You are on an interstellar mission from the Earth to the 8.7 light-years distant star Sirius. Your spaceship can travel with 70% the speed of light and has a cylindrical shape with a diameter of 6 m at the front surface and a length of 25 m. Because you are moving with an enormous speed, your mission will be influenced by the effects 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?

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You are on an interstellar mission from the Earth to the 8.7 light-years distant star Sirius. Your spaceship can travel with 70% the speed of light and has a cylindrical shape with a diameter of 6 m at the front surface and a length of 25 m. Because you are moving with an enormous speed, your mission will be influenced by the effects 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?

Expert Solution
Step 1

(a) since the space ship travels at a speed comparable to the speed of light, the distance to the star is contracted in the frame of reference of the spaceship

Time to reach Sirius

Advanced Physics homework question answer, step 1, image 1

Step 2

Time to return to Earth

Advanced Physics homework question answer, step 2, image 1

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