Applications of Special Relativity

Problem : A spacecraft travels at 0.99c to a star 3.787×10¹³ kilometers away. How long will a roundtrip to this star take from the point of view of someone on the earth?

Problem : With reference to the previous problem, how long will the roundtrip take for someone in the spaceship, according to someone measuring from the earth?

Solution for Problem 2 >>

According to an observer on the earth, since the spacecraft is moving, its passengers' time is dilated. The factor by which this occurs is γ = = 7.09 . The passengers measure less time so, the roundtrip time is (1/7.09)×8 = 0.14×8 = 1.1 years.

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Problem : Now in the reference frame of someone in the spaceship, what is the time taken for the roundtrip as observed by a passenger, and by someone on earth (ignoring the times when the spaceship is accelerating or decelerating).

Problem : If one person stays on earth and one person travels to the distant star, who will age more during the trip and by what amount?

Problem : Twin A floats freely in outer space. Twin B flies past in a spaceship at speed v ₀ . Just as they pass each other they both start timers at t = 0 . At the instant of passing B also turns on his engines so as to decelerate at g . This causes B to slow down and eventually to stop and accelerate back towards A so that when the twins pass each other again B is traveling at speed v ₀ again. If they compare their clocks, who is younger?