  The capture of compact bodies by black holes in galactic nuclei is an
important 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 momentum
lost to gravitational radiation by compact bodies on very high eccentricity
orbits passing close to a supermassive, nonspinning black hole; these
quantities determine the characteristics of the orbital evolution necessary to
estimate the capture rate. The semirelativistic approximation improves upon
treatments which use orbits at Newtonian-order and quadrupolar radiation
emission, and matches well onto accurate Teukolsky simulations for low
eccentricity orbits. Formulae are presented for the semirelativistic energy and
angular momentum fluxes as a function of general orbital parameters.
