Question

Suppose astronomers discover a radio message from a civilization whose planet orbits a star 35 light-years away. Their message encourages us to send a radio answer, which we decide to do. Suppose our governing bodies take 2 years to decide whether and how to answer. When our answer arrives there, their governing bodies also take two of our years to frame an answer to us. How long after we get their first message can we hope to get their reply to ours? Enter your answer in years.

Answer 1

The duration is
`T  =72 \  years /tex]</p><p>Explanation:</p><p>From the question we are told that </p><p>    The  distance is  [tex]D  =  35 \ light-years = 35 *  9.46 *10^(15) = 3.311 *10^(17) \  m`

Generally the time it would take for the message to get the the other civilization is mathematically represented as

`t =  (D)/(c)`

Here c is the speed of light with the value
`c =  3.08 *10^(8) \  m/s`

=>
`t =  (3.311 *10^(17) )/(3.08 *10^(8))`

=>
`t =  1.075 *10^9 \ s`

converting to years

`t =  1.075 *10^9 *  3.17 *10^(-8)`

`t =  1.075 *10^9 *  3.17 *10^(-8)`

`t =  34 \ years`

Now the total time taken is mathematically represented as

`T  =  2*  t  +  2 + 2`

=>
`T  =  2* 34  +  2 + 2`

=> [tex]T =72 \ years /tex]