Question

At what speed, at a fraction of c, must rocket travel on a journey to and from a distant star so that the astronaut's age 11 years while the Mission Control workers on earth age 130 years?

Answer 1

0.99641 c

Step-by-step explanation:

`\Delta t'` = 130 years

`\Delta t` = 11 years

c = Speed of light =
`3* 10^8\ m/s`

Time dilation is given by

`\Delta t'=\frac{\Delta t}{\sqrt{1-(v^2)/(c^2)}}\\\Rightarrow \sqrt{1-(v^2)/(c^2)}=(\Delta t)/(\Delta t')\\\Rightarrow 1-(v^2)/(c^2)=(\Delta t^2)/(\Delta t'^2)\\\Rightarrow (v)/(c)=\sqrt{1-(\Delta t^2)/(\Delta t'^2)}\\\Rightarrow (v)/(c)=\sqrt{1-(11^2)/(130^2)}\\\Rightarrow (v)/(c)=0.99641\\\Rightarrow v=0.99641c`

The speed of the rocket is 0.99641 c