Tidal shocking by extended mass distributions

We derive expressions for the tidal field exerted by a spherically symmetri c galaxy having an extended mass distribution and use our analysis to calcu late tidal heating of stars in a globular cluster or a satellite galaxy. We integrate the tidal force over accurate orbits in various models for the p rimary by using the impulse approximation, coupled with adiabatic correctio ns that allow for time variation of the perturbation. We verify the results with direct N-body simulations, and we also compare them with the conventi onal straight-path approximation. Heating on highly eccentric orbits domina tes, since adiabatic corrections strictly prohibit energy changes on low-ec centricity orbits. The results are illustrated for globular cluster NGC 671 2. For the orbital eccentricities higher than 0.9, the future lifetime of N GC 6712 is less than 10(10) yr. Our analysis can be used to study tidal int eractions of star clusters and galaxies in a semianalytical manner.