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We calculate to post^3. 5-Newtonian order of approximation of general relativity the radiation-reaction part of the ADM Hamiltonian for a many-body system of nonspinning point masses. The Hamiltonian is applied to the derivation of the gravitational energy loss of a gravitationally bound two-body system in quasielliptic motion. Agreement with the known result for the time-averaged energy loss is obtained to order (v/c) ^7.
Jaranowski et al. (1997) studied this question.