Answer to Question #123362 in Astronomy | Astrophysics for Siddharth Kumar Jena

Question

Because you are moving with an enormous speed, your mission from the previous problem A.1
will be influenced by the eects of time dilation described by special relativity: Your spaceship
launches in June 2020 and returns back to Earth directly aer arriving at Sirius.
(a) How many years will have passed from your perspective?
(b) At which Earth date (year and month) will you arrive back to Earth?

Answer 1

(a) The time for the astronauts will be

$$t=\frac{D}{v}=\frac{8.7c}{0.7c}=12.42\text{ y (12 y 153 d)}.$$

From June 2020 it will be November 2032.

(b) For people on the Earth this will take

$$t_e=\frac{t}{\sqrt{1-(v/c)^2}}=\frac{12.42}{\sqrt{1-(0.7)^2}}=17.39\text{ y (17 y 142 d)}.$$

From June 1, 2020 it will be October 21, 2037.