Question

calculate the time (in years) it would take to send a message to the Galactic Capitol located at the center of our Milky Way galaxy and then receive the reply. We live about 2.5x10^20 meters away from the Galaxy center. Assume the message leaves the Earth and travels at the speed of light and that they take 1 year to decide what to answer..

Answer 1

The total time is
`\bf{52850~Yr}`.

Step-by-step explanation:

Given:

The distance between Galactic Capitol and Earth is,
`d = 2.5 * 10^(20)~m`

The speed of light is,
`c = 3 * 10^(8)~m/s`

The time taken by the message to reach and come back to Earth is given by

`t &=& (2d)/(c)\\~~&=& (2(2.5 * 10^(20)~m))/(3 * 10^(8)~m/s)\\~~&=& 1.6 * 10^(12)~s\\~~&=& (1.6 * 10^(12)~s)/((86400 * 365)~s)~Yr\\~~&\approx& 52849~Yr`

In addition they take 1 year to decide to reply.

Thus, the total time is
`25850~Yr`.