Marginally stable circular orbit of a test body in spherically symmetric   and static spacetimes
  We study a marginally stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a timelike geodesic in any spherically symmetric and static spacetime. It turns out that the metric components are separable from the constants of motion along geodesics. We show also that a metric component $g_{rr}$ with a radial coordinate $r$ does not affect MSCOs. This suggests that, as a test of gravity, any ISCO measurement may be put into the same category as gravitational redshift experiments. MSCOs for exact solutions to the Einstein's equation are also mentioned. 
Toshiaki Ono, Tomohito Suzuki, Naomasa Fushimi, Kei Yamada, Hideki   Asada
gr-qc astro-ph.HE hep-th