Calculating the ring relative velocities

In order to be able to calculate the Doppler shift of the radiation emitted from one ring on the line of sight as it impacts another ring on the line of sight it is necessary to calculate the relative velocities between each ring on each line of sight. Once again this problem lends itself to using vectors. First consider the possible velocities that the cloud may have. In order to be completely general it is necessary to describe three components of velocity:

• Radial velocity - This defines infall (negative) or expansion (positive) (stored in $velvr$)
• Rotational velocity - This defines the rotation of the cloud (positive is clockwise rotation when the cloud is viewed from 'above')(stored in $velvt$)
• Vertical velocity - This defines velocity along the z-axis (and can be used to define the motion in bi-polar outflows for example)(stored in $velvz$)