Bridging the $\mu$Hz gap in the gravitational-wave landscape with binary resonance

Gravitational-wave (GW) astronomy is transforming our understanding of the Universe by probing phenomena invisible to electromagnetic observatories. A comprehensive exploration of the GW frequency spectrum is essential to fully harness this potential. Remarkably, current methods have left the $\mu$Hz frequency band almost untouched. Here, we show that this $\mu$Hz gap can be filled by searching for deviations in the orbits of binary systems caused by their resonant interaction with GWs. In particular, we show that laser ranging of the Moon and artificial satellites around the Earth, as well as timing of binary pulsars, may discover the first GW signals in this band, or otherwise set stringent new constraints. To illustrate the discovery potential of these binary resonance searches, we consider the GW signal from a cosmological first-order phase transition, showing that our methods will probe models of the early Universe that are inaccessible to any other near-future GW mission. We also discuss how our methods can shed light on the possible GW signal detected by NANOGrav, either constraining its spectral properties or even giving an independent confirmation.