Question

Obtain an expression for the radial velocity of objects in the galaxy as a function of their
galactic longitude.

Answer 1

Radial velocity components projected on to the line of sight:

$$v_r=\theta v_0 \cos{l} – Δv \sin{l} (1)$$

Using (1) we got:

$$v_r = \frac {v_0} {R_0} r \sin{l} \cos{l} - \frac {dv} {dR} r \sin{l} \cos{l} (2)$$

$$v_r = \frac {v_0} {R_0} r \sin{l} \cos{l} - \frac {dv} {dR} r \sin{l} \cos{l} (3)$$

where

$$A = \frac {1} {2} (\frac {v_0} {R_0} - \frac {dv} {dR})$$

is Oort's first (sheer) constant