A theory created by Albert Einstein . It's a radical revision of Newton’s theory, predicting important new results for fast-moving and/or very massive bodies. This implies that we're heading into space travel, and we will be dealing with "black holes". 

Video introduction to the theory, 8 min., kids level

“Einstein’s theories of both special and general relativity have been confirmed to be accurate to a very high degree over recent years, and the data has been shown to corroborate many key predictions; the most famous being the solar eclipse of 1919 bearing testimony that the light of stars is indeed deflected by the sun as the light passes near the sun on its way to earth. The total solar eclipse allowed astronomers to -- for the first time -- analyse starlight near the edge of the sun, which had been previously inaccessible to observers due to the intense brightness of the sun. It also predicted the rate at which two neutron stars orbiting one another will move toward each other. When this phenomenon was first documented, general relativity proved itself accurate to better than a trillionth of a percent precision, thus making it one of the best confirmed principles in all of physics”.

Here you can see a nice illustration of gravity according to Einstein , i.e. bending of "space-time", and hence "attraction" of various objects to each other.

"Relativity: special and general theory" by A. Einstein. Primary source. Part III: “Consideration of the Universe as a whole”

Gravity can bend light, allowing huge clusters of galaxies to act as telescopes. Almost all of the bright objects in this released Hubble Space Telescopeimage are galaxies in the cluster known as Abell 2218. The cluster is so massive and so compact that its gravity bends and focuses the light from galaxies that lie behind it. As a result, multiple images of these background galaxies are distorted into long faint arcs - a simple lensing effect analogous to viewing distant street lamps through a glass of wine. The cluster of galaxies Abell 2218 is itself about three billion light-years away in the northern constellation Draco.

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