# 4.5.2 Properties of the astrometric data

Author(s): Lennart Lindegren

The astrometric results in Gaia EDR3 were not produced in a single large least-squares process, but were the end result of a long series of solutions using different versions of the input data and testing different calibration models and solution strategies. A complete astrometric solution consists of two parts, known as the primary solution and the secondary solution.

In the primary solution, which involves only a small fraction of the sources known as primary sources, the attitude and calibration parameters (and optionally the global parameters) are adjusted simultaneously with the astrometric parameters of the primary sources using an iterative algorithm. The reference frame is also adjusted using a subset of the primary sources identified as quasars.

In the secondary solutions the five astrometric parameters of every star are adjusted using fixed attitude, calibration, and global parameters from the preceding primary solution. The restriction on the number of primary sources comes mainly from practical considerations, as the primary solution is computationally and numerically demanding due to the large systems of equations that need to be solved. By contrast, the secondary solutions can be made one source at a time essentially by solving a system with only five unknowns (or six if pseudo-colour is also estimated). For consistency, the astrometric parameters of the primary sources are re-computed in the secondary solutions.

Gaia EDR3 finally gives full astrometric solutions (that is, positions, parallaxes, and proper motions) for about 1468 million sources (of which 882 million had six-parameter solutions, that is including the pseudocolour), with formal uncertainties ranging from about 0.015 mas to 2 mas in position at J2016.0, parallax, annual proper motion. For about 344 million sources with fall-back solutions the positional uncertainty at J2016 is about 1 to 4 mas. Basic statistics are given in Table 4.4 and Table 4.5 for sources with five- and six-parameter solutions, and in Table 4.6 for source with two-parameter (fallback) solutions.