Thank you for detailed calculation!
I can also share my calculation in the non-inertial reference frame of the ship. I used Rindler coordinates and just integrated them along the trip.
First I calculated traveled distance and got the exact same number as observed from the Earth:
$$dx = c\cdot...
I am able to calculate:
a) time elapsed on the ship is 3.54 years
b) spacetime interval of the trip is 33483585728808616 m
How can I prove within SR that time elapsed on Earth is still 5.87 years when reversing the logic and considering that Earth accelerates away from the ship?
I don't understand why coordinates (or rather coordinate's origin) onboard the ship doesn't make any sense.
Anyway, the purpose of this task is to explain the twin paradox. If you check wiki, the traveler's perspective takes into account the length contraction "between the Earth and the star...
Let's assume a spaceship traveling from the Earth to the Proxima Centauri with constant acceleration g = 9.81 m/s2.
The ship is accelerating the first half of the trajectory and decelerating the second half.
I calculated the velocity profile from the Earth reference:
The travel time on...