I'm making research for an article about constant acceleration / deceleration ship propulsion. Now, it's about 30 years since I was solving differential equations so there's no way I could solve, let alone devise, an appropriate differential equation. I'm not even sure an appropriate differential equation exists. What I'm interested in is the following. Let's suppose a ship leaves the earth and accelerates constantly at 1G. How much ship time will be required for the ship to reach, say, 0.99 c ? And conversely, What will be the ship velocity (relative to c) after, say, 10 years of the ship time (assuming it's accelerating at 1G starting at rest relative to the Earth). In general, given acceleration a and ship time interval t, what will be the speed relative to c at t0 + t. And conversely, given acceleration a and speed (relative to c), how much ship time is required to reach it. Basically, I'm interested in how much ship time is required to reach different destinations in cosmos if a ship were to use constant acceleration / deceleration propulsion (accelerating half a way and decelerating half a way).