Answer to Question #123114 in Astronomy | Astrophysics for Kevin

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 June2020andreturnsbacktoEarthdirectly aer arriving at Sirius.
a) How many years will have passed from your prespwctive
b) At what Earth date (year and month) will you arrive back to Earth?

Answer 1

a) From the astronauts' perspective, the time will be

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

Therefore, for them it will be June 1, 2020 + 12 years 153 days = November 1, 2032.

b) From the perspective of people left on the Earth the time will be

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

For people on Earth the date of arrival will be 1, 2020 + 17 years 142 days = October 21, 2037.