In summary, gravitational waves are disturbances in spacetime caused by massive, asymmetrically moving objects. The most massive and relativistic objects produce detectable GW's, which can be detected using laser interferometry by detectors like LIGO and Virgo. They have already detected dozens of GW's from black hole and neutron star binaries. Another method of detection is using a pulsar timing array, where multiple millisecond pulsars are monitored for nanohertz GW's. A new method being explored is using astrometry, but it is still uncertain how sensitive it will be as it depends on the relative positions of stars, which can be difficult to measure over large separations.
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Gravitational waves (GW’s) are disturbances in spacetime produced by any massive object moving asymmetrically. However, only the most massive and most relativistic objects produce large enough GW’s to be detectable. The Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo detectors are using laser interferometry to detect tiny ripples in the fabric of spacetime. They have detected dozens of GW’s from binaries of black holes and neutron stars. An additional method of detecting GW’s is creating a pulsar timing array (PTA), where dozens of millisecond pulsars are monitored to look for the signatures of nanohertz GW’s, that is waves with much lower frequencies than those seen by LIGO and Virgo.
Another way of detecting GW’s is using astrometry...

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Always nice to see how experiments get more tasks than they were designed for.
Do you have numbers how much we expect each star position to change? Is this something in the range of the parallax resolution of stars, or is this more like "everything shifts by 0.001 standard deviations and we need millions of stars to be sensitive" (i.e. nano-arcseconds)?
I know it's difficult for Gaia to get relative positions of stars across large separation in the sky, and that's probably what they need here: They just have two relatively narrow fields of view 60 degrees apart, so their correlation matrix is very thin.
 

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