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. 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.^[1] From the Oort constants, it is possible to determine the orbital properties of the Sun, such as the orbital velocity and period, and infer local properties of the Galactic disk, such as the mass density and how the rotational velocity changes as a function of radius from the Galactic Center.