There really isn't a groove or indentation left over where the Earth
used to be. In fact, if you ignore the orbit and just think of the
earth by itself, how would you even say where the Earth used to be.
Different observers, travelling at different velocities with respect to
the Earth, would point to entirely different regions as the places
where they say the Earth used to be. Somebody on Earth would just point
to where it is now.
However, your basic insight is correct. The gravitational effects
are in some sense left in space where they can do their own thing, not
directly involving their source any more. For example, as the Earth
accelerates in (almost) uniform circular motion around the Sun, it
emits gravitational waves which then travel out away from the Earth and
Sun. These are very weak, but for some massive objects rotating very
rapidly, the same effect carries away enough energy to measurably slow
If the Earth were to blow apart into two parts heading opposite
directions, gravity on the Sun would be entirely unaffected for about 8
minutes. The gravitational changes only travel at the speed of light.
So that's another aspect to the way in which the gravity sits in the
structure of space itself, not immediately dependent on the original
source. However, none of those effects give any long-time grooves.
(published on 10/22/2007)