I was reading this Reddit post and was curious about whether the passengers of this theoretical spaceship could experience 1g of acceleration forever assuming the ship has an infinite fuel source.

They shouldn’t be able to pass the speed of light relative to an outside observer, but is there some phenomenon where the passengers can feel like they are accelerating forever?

I am writing this short story. It is part of the overall book that I am writing, but it is also a story that can be enjoyed completely on its own. In that story, a planet-sized ship approaches our Solar System, and, ultimately maybe, Earth. For dimensions, let's say it is equal to 1.5 of Earth's diameter. According to Google, that's 25,512 19,134 kilometers. The Planet-Ship is probably less dense than Earth, as it is largely occupied by biomass and weird alien electronics. You may think of it as a round Borg cube, from Star Trek.

My "Round Borg Cube" is completely black and spherical, with a smooth surface without any visible features.

What I wanna know is...

• Assuming that the object is on a very slow path towards Earth, at what proximity will its effects be known?
• At which point will scientists observe its effects, view it, or detect it with instruments?
• If that is at all possible, what would be a threshold in which the "Round Borgs" would have to interrupt their movement in order to remain undetected?
• At which distance will it be visible to the naked eye (if at all)?
• And if they chose to get dangerously close to Earth, what would be the impact on our environment?

I understand that is a lot to ask, but I just can't trust GPT for that kind of stuff, even if their answers sound plausible. Perhaps someone with astronomical knowledge as well as an interest in science fiction will find my questions enticing. I don't expect precise answers because I am not providing precise information. So feel free to speculate on that scenario. In any case, I am grateful for any answer I can get.

Thanks!