Triangles in Space: The Design of Gravitational-Wave Observatories for the Millihertz Universe

Abstract

Ground-based interferometers detect gravitational waves down to only a few hertz; below that threshold, seismic motion on Earth makes further sensitivity impossible. Yet the loudest and most scientifically valuable sources in the Universe—merging supermassive black holes, extreme-mass-ratio inspirals, and the vast population of compact binaries within our own Galaxy—radiate at millihertz frequencies, well below what any Earth-bound detector can reach. Observing this band requires leaving the Earth entirely. This paper reviews the observatories, operational, proposed, and conceptual, that are designed to close this gap, and argues that the reach of any gravitational-wave observatory is fixed at the design stage by two architectural choices: its orbit and the length of its interferometer arms. Longer arms convert a passing wave's tiny strain into a larger, more measurable displacement, while the same arm length sets an upper bound on the frequencies a detector can sense. These two relationships explain why heliocentric missions with arms of millions of kilometres reach the millihertz band, while detectors with shorter, geocentric or deci-hertz-scale arms trade low-frequency sensitivity for higher-frequency reach. Atom-interferometric, lunar-surface, and pulsar-timing concepts extend the picture further still, each occupying a niche the interferometric missions cannot. Ten architectures are classified by orbit and compared against shared physical metrics; the resulting picture is not one dominant design but a complementary network, each observatory suited to a different slice of the gravitational-wave spectrum.