  We first provide a classification of the pure rotational motion of 2
particles on a sphere interacting via a repelling potential. This is achieved
by providing a simple geometric equivalence between repelling particles and
attracting particles, and relying on previous work on the similar
classification for attracting particles. The second theme of the paper is to
study the 2-body problem on a surface of constant curvature treating the
curvature as a parameter, and with particular interest in how families of
relative equilibria and their stability behave as the curvature passes through
zero and changes sign. We consider two cases: firstly one where the particles
are always attracting throughout the family, and secondly where they are
attracting for negative curvature and repelling for positive curvature,
interpolated by no interaction when the curvature vanishes. Our analysis
clarifies the role of curvature in the existence and stability of relative
equilibria.
