The solution is a math model describing the corresponding astronomical position of each image pixel.
With the astrometric solution it is possible to: In the past, plate solving was done manually by accurately measuring photographic glass plates taken with an astrograph (astrographic camera)[2][3] Currently, astrometric solving is exclusively done by software programs.
The program extracts the star x,y positions from the celestial image, groups them in three-star triangles or four-star quads.
If it finds sufficient statistically reliable matches, it can calculate transformation factors.
There are several conventions to model the transformation from image pixel location to the corresponding celestial coordinates.