A geometric (0-dimensional) point that may be assigned a finite mass. Since a point has zero volume, the density of a point mass having a finite mass is infinite, so point masses do not exist in reality. However, it is often a useful simplification in real problems to consider bodies point masses, especially when the dimensions of the bodies are much less than the distances among them.
The approximation is actually rigorous in the case of the gravity of a solid body having mass distributed with spherical symmetry, since an analytic derivation shows that the body acts exactly as a point mass at the body's center containing the body's entire mass.
