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

The value is
`v  =  2.999 *10^(8) \  m/s`

Step-by-step 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 -  (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 -  (v^2)/((3.0*10^(8))^2 ) }`

=>
`v  =  2.999 *10^(8) \  m/s`