Deep Seek, how long would a 2 G acceleration get you near light speed
DeepSeek , a LLM that I love, gave me the answer to a nagging question, if we could accelerate constantly at 2G how long would it take to get near light speed, here is the answer: To determine how long it would take for a spaceship accelerating at 2 G (where 1 G = 9.81 m/s² ) to reach near light speed ( c ≈ 299,792,458 m/s ) as observed from Earth , we can use the principles of relativistic motion under constant proper acceleration . Key Equations: Proper Acceleration (a): The acceleration experienced by the spaceship's crew (2 G = 19.62 m/s²). Relativistic Velocity (v) as a function of time (t) in Earth's frame: v ( t ) = a t 1 + ( a t c ) 2 v ( t ) = 1 + ( c a t ) 2 a t As t t increases, v v approaches c c but never exceeds it. Time to reach a significant fraction of c c : The spaceship's velocity approaches c c asymptotically , so we define "near light speed" as some high frac...