General relativity predicts that massless waves scatter off the Riemann curvature of their background and arrive inside the lightcone as a tail, an effect never directly observed. This work computes the backward-direction scattered gravitational wave from the weak-field curvature of an extended body with a smooth density profile, recovers the fifty-year-old long-wavelength differential cross-section, and applies it to millihertz waves scattering off the Sun and planets. It finds that a near-alignment of the Sun or an outer planet with the line of sight to a source would imprint an amplitude modulation of order one part in a thousand on LISA observations.
General relativity predicts that massless waves should scatter from the Riemann curvature of their backgrounds. These scattered waves are sometimes called $\textit{tails}$ and have never been directl…