# Oribtal and rotational velocities

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 20, 2012

### mathman

There may be some terminology confusion. Orbital speed refers to individual stars, while rotational velocity refers to the galaxy as a whole.

3. Mar 20, 2012

### colin456

Hi Mun

I am not sure that there actually is a particularly rigidly defined set of definitions for these terms and I find that they are often used to mean different things. In my experience, 'orbital velocity' and 'rotational velocity' generally mean the same thing when you are discussing an object orbiting another body, i.e. the Earth around the sun, or the sun around the centre of a galaxy. In this case, both terms usually refer to the actual velocities of the orbiting objects, and not the angular velocities (though I suspect it may rarely be used this way).

The term 'rotational velocity' is used in a lot more situations, and usually refers to the velocity of a thing that is rotating around some point. For instance, you may be looking at a frisbee that is spinning: the rotational velocity of some point on that frisbee is its actual velocity.

I do not know where the sin i term comes into all this, but I suspect it has to do with what is normally called 'projected rotational velocity'. That is the component on the rotational velocity in the direction towards or away from us (i.e. in the 'radial direction') and is given by vsini, where v is the actual rotational velocity of the object in question, and i is the angle between our line-of-sight, and the axis around which the object is rotating. For instance, consider the spinning frisbee again. If you look down on the frisbee from above, such that it looks like a circle, the i in vsini is going to be zero, and so the projected rotational velocity of each point on the frisbee is zero, corresponding to the fact that no point on the frisbee is moving towards you or away from you. If you look at the frisbee edge on, such that is looks more or less like a line, i will be 90 degrees, and so vsini with equal v.

This is important in astronomy since the velocities of objects are often measures using Doppler shift, which really measures the 'radial velocity'.