 The Hubble Space Telescope can resolve angles on the sky as small as 50 mAh. The angular distance between S2 and SAGA star at Paris Center was just 15 mAh. That's 42 billionths of one degree and three times smaller than Hubble can resolve. To follow S2 as closely as they did, astronomers had to use a stellar interferometer. These kinds of telescopes can resolve images 30 to 40 times smaller than optical telescopes. This makes them extremely important tools for studying the galactic center, as well as exoplanets. They can even resolve sunspots on nearby stars. So to understand how we know how close S2 got to SAGA star, we need to understand how these stellar interferometers telescopes work. In the Speed of Light chapter of the How Far Away Is It? video book, we covered the Michelson interferometer used to measure minute distances in the lab. Interferometers can measure distances on the order of a few nanometers. Michelson immorally used it to show that the speed of light was a constant. In order to create light interference, Michelson illuminated the interferometer with fully coherent light. Coherent light has a common frequency and phase. It always produces interference patterns on the far side of a double slit. Fully coherent light, like the kind that lasers create, will produce regions of fully destructive interference. That is the dark regions have no light falling on them at all. Fully coherent light will produce regions of partially destructive interference, meaning some light falls in the dark regions. And incoherent light will not produce interference patterns at all. We find in nature that waves can start out as incoherent and become partially coherent as they spread out. Watch how these ducks start with a chaotic mix of water waves as they enter the pond. But as the waves move out, they become quite orderly. This is a geometrical effect. The further away one travels from the source, the less significant the distance between the individual wave generators becomes. A point source for starlight would produce coherent light, and at any distance from the source the light would create interference patterns. But there are no point sources in nature. Ducks have a diameter on the sky. An extended thermal light source would start out with incoherent light, but as the light moves away from the source, its coherence increases just like with the ducks on the pond. The relationship between the diameter of the source is a distance from the interferometer, and the distance between the two slits was determined in the lab. Michelson used this property to measure the diameter of Betelgeuse in 1921. It is fascinating to note that incoherent light waves created by excited atoms in stars 20 billion kilometers apart can travel for 26,000 years and still carry the remnants of that starting condition. A large enough stellar interferometer can use the visibility dimming of the interferous pattern created by the light to detect the original star separation. See how the amount the image fades is greater the further apart the two stars are. The math involved was developed independently by Dutch physicist P. H. van Sittert in 1934 and F. Zernik in 1939. It's known as the van Sittert-Zerniky theorem. It has taken 80 years to extrapolate the basic physics of interferometry into the working instruments we have today. There are currently over 20 stellar interferometers in operation around the globe. It was the four 8.2 meter ESO-VLT optical telescopes with an attached four-way interferometer called gravity that covered the S-2 Perry Center passage around SAG-A star.