### The doppler factor

Note that the systemic velocity is often given in a different frame (LSR, heliocentric) than the measervatory frame. As long as the new systemic velocity is given in the same frame as the old systemic velocity, it is possible to compute the new doppler factor from the old one. Let's assume that the systemic velocity is given in the LSR frame. We have

(64)
Subtracting both equation gives
(65)