I need to correct myself and point out that the values I got were wrong.
Formulae:
t = sqrt(x²/c² + 2x/g) - time measured on Earth
t' = (c / g) * asinh(gt/c) - time measured by ship's crew
Numerical values:
c = 3.00E8 m/sg = 9.81 m/s²
x = 4.3 ly = 4.07E16 m
Time from the perspective of people on Earth (t): 1.63E8 seconds = 5.18 years.
Time from the perspective of people on the ship (t'): 7.27E7 seconds = 2.31 years.
Derivation was OK, had four other people check it for me and can show the work. It's not a new result anyway. Regardless, sorry for the mistake.
am_Unition, ButterflyEffect, nil - you also shared that post, so I'm shouting out just in case it has any relevance for you guys.
I’m in the kleinbl00 bucket of “studied engineering but fuck that”. I sometimes, kind of work as an engineer but it’s mostly stats and more simplistic math based. No derivations here woo-hoo.
Am always interested in what the smart folks like you and am_Unition get to saying about math, though!
Pedantry above and beyond the call.
The fact that this was worrying in the back of your head like a loose tooth says a lot about your character. The fact that you decided to drag your friends down with you says a lot about the people you hang out with.