When an object is close enough to us, it is possible to estimate its radial velocity based on the change of the parallax with time. We recall that if the parallax of some distance object is $ \alpha $ and the distance to the sun is $ A $, then the distance to the object is

$ d = \frac{A}{\alpha} $

If the time derivative of the parallax can be measured, then the radial velocity of the object is

$ v_{r} = \dot{d} = - A \frac{\dot{\alpha}}{\alpha^2} $