Pairs of short root subgroups in the Chevalley group of type $G_2$

The present paper is devoted to the pairs of unipotent short root subgroups in the Chevalley group of type $G_2$ over a field of characteristic distinct from 2. Namely, we describe the subgroups generated by a pair of short root subgroups and classify the orbits of the Chevalley group acting by the simultaneous conjugation on such pairs. Most of the calculations are valid for fields of characteristic 2.