  We compute the geodesic curvature of logarithmic spirals on surfaces of
constant Gaussian curvature. In addition, we show that the asymptotic behavior
of the geodesic curvature is independent of the curvature of the ambient
surface. We also show that, at a fixed distance from the center of the spiral,
the geodesic curvature is continuously differentiable as a function of the
Gaussian curvature.
