Note***three problems 1) An astronaut wears a new Rolex watch on a journey at a

Question

Note***three problems

1) An astronaut wears a new Rolex watch on a journey at a speed of 1.57 x 108 m/s with respect to Earth. According to mission control in Houston, the trip lasts 11.7 h. How long is the trip as measured on the Rolex?

2) A spaceship is traveling away from Earth at 0.809c. The astronauts report home by radio every 19.1 h (by their own clocks). At what interval are the reports sent to Earth, according to Earth clocks?

3) A spaceship is moving at a constant velocity of 0.662c relative to an Earth observer. The Earth observer measures the length of the spaceship to be 38.5 m. How long is the spaceship as measured by its pilot?

Explanation / Answer

a)

tp = t/gamma = 11.7/(1/(1 - (1.57e8/3e8)y2)y0.5) = 9.97 hr

b)

t = gamma tp = (1/(1 - 0.809*0.809)y0.5) * 19.1 = 32.5 hr

c)

Lp = gamma L = 1/(1 - 0.662*0.662)y0.5 * 38.5 = 51.4 m

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