The Eddington limit, the natural limit to the luminosity of stars, or the radiation generated by accretion onto a compact object, is named in his honour.

He is famous for his work regarding the Theory of Relativity. Eddington wrote a number of articles which announced and explained Einstein's theory of general relativity to the English-speaking world. World War I severed many lines of scientific communication and new developments in German science were not well known in England. He also conducted an expedition to observe the Solar eclipse of 29 May 1919 that provided one of the earliest confirmations of relativity, and he became known for his popular expositions and interpretations of the theory. (from wikipedia.org)