed to plot the rotational velocity of a star, but then some articles e.g. http://en.wikipedia.org/wiki/Galaxy_rotation_problem claim "orbital speed" is plotted.

The equation for rotational velocity seems to be in the shape of V sin(i) but the equation for orbital velocity doesn't depend on sin.

Any help will be much appreciated.

Thanks!

2. Mar 19, 2012

### fzero

In this case the "orbital velocity" and "rotational velocity" refer to different objects. Galactic rotation refers to rotation of a galaxy, which is in turn composed of many stars. It is the orbital motion of these stars around the center of mass that corresponds to the rotation of the galaxy as a whole. So the rotational velocity of a galaxy is related to the the orbital speed of the constituent stars.

3. Mar 20, 2012

### mun

Hi

Thanks for the reply. So how is the rotational velocity of a galaxy related to the orbital speed of the constituent stars? It's probably not as simple as being related by a factor of a constant. What are the dependent factors here?

Thanks

4. Mar 20, 2012

### mun

Actually, some speak about the rotational velocity of stars: http://astro.berkeley.edu/~mwhite/darkmatter/rotcurve.html

"To make a rotation curve one calculates the rotational velocity of e.g. stars along the length of a galaxy by measuring their Doppler shifts..."

I thought a rotation curve plots the orbital velocity of stars (?)

Thanks

5. Mar 20, 2012

### fzero

In practice what is measured are the orbital speeds of stars at a given distance from the galactic center. The orbital speeds are found to be roughly constant, but that means that the angular speeds are still decreasing as we go to further distances. So the different parts of the galaxy are not moving together like a solid object. Therefore, it's not straightforward to just convert the orbital motion into a rotation of the galaxy at a whole.

It still makes sense to talk about a rotational speed at a given distance, since the orbital speed at a fixed distance is essentially the same for any star because of the relationship between the centripetal force and gravitational force. Some stars may have orbits that deviate from the galactic plane, though, so the reported rotational velocity at a given distance is an average of several measurements.

It seems to be just an abuse of terminology. It's clear from the discussion there that no one is measuring the rotation of the individual stars about their own axes.