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Gravitational wave energy spectrum of hyperbolic encounters

The emission of gravitational waves is studied for a system of massive objects interacting on hyperbolic orbits within the quadrupole approximation following the work of Capozziello et al. Here we focus on the derivation of an analytic formula for the energy spectrum of the emitted waves. We checked numerically that our formula is in agreement with the two limiting cases for which results were already available: for the eccentricity ε = 1, the parabolic case whose spectrum was computed by Berry and Gair, and the large ε limit with the formula given by Turner.