Jacobi vs tidal radius for star cluster
In the book Galactic Dynamics by Binney and Tremaine (second edition) there is a whole section explaining the difference between the Jacobi radius and the tidal radius (page 677-chapter 8).

Here, $r_J$ is defined as:


  $$r_J=  R_0\left(\frac{m}{3M}\right)^{1/3}$$ 
  The Jacobi radius $r_J$ (also, Roche or Hill radius) of an orbiting stellar system is expected to correspond to the observational tidal radius, the maximum extent of the satellite system. However this correspondence is only approximate.


Five reasons are subsequently given to explain why the correspondence is only approximate.