Consideration of antigravity for antiparticles is an attractive target for
various experimental projects. There are a number of theoretical arguments
against it but it is not quite clear what kind of experimental data and
theoretical suggestions are involved. In this paper we present straightforward
arguments against a possibility of antigravity based on a few simple
theoretical suggestions and some experimental data. The data are: astrophysical
data on rotation of the Solar System in respect to the center of our galaxy and
precision spectroscopy data on hydrogen and positronium. The theoretical
suggestions for the case of absence of the gravitational field are: equality of
electron and positron mass and equality of proton and positron charge. We also
assume that QED is correct at the level of accuracy where it is clearly
confirmed experimentally