Application of Sturms theorem to marginal stable circular orbits of a test body in spherically symmetric and static spacetimes

In terms of Sturms theorem, we reexamine a marginal stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a timelike geodesic in any spherically symmetric and static spacetime. MSCOs for some of exact solutions to the Einsteins equation are discussed. Strums theorem is explicitly applied to the Kottler (often called Schwarzschild-de Sitter) spacetime. Moreover, we analyze MSCOs for a spherically symmetric, static and vacuum solution in Weyl conformal gravity.