The gravitational field effects are instantaneous for all practical purposes. If they weren’t the planets would have spiraled into the sun a long time ago. Newtonian physics works just fine for non relativistic acceleration.
From Wiki:
Speed of gravity
In the context of classical theories of gravitation, the speed of gravity refers to the ultimate speed at which a gravitational field propagates. This is the speed at which a change in the distribution of energy and momentum of matter results in subsequent alteration of the gravitational field which it produces.
The speed of gravity in general theory of relativity is equal to the speed of light in vacuum, c. Within the well-accepted theory of special relativity, the fundamental constant c is not all about light, it is a fundamental ultimate speed for any physical interaction in Nature. Formally, c is a conversion factor for changing the unit of time to the unit of space in a Lorentz transformation of physical laws. However, this makes it the only speed which does not depend either on the motion of observer or a source of light and/or gravity, and equals the speed of gravity and of light, and of any other massless particle.
Newtonian gravitation:
Isaac Newton’s formulation of a gravitational force law requires that each particle with mass respond instantaneously to every other particle with mass irrespective of the distance between them. In modern terms, Newtonian gravitation is described by the Poisson equation, according to which, when the mass distribution of a system changes, its gravitational field instantaneously adjusts. Therefore the theory assumes the speed of gravity to be infinite. This assumption was adequate to account for all phenomena with the observational accuracy of that time. It was not until the 19th century that an anomaly in astronomical observations which could not be reconciled with the Newtonian gravitational model of instantaneous action was noted: the French astronomer Leverier determined in 1847 that the elliptical orbit of Mercury precesses at a significantly different rate than is predicted by Newtonian theory.
http://en.wikipedia.org/wiki/Speed_of_gravity