If our civilization collapses, extraterrestrial archeologists can look at this and be impressed. Three satellites following the Earth in an equilateral triangle, each 2.5 million kilometers from the other two. Each contains two gold cubes in free-fall. The satellites accelerate just enough so they don't get blown off course by the solar wind. The gold cubes inside feel nothing but gravity.
Lasers bounce between each cube and its partner in another satellite, measuring the distance between them to an accuracy of 20 picometers: less than the diameter of a helium atom! This lets the satellites detect gravitational waves — ripples in the curvature of spacetime — with very long wavelengths, and correspondingly low frequencies.
It should see so many binary white dwarfs, neutron stars and black holes in the Milky Way that these will be nothing but foreground noise. More excitingly, it should see mergers of supermassive black holes at the centers of galaxies as far as... the dawn of time, or whenever such black holes were first formed. (The farther you look, the older things you see.)
It may even be able to see the "gravitational background radiation": the thrumming vibrations in the fabric of spacetime left over from the Big Bang. These gravitational waves were created before the hot gas in the Universe cooled down enough to become transparent to light. So they're older than the microwave background radiation, which is the oldest thing we see now.
It's called LISA - the Laser Interferometric Satellite Antenna. And we're in luck: ESA has just decided to launch it in 2035.
@johncarlosbaez wow that's so cool!