  The nonlinear gravitational-wave memory causes a time-varying but
nonoscillatory correction to the gravitational-wave polarizations. It arises
from gravitational waves that are sourced by gravitational waves. Previous
considerations of the nonlinear memory effect have focused on quasicircular
binaries. Here, I consider the nonlinear memory from Newtonian orbits with
arbitrary eccentricity. Expressions for the waveform polarizations and
spin-weighted spherical-harmonic modes are derived for elliptic, hyperbolic,
parabolic, and radial orbits. In the hyperbolic, parabolic, and radial cases
the nonlinear memory provides a 2.5 post-Newtonian (PN) correction to the
leading-order waveforms. This is in contrast to the elliptical and
quasicircular cases, where the nonlinear memory corrects the waveform at
leading (0PN) order. This difference in PN order arises from the fact that the
memory builds up over a short "scattering" time scale in the hyperbolic case,
as opposed to a much longer radiation-reaction time scale in the elliptical
case. The nonlinear memory corrections presented here complete our knowledge of
the leading-order (Peters-Mathews) waveforms for elliptical orbits. These
calculations are also relevant for binaries with quasicircular orbits in the
present epoch which had, in the past, large eccentricities. Because the
nonlinear memory depends sensitively on the past evolution of a binary, I
discuss the effect of this early-time eccentricity on the value of the
late-time memory in nearly circularized binaries. I also discuss the
observability of large "memory jumps" in a binary's past that could arise from
its formation in a capture process. Lastly, I provide estimates of the
signal-to-noise ratio of the linear and nonlinear memories from hyperbolic and
parabolic binaries.
