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The authors have developed a hybrid computing system called HMCS-G, a Grid-enabled Heterogeneous Multi-Computer System, that provides a multiple cluster environment centered around a dedicated machine for gravity calculation. The purpose of HMCS-G is to provide an ideal computational environment for astrophysical study involving multiple physical phenomena. The worker cluster may comprise general-purpose PCs to perform tasks such as hydrodynamics computations, while the special-purpose machine, in this case a GRAPE-6 cluster, performs gravity calculations for all pairs of particles in the system. These systems are connected by OmniRPC, a grid-enabled RPC system that supports Globus and ssh for authentication. HMCS-G effectively provides worldwide access to a GRAPE-6 cluster, thereby securing several TFLOPS performance for intensive computations such as gravity calculation. All participating PC-clusters share this resource in a time-based manner using grid technology. The actual turn-around response time was measured for a system implemented over a number of institutions, and it was confirmed that HMCS-G provides acceptable real-world application performance. Precise simulations of galaxy formation are currently being performed on clusters in several institutes, involving smoothed particle hydrodynamics and radiative transfer in the context of complete gravity calculation as the first real application of HMCS-G.