Einstein's theory of Special Relativity, he did not deal with accelerated motions or gravitation.
These were treated in his General Theory Of Relativity which Einstein published in 1915.
The General Theory presented gravity in a completely new way. Gravitation was viewed in the General Theory as a geometric property of space rather then a force between bodies. From the point of view of General Relativity, space becomes curved in the presence of matter, and bodies followed the least resistance along these curves.
Einstein's Theory sounded very strange at the time when he first published it, but it explained many things that the Newtonian law of gravity could not explain, such as the orbital motions of the planet mercury, where its nearest approach to the sun (its perihelion) advanced steadily in the course of its ongoing revolutions around the sun. These small perturbations in mercury's orbit could not be explained by Newtonian Laws. However, Einstein's General Theory supplied the answer by showing that the perihelion of any revolving body should have a motion beyond that predicted by Newton's law. The calculations derived from Einstein's new theory, when now applied to the planet mercury, explained the shift of mercury's perihelion exactly.
From Wikipedia: General relativity (GR) or general relativity theory (GRT) is a fundamental physical theory of gravitation which corrects and extends Newtonian gravitation, especially at the macroscopic level of stars or planets.
General relativity may be regarded as an extension of special relativity, this latter theory correcting Newtonian mechanics at high velocities. General relativity has a unique role amongst physical theories in the sense that it interprets the gravitational field as a geometric phenomenon. More specifically, it assumes that any object possessing mass curves the 'space' in which it exists, this curvature being equated to gravity. It deals with the motion of bodies in such 'curved spaces' and has survived every experimental test performed on it since its formulation by Albert Einstein in 1915.