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In this article we address a number of features of the moduli space ofspherical metrics on connected, compact, orientable surfaces with conicalsingularities of assigned angles, such as its non-emptiness and connectedness.We also consider some features of the forgetful map from the above moduli spaceof spherical surfaces with conical points to the associated moduli space ofpointed Riemann surfaces, such as its properness, which follows from anexplicit systole inequality that relates metric invariants (spherical systole)and conformal invariant (extremal systole).

Spherical surfaces with conical points: systole inequality and moduli spaces with many connected components