We derive an analytic expression for the energy spectrum of gravitational waves from a parabolic Keplerian binary by taking the limit of the Peters and Mathews spectrum for eccentric orbits .
This demonstrates that the location of the peak of the energy spectrum depends primarily on the orbital periapse rather than the eccentricity .
We compare this weak-field result to strong-field calculations and find it is reasonably accurate ( \sim 10 \% ) provided that the azimuthal and radial orbital frequencies do not differ by more than \sim 10 \% .
For equatorial orbits in the Kerr spacetime , this corresponds to periapse radii of r _ { p } \gtrsim 20 M .
These results can be used to model radiation bursts from compact objects on highly eccentric orbits about massive black holes in the local Universe , which could be detected by the Laser Interferometer Space Antenna ( LISA ) .