Okay.
Assuming the Earth has been around for 4 point whatever billion years:
The Earth would be moving at roughly the speed of light right now, considering the constant 1G acceleration through a vacuum.
I use the word "roughly" here pretty loosely. Let's consider that it's even moving at .7c.
Saying "the Earth would never reach (roughly) the speed of light, because it would take a (roughly) infinite amount of energy is true according to special relativity, which I don't adhere to, but we can talk about that later if you'd like.
From an outside reference point :
the ship will appear to be gaining mass due to its high kinetic energy, and the Mass-energy equivalence principle. Should the engines be giving a constant thrust, this will result in progressively smaller acceleration due to the higher mass it is required to accelerate.
However, from the Earth as a reference point :
the acceleration would continue at the same rate. However, due to the Lorentz contraction The galaxy around the ship would appear to become squashed in the direction of travel, and a destination many light years away, would appear to become much closer.
Okay. That being said, we should be experiencing major Lorentz contraction at this point.
Even if we are only close to the speed of light, there would be a noticeable effect relative to the other photons that deliver to us our visual stimuli.
As the magnitude of the velocity approaches the speed of light, the effect becomes dominant, as can be seen from the formula:
where
L0 is the proper length (the length of the object in its rest frame),
L is the length observed by an observer in relative motion with respect to the object,
v is the relative velocity between the observer and the moving object,
c is the speed of light,
and the Lorentz factor, γ(v), is defined as
Also, if you adhere to special relativity, the mass-energy relation equation would say that the closer you are to the speed of light, the more mass you appear to have.
If we were, for the sake of argument, .8c, we would exhibit properties of having much more mass than we actually do from the outside reference point.
If we ignore special relativity, which I advise most of you to do, considering that the most popular FE belief rejects gravity, we would definitely notice ourselves going (1.357e+17)G, or 4435859637.269461 times the speed of light.