Applied Physics and Mathematics Annotation << Back ON THE SIZE OF THE POSITRONIUM ATOM IN THE CONTEXT OF THE TWO-BODY PROBLEM I.P. POPOV From the fact that the Bohr radius of positronium is twice that of hydrogen, it naturally follows that the volume of a sphere described around a positronium atom is eight times greater than the volume of a sphere described around a hydrogen atom. The double Bohr radius of positronium is the magnitude of the displacement vector, which is twice the distance from the electron and positron to the positronium center of mass. This means that the sphere described around the positronium atom is identical to the sphere described around the hydrogen atom. In other words, the hydrogen and positronium atoms have almost the same size, which contradicts the initial idea. Keywords: positronium, hydrogen, electron, positron, Bohr radius, two-body problem, displacement vector, reduced mass. DOI: 10.25791/pfi m.02.2024.1291 Pp. 14-16.