  Let $\Omega$ be a domain in $\mathbb{C}$ with hyperbolic metric
$\lambda_\Omega(z)|dz|$ of Gaussian curvature $-4.$ Mejia and Minda proved in
their 1990 paper that $\Omega$ is (Euclidean) convex if and only if
$d(z,\partial\Omega)\lambda_\Omega(z)\ge1/2$ for $z\in\Omega,$ where
$d(z,\partial\Omega)$ denotes the Euclidean distance from $z$ to the boundary
$\partial\Omega.$ In the present note, we will provide similar
characterizations of spherically convex domains in terms of the spherical
density of the hyperbolic metric.
