We study relative equilibria (\(RE\)) for the 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, isosceles, and equilateral Euler \(RE\), and isosceles and equilateral Lagrange \(RE\). We also show that the equilateral Euler \(RE\) on a rotating meridian exists for general potential \(\sum_{i<j}m_{i}m_{j}U(\cos\sigma_{ij})\) with any mass ratios.

我们在仅取决于 \( \cos\sigma_{的一般势的影响下，研究\(\mathbb{S}^{2}\)上三体问题的相对平衡 ( \ (RE\) ) ij}\)其中\(\sigma_{ij}\)是质量之间的相互角度。显示了质量\(m_{k}\)和\(\cos\sigma_{ij}\) 形成相对平衡的显式条件。利用上述条件，我们研究了余切势下的等质量情况。我们证明了斜角线、等腰和等边欧拉\(RE\)以及等腰和等边拉格朗日\(RE\)的存在性。我们还证明，对于一般势\(\sum_{i<j}m_{i}m_{j}U(\cos\sigma_{ij})\) 而言，旋转 子午线上的等边欧拉\(RE\)存在，其中任何质量比。