  We study relative equilibria ($RE$ in short) for three-body problem on
$\mathbb{S}^2$, under the influence of a general potential which only depends
on $\cos\sigma_{ij}$ where $\sigma_{ij}$ are the mutual angles among the
masses. Explicit conditions for masses $m_k$ and $\cos\sigma_{ij}$ to form
relative equilibrium are shown. Using the above conditions, we study the equal
masses case under the cotangent potential. We show the existence of scalene and
isosceles Euler $RE$, and isosceles and equilateral Lagrange $RE$.
