The derivation also implicitly assumes that the gravitational potential of the Milky Way is axisymmetric and always directed towards the center. This ignores the effects of spiral arms and the Galaxy's bar. Finally, both transverse velocity and distance are notoriously difficult to measure for objects which are not relatively nearby.
The derivation also assumes that the gravitational potential of the Milky Way is symmetrical and always points towards the center, which ignores the effects of spiral arms and the Galaxy's bar. Additionally, both transverse velocity and distance are notoriously difficult to measure for objects that are not close by.