I present three methods to determine the distance to the Galactic Centre R0, the solar azimuthal velocity in the Galactic rest frame Vg, ⊙ and hence the local circular speed Vc at R0. These simple, model-independent strategies reduce the set of assumptions to near-axisymmetry of the disc and are designed for kinematically hot stars, which are less affected by spiral arms and other effects. The first two methods use the position-dependent rotational streaming in the heliocentric radial velocities (U). The resulting rotation estimate θ from U velocities does not depend on Vg, ⊙.
The first approach compares this with rotation from the Galactic azimuthal velocities to constrain Vg, ⊙ at an assumed R0. Both Vg, ⊙ and R0 can be determined using the proper motion of Sgr A* as a second constraint. The second strategy makes use of θ being roughly proportional to R0. Therefore a wrong R0 can be detected by an unphysical trend of Vg, ⊙ with the intrinsic rotation of different populations. From these two strategies I estimate R0 = (8.27 ± 0.29) kpc and Vg, ⊙ = (250 ± 9) km s−1 for a stellar sample from Sloan Extension for Galactic Understanding and Exploration, or, respectively, Vc = (238 ± 9) km s−1. The result is consistent with the third estimator, where I use the angle of the mean motion of stars, which should follow the geometry of the Galactic disc. This method also gives the solar radial motion with high accuracy.
The rotation effect on U velocities must not be neglected when measuring the solar radial velocity U⊙. It biases U⊙ in any extended sample that is lop-sided in position angle α by of the order of 10 km s−1. Combining different methods I find U⊙ ∼ 14 km s−1, moderately higher than previous results from the Geneva–Copenhagen Survey.