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ISCOs and OSCOs in the presence of positive cosmological constant

Normally one thinks of the observed cosmological constant as being so small that it can be utterly neglected on typical astrophysical scales, only affecting extremely large-scale cosmology at Gigaparsec scales. Indeed, in those situations where the cosmological constant only has a quantitative influence on the physics, a separation of scales argument guarantees the effect is indeed negligible. The exception to this argument arises when the presence of a cosmological constant qualitatively changes the physics. One example of this phenomenon is the existence of outermost stable circular orbits (OSCOs) in the presence of a positive cosmological constant. Remarkably the size of these OSCOs are of a magnitude to be astrophysically interesting. For instance: for galactic masses the OSCOs are of order the inter-galactic spacing, for galaxy cluster masses the OSCOs are of order the size of the cluster.