# Outer Solar System spacecraft without drag-free control to probe the $μ$Hz gravitational wave frontier

**Authors:** Matthew McQuinn, Casey McGrath  
**arXiv:** [2411.15072](https://arxiv.org/abs/2411.15072)  
**Date:** 2024-11-22  
**Summary page:** https://www.summarizepaper.com/fr/arxiv-id/2411.15072v1/

## Abstract

The microhertz frequency band of gravitational waves probes the merger of supermassive black holes as well as many other gravitational wave phenomena. However, space-interferometry methods that use test masses would require substantial development of test-mass isolation systems to detect anticipated astrophysical events. We propose an approach that avoids inertial test masses by situating spacecraft in the low-acceleration environment of the outer Solar System. We show that for Earth-spacecraft and inter-spacecraft distances of $\gtrsim 10$ AU, the accelerations on the spacecraft would be sufficiently small to potentially achieve sensitivities determined by stochastic gravitational wave backgrounds. We further argue, for arm lengths of $10-30$ AU and $10$ Watt transmissions, that stable phase locks should be achievable with 20 cm mirrors or 5 m radio dishes. We discuss designs that send both laser beams and radio waves between the spacecraft, finding that despite the $\sim10^4\times$ longer wavelengths, even a design with radio transmissions could reach stochastic background-limited sensitivities at $\lesssim 0.3\times 10^{-4}$ Hz. Operating in the radio significantly reduces many spacecraft design tolerances. Our baseline concept requires two arms to do interferometry. However, if one spacecraft carries a clock with Allan deviations at $10^4$ seconds of $10^{-17}$, a comparable sensitivity could be achieved with a single arm. Finally, we discuss the feasibility of achieving similar gravitational wave sensitivities in a `Doppler tracking' configuration where the single arm is anchored to Earth.