Aberration in proper motions

Approved space astrometric missions ( SIM, GAIA) are aiming at a few microarcseconds per year precision in yearly proper motions and even less than a microarcsecond in the definition of an extragalactic reference frame. At such a level of accuracy, the curvature of stellar orbits around the center of the Galaxy cannot be neglected. The curvature of the Solar system barycentric motion induces a time- dependent component of the aberration, which has the properties of an apparent proper motion of the galaxies. This effect reaches 4 muas per year in some regions of the sky. In the case of stars, it is combined with a similar effect due to the curvature of the circular galactocentric orbit of the star, which may reach 60 muas per year for a star situated at 500 parsecs from the center of the Galaxy, and much larger closer to it. The paper gives the proofs and the formulae permitting one to compute this aberration in proper motions. The conclusion is that, at this high level of accuracy, one should present the astrometric data in a galacto- centric rather than in a barycentric reference frame.