The International Space Federation constructs a new spaceship that can travel at

Question

The International Space Federation constructs a new spaceship that can travel at a speed of 0.814c. Mary, the astronaut, boards the spaceship to travel to Barnard's star, which is the second nearest star to our solar system after Alpha Centauri and is 5.98 ly away. After reaching Barnard's star, the spaceship travels slowly around the star system for 5 years doing research before returning back to Earth.

(a) How much time does the journey take in years

(b) How much older is her twin Frank when she returns in years

Explanation / Answer

(A) time taken to reach the star,

t = (5.98)/(0.814) = 7.346 years

as seen from earth.

total time taken = 2(7.346) + 5 = 19.69 years

{ as seen by astronaut's frame, t0 = t/Y

Y = 1 / sqrt[1 - (0.814^2)] = 1.722

so t0 = 7.346 / 1.722 = 4.267 years

total time= 2(4.267) + 5 = 13.53 years }

(B) for Mary 13.53 years has passed and for Frank 19.69 years has passed.

so Frank is 19.69 - 13.53= 6.16 years older.

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