The Speed of Gravity – What the Experiments SayAs viewed from the Earth's frame, light from the Sun has aberration. Light requires about 8.3 minutes to arrive from the Sun, during which time the Sun seems to move through an angle of 20 arc seconds. The arriving sunlight shows us where the Sun was 8.3 minutes ago. The true, instantaneous position of the Sun is about 20 arc seconds east of its visible position, and we will see the Sun in its true present position about 8.3 minutes into the future. In the same way, star positions are displaced from their yearly average position by up to 20 arc seconds, depending on the relative direction of the Earth's motion around the Sun. This well-known phenomenon is classical aberration, and was discovered by the astronomer Bradley in 1728.
by Tom Van Flandern
Physics Letters A 250:1-11 (1998)
Orbit computations must use true, instantaneous positions of all masses when computing accelerations due to gravity for the reason given by Eddington.
The fields already exist. The Earth basically follows the geometry of space due to the presence of the energy of the bodies contained within that space. The Sun being the major energy body, is the object that is cheifly responsible for the curvature of the space around it. It's akin to laying tracks. The Earth follows the track in space laid down by the Sun. The Sun does not radiate gravity, as it does light.