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 after 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

Given:

Your spaceship launches in June 2020 and returns back to Earth directly aer arriving at Sirius.

To find:

(a) How many years will have passed from your perspective?

(b) At which Earth date (year and month) will you arrive back to Earth?​

Solution:

(a)

The time is given by, (from the astronomer's perspective)

t = D/v = 8.7c/0.7c = 12.42 years = 12 years 153 days.

Therefore, for the astronomers, the time will be June 1, 2020 + 12 years 153 days = Nov 1, 2032.

(b)

From the perspective of people left on the Earth, the time will be given by

te = t/√[1 - (v/c)²] = 12.42/√[1 - (0.7)²] = 17.39 years = 17 years 142 days

= October 21, 2037.