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RE: Detecting black holes with telescopes and gravitational waves
Gastrophysics is now a term used in astrophysics too, believe it or not. Just try to google the term together with gravitation (instead of nothing or food :D)
What sort of detector can measure that?
LIGO or Virgo. They measure interference pattern in lasers traveling in arms of 4 km. Being super well isolated from the background, they can detect a tiny change in the pattern that would indirectly correspond to this distance.
I guess I need to read more about what exactly these detectors are. I am just surprised by the level of precision (10-19 is pretty small, 1000X smaller then the radius of an electron)
The key is really the interferences. I tiny variation in the length of the arms induce a noticeable (and much easier to observe) interference pattern.