Ice-giant missions as gravitational-wave detectors

Proposed missions to Uranus and Neptune usually involve a ∼10 year cruise time to the ice giants. This cruise time can be utilized to search for low-frequency gravitational waves (GWs) by observing the Doppler shift caused by them in the Earth-spacecraft radio link. We calculate the sensitivity of prospective ice giant missions to GWs, as well as that of past planetary missions which also searched for GWs. Then, adopting a steady-state black hole binary population, we derive a conservative estimate for the detection rate of extreme mass ratio inspirals (EMRIs), supermassive- (SMBH) and stellar mass binary black hole (sBBH) mergers. For a total of ten 40-day observations during the cruise of a single spacecraft, approximately 0.5 detections of SMBH mergers are likely, if Allan deviation of Cassini-era noise is improved by ∼10² in the 10⁻⁵ − 10⁻³ Hz range. For EMRIs the number of detections lies between O(0.1) − O(100). Furthermore, ice giant missions combined with the Laser Interferometer Space Antenna (LISA) would improve the GW source localisation by an order of magnitude compared to LISA by itself. With a significant improvement in the total Allan deviation, a Doppler tracking experiment might become as capable as LISA at such low frequencies, and help bridge the gap between mHz detectors and Pulsar Timing Arrays. Thus, ice-giant missions could play a critical role in expanding the horizon of gravitational wave searches and maybe even be the first to detect the first SMBH merger.