Oort constants

The Oort constants (discovered by Jan Oort) ${\displaystyle A}$ and ${\displaystyle B}$ are empirically derived parameters that characterize the local rotational properties of our galaxy, the Milky Way, in the following manner:

${\displaystyle {\begin{aligned}&A={\frac {1}{2}}\left({\frac {V_{0}}{R_{0}}}-{\frac {dv}{dr}}{\Bigg \vert }_{R_{0}}\right)\\&B=-{\frac {1}{2}}\left({\frac {V_{0}}{R_{0}}}+{\frac {dv}{dr}}{\Bigg \vert }_{R_{0}}\right)\\\end{aligned}}}$

where ${\displaystyle V_{0}}$ and ${\displaystyle R_{0}}$ are the rotational velocity and distance to the Galactic Center, respectively, measured at the position of the Sun, and v and r are the velocities and distances at other positions in our part of the galaxy. The rotational velocity means the average speed of stars in the circumferential direction, which differs from that of a particular star or the sun. As derived below, A and B depend only on the motions and positions of stars in the solar neighborhood. As of 2018, the most accurate values of these constants are ${\displaystyle A}$ = 15.3 ± 0.4 km s⁻¹ kpc⁻¹, ${\displaystyle B}$ = −11.9 ± 0.4 km s⁻¹ kpc⁻¹.