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The capture of compact bodies by black holes in galactic nuclei is animportant prospective source for low frequency gravitational wave detectors,such as the planned Laser Interferometer Space Antenna. This paper calculates,using a semirelativistic approximation, the total energy and angular momentumlost to gravitational radiation by compact bodies on very high eccentricityorbits passing close to a supermassive, nonspinning black hole; thesequantities determine the characteristics of the orbital evolution necessary toestimate the capture rate. The semirelativistic approximation improves upontreatments which use orbits at Newtonian-order and quadrupolar radiationemission, and matches well onto accurate Teukolsky simulations for loweccentricity orbits. Formulae are presented for the semirelativistic energy andangular momentum fluxes as a function of general orbital parameters.Comment: 27 pages, 12 figures; v2: revised manuscript includes small changes  to make paper consistent with published version; v3: a statement about how to  generalise our results to hyperbolic orbits was incorrect, new version  includes published erratum as an appendi

Semirelativistic approximation to gravitational radiation from encounters with nonspinning black holes