Born at Kendal, Eddington moved with his mother and sister to Somerset after the death of his father in 1884. He was a brilliant scholar, graduating from Owens College (now the University of Manchester) in 1902 and from Cambridge University in 1905. From 1906 to 1913 he was chief assistant to the Astronomer Royal at Greenwich after which he returned to Cambridge as Plumian Professor of Astronomy. He was knighted in 1930. Eddington was a Quaker throughout his life.

Eddington was the major British astronomer of the interwar period. His early work on the motions of stars was followed, from 1916 onward, by his work on the interior of stars, which was published in his first major book, The Internal Constitution of the Stars (1926). He introduced “a phenomenon ignored in early investigations, which may have considerable effect on the equilibrium of a star, viz. the pressure of radiation.” He showed that for equilibrium to be maintained in a star, the inwardly directed force of gravitation must be balanced by the outwardly directed forces of both gas pressure and radiation pressure. He also proposed that heat energy was transported from the center to the outer regions of a star not by convection, as thought hitherto, but by radiation.

It was in this work that Eddington gave a full account of his mass-luminosity relationship, which was discovered in 1924 and shows that the more massive a star the more luminous it will be. The value of the relation is that it allows the mass of a star to be determined if its intrinsic brightness is known. This is of considerable significance since only the masses of binary stars can be directly calculated. Eddington realized that there was a limit to the size of stars: relatively few would have masses exceeding 10 times the mass of the Sun while any exceeding 50 solar masses would be unstable owing to excessive radiation pressure.

Eddington wrote a number of books for both scientists and laymen. His more popular books, including The Expanding Universe (1933), were widely read, went through many editions, and opened new worlds to many enquiring minds of the interwar years. It was through Eddington that Einstein's general theory of relativity reached the English-speaking world. He was greatly impressed by the theory and was able to provide experimental evidence for it. He observed the total solar eclipse of 1919 and submitted a report that captured the intellectual imagination of his generation. He reported that a very precise and unexpected prediction made by Einstein in his general theory had been successfully observed; this was the very slight bending of light by the gravitational field of a star – the Sun. Further support came in 1924 when Einstein's prediction of the reddening of starlight by the gravitational field of the star was tested: at Eddington's request Walter Adams detected and measured the shift in wavelength of the spectral lines of Sirius B, the dense white-dwarf companion of the star Sirius. Eddington thus did much to establish Einstein's theory on a sound and rigorous foundation and gave a very fine presentation of the subject in his Mathematical Theory of Relativity (1923).

Eddington also worked for many years on an obscure but challenging theory, which was only published in his posthumous work, Fundamental Theory (1946). Basically, he claimed that the fundamental constants of science, such as the mass of the proton and the mass and charge of the electron were a “natural and complete specification for constructing a universe” and that their values were not accidental. He then set out to develop a theory from which such values would follow as a consequence, but never completed it.