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A Fortran implementation of the Barnes-Hut hierarchical tree algorithm is presented and analyzed in the context of the astrophysical N-body problem. The errors introduced into the force calculation as a result of the clustering of distant particles, and their influence on the relaxation time and physical conservation laws, are considered. Tree algorithms should be suitable for studying a wide range of astrophysical phenomena, including potentially both collisional and collisionless systems. As an example, a simulation of the decay of a satellite orbit around a self-gravitating disk with N = 32,768, performed with the tree method, is compared with previous calculations.
Lars Hernquist (1987) studied this question.