Question

An astronaut must journey to a distant planet, which is 211 light-years from Earth. What speed will be necessary if the astronaut wishes to age only 15 years during the trip? (Give your answer accurater to five decimal places.) Hint: The astronaut will be traveling at very close to the speed of light. Therefore, approximate the dilated trip time At to be 211 years

Answer 1

Answer:

At 99.7% of the speed of light

Explanation:

For the astronaut traveling, the perceived time elapsed $t'$ with respect to the perceived time elapsed $t$ of an observer at rest with respect to the astronaut is:

$t'=t\sqrt{1-\frac{v^2}{c^2}}$

where c is the speed of light and v is the speed of the traveler.

Solving for v we have:

$v=c\sqrt{1-(t'/t)^2)}\implies \frac{v}{c}=\sqrt{1-(t'/t}^2)}=99.7\%\,c$