Question

g An astronaut must journey to a distant planet, which is 189 light-years from Earth. What speed will be necessary if the astronaut wishes to age only 12 years during the round trip? (Give your answer accurate to four decimal places.)

Answer 1

Answer:

The value is $v = 2.999 *10^{8} \ m/s$

Explanation:

From the question we are told that

   The time taken to travel to the planet from earth is $t = 189 \ light-years$

    The  time to be spent on the ship is  $t_{s} = 12 \ years$

Generally speed can be obtained using the mathematical relation represented below

       $t_s = 2 * t * \sqrt{1 - \frac{v^2}{c^2 } }$

The 2 in the equation show that the trip is a round trip i.e going and coming back

=>    $12 = 2 * 189 * \sqrt{1 - \frac{v^2}{(3.0*10^{8})^2 } }$

=>     $v = 2.999 *10^{8} \ m/s$