How can gravitational waves be measured?
Gravitational waves are measured, or detected rather, by the "swinging" of mirrors.
"All you need to build a gravitational-wave interferometer is two light beams, travelling between pairs of mirrors down pipes running in different directions, say north and west. The effect of a passing gravitational wave should stretch space in one direction and shrink it in the direction that is at right angles. On Earth, that would cause the mirrors to swing by tiny amounts, so that the distance between one pair of mirrors gets smaller, while the other gets larger. The swinging is actually the mirrors responding to the stretching and compression of space-time, which is just amazing." - Ed Daw, Reader in Physics, University of Sheffield
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The reason Earth is effected by gravitational waves is typically two supermassive objects interacting in a way in which the object is non-consistent, such as two black holes orbiting one another.