A new spaceship that can travel at a speed of0.900 c . Mary, the astronaut,board

Question

A new spaceship that can travel at a speed of0.900c. Mary, the astronaut,boards the spaceship to travel to Barnard's star, which is thesecond nearest star to our solar system after Alpha Centauri and is5.98 ly away. After reaching Barnard's star, the spaceship travelsslowly around the star system for 3 yearsdoing research before returning back to Earth. (a) How much time does the journey take?(years)
(b) How much older is her twin Frank when she returns?(years) (a) How much time does the journey take?(years)
(b) How much older is her twin Frank when she returns?(years)

Explanation / Answer

The time taken for the whole journey, according to Frank is 5,98 ly/0,9 c *2+3=16,3 (y) While according to Mary, the time taken for going to Barnard and goback is T0=5,98ly/0,9 c *2 /=13,28 * sqrt(1-0,9^2)=5,78 y the total time is 5,78+3=8,78(y) So Frank is 7,5 years older than Mary

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