To find out how long it would take for a rocket to reach a speed of \( 0.999c \) (where \( c \) is the speed of light) while accelerating at a constant acceleration of \( 1g \), we can use the principles of special relativity.
1. **Acceleration**: We define the proper acceleration as \( a = 1g \approx 9.81 \, \text{m/s}^2 \).
2. **Time Dilation**: The relativistic acceleration means that the relationship between the time experienced by an