  The study of circular orbits in spacetime is of astrophysical importance. The
identification and classification of circular orbits in both static and
stationary spacetimes remains an active area of interest. Even in the simplest
static spherically symmetric case, it is well known that the introduction of a
cosmological constant in vacuum leads to the study of quartic polynomials in
order to locate \textit{boundary orbits}, those that straddle between stable
and unstable orbits. These orbits are often referred to as `marginally stable
orbits' or `indifferently stable orbits'. A comprehensive study of texts offers
little clarification as to the stability or instability of these boundary
orbits. Here we argue that the direct use of second order perturbation theory
immediately shows that these boundary orbits are unstable in the perturbative
sense. Our study here includes the two-particle Curzon-Chazy solution.
