The local stellar kinematics of the Milky Way offer a useful tool for studying the rotation curve of the Galaxy .
These kinematics – usually parameterized by the Oort constants A and B – depend on the local gradient of the rotation curve as well as its absolute value ( \Theta _ { 0 } ) , and the Sun ’ s distance to the Galactic center ( R _ { 0 } ) .
The density of interstellar gas in the Milky Way is shown to vary non-monotonically with radius , and so contributes significantly to the local gradient of the rotation curve .
We have therefore calculated mass models for the Milky Way that include this component , and have derived the corresponding radial variation in the Oort constants .
Between 0.9 R _ { 0 } and 1.2 R _ { 0 } the Oort functions A ( R ) and B ( R ) differ significantly from the general \sim \Theta _ { 0 } / R dependence .
Various previously-inexplicable observations are shown to be consistent with these new predictions .
For example , these models may explain the \sim 40 % difference between the values for 2 A \mbox { $R _ { 0 } $ } derived from radial velocity data originating in the inner and outer Galaxy [ Merrifield 1992 ] .
They also go some way toward explaining the different shapes of the velocity ellipsoids of giant and dwarf stars in the solar neighbourhood .
However , a consistent picture only emerges if one adopts small values for the radius of the solar circle ( R _ { 0 } = 7.1 \pm 0.4 kpc ) and local circular speed ( \Theta _ { 0 } = 184 \pm 8 { km s } ^ { -1 } ) .
With these Galactic constants the Milky Way ’ s rotation curve declines slowly in the outer Galaxy ; V _ { rot } ( 20 kpc ) = 166 { km s } ^ { -1 } .
Our low value for the distance to the Galactic center agrees well with the only direct determination of R _ { 0 } ( 7.2 \pm 0.7 kpc , Reid 1993 ) .
Using these Galactic constants , we find that the proper motion of Sgr A ^ { * } is consistent with the observational constraints [ Backer & Sramek 1987 , Backer 1996 , Reid 1998 ] .
Simple analytic arguments as well as detailed calculations show that the radial velocities and proper motions of our best fit model are entirely consistent with the radial velocities of Cepheids [ Pont , Mayor & Burki 1994 ] and the Hipparcos measurements of their proper motions [ Feast & Whitelock 1997 ] .