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Relative equilibria on a rotating meridian on $\mathbb{S}^2$ in equal-massthree-body problem under the cotangent potential are determined. We show theexistence of scalene and isosceles relative equilibria. Almost all isoscelestriangles, including equilateral, can form a relative equilibrium, except forthe two equal arc angles $\theta = \pi/2$. For $\theta\in (0,2\pi/3)\setminus\{\pi/2\}$, the mid mass must be on the rotation axis, in our case, at thenorth or south pole of $\mathbb{S}^2$. For $\theta\in (2\pi/3,\pi)$, the midmass must be on the equator. For $\theta=2\pi/3$, we obtain the equilateraltriangle, where the position of the masses is arbitrary. When the largest arcangle $a_\ell$ is in $a_\ell\in (\pi/2,a_c)$, with $a_c=1.8124...$, two scaleneconfigurations exist for given $a_\ell$.

Equal masses Eulerian relative equilibria on a rotating meridian of S^2