So i read this short bit on Time Dilation which left me with a question. It states that when approaching speed of light at 0.999999 then for each day on board of a vessel about 2 earth years pass. When we speed up to 0.99999999999999 of speed of light this single day will amount to about 20000 earth years.
When looking at this from a SF writing point of view, does this mean that as long as we speak of approaching the speed of light basically anything within those boundaries goes? I'm doing a short story where picking the ship/time earth/time ratio is important and I'd like it to be at least somewhat scientifically accurate.
Apart from that, it makes me wonder how the difference between those two very close approximations can differ so much in effect? I understand speed of light represents a very large distance/time and as such even so far after the comma differences might be great, but still this feels a bit unintuitive. Is the source more or less correct?