Answer to Question #123074 in Astronomy | Astrophysics for malak mohamed

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) For the people in the ship this will take

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

Starting from June 2020, they will finish in November 2032.

(b) For the observers on earth this will take

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

Starting from June 2020, people on earth will see this on the 21st of October, 2037.