# Reaching 99.9% of the speed of light $c$ at 1G acceleration [duplicate]

If an object in space accelerated at $$9.8$$ms$$^{-2}$$ constantly, and no other forces were experienced, how long would it take for the object to reach the $$99.9\%$$ of the speed of light $$c$$.

## marked as duplicate by John Rennie, David Z♦Mar 6 at 10:04

• About 1345.5 days, for constant acceleration according to the ship (i.e., so it feels like constant gravity to the crew). Using 9.81 $m/s^2$, it's about 1.4 days quicker. – PM 2Ring Mar 6 at 11:17
$$t=\frac {\delta v}{a}$$ $$t=\frac {299,792,458-0}{9.8}=30591067.14 s$$
• At relativistic velocities the acceleration measured by the accelerating observer, $a$, and the acceleration measured by the Earth observer, $a'$, are not the same. Specifically $a' = a/\gamma^3$, where $\gamma$ is the Lorentz factor. Your answer assumes the constant acceleration is the acceleration measured on Earth. Admittedly the OP doesn't say which acceleration is the constant one, but for the Earth acceleration to stay constant the acceleration on the spaceship would have to go to infinity as the object approached the speed of light. – John Rennie Mar 6 at 10:42