Calculating Length Contraction: The Distance between Stars Contracts when You Travel at High Velocity Suppose an astronaut, such as the twin discussed in Simultaneity and Time Dilation, travels so fast that y = 30.00. (a) She travels from the Earth to the nearest star system, Alpha Centauri, 4.300 light years (ly) away as measured by an Earth-bound observer. How far apart are the Earth and Alpha Centauri as measured by the astronaut? (b) In terms of c, what is her velocity relative to the Earth? You may neglect the motion of the Earth relative to the Sun. (See Figure 28.11.) At Alpha Centauri Earth Lo v = Δt (а) At, At, Alpha Centauri (b) Figure 28.11 (a) The Earth-bound observer measures the proper distance between the Earth and the Alpha Centauri. (b) The astronaut observes a length contraction, since the Earth and the Alpha Centauri move relative to her ship. She can travel this shorter distance in a smaller time (her proper time) without exceeding the speed of light.
Calculating Length Contraction: The Distance between Stars Contracts when You Travel at High Velocity Suppose an astronaut, such as the twin discussed in Simultaneity and Time Dilation, travels so fast that y = 30.00. (a) She travels from the Earth to the nearest star system, Alpha Centauri, 4.300 light years (ly) away as measured by an Earth-bound observer. How far apart are the Earth and Alpha Centauri as measured by the astronaut? (b) In terms of c, what is her velocity relative to the Earth? You may neglect the motion of the Earth relative to the Sun. (See Figure 28.11.) At Alpha Centauri Earth Lo v = Δt (а) At, At, Alpha Centauri (b) Figure 28.11 (a) The Earth-bound observer measures the proper distance between the Earth and the Alpha Centauri. (b) The astronaut observes a length contraction, since the Earth and the Alpha Centauri move relative to her ship. She can travel this shorter distance in a smaller time (her proper time) without exceeding the speed of light.
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How long does it take according to the astronaut?
Transcribed Image Text:Calculating Length Contraction: The Distance between Stars Contracts when You Travel at
High Velocity
Suppose an astronaut, such as the twin discussed in Simultaneity and Time Dilation, travels so fast that y = 30.00. (a) She
travels from the Earth to the nearest star system, Alpha Centauri, 4.300 light years (ly) away as measured by an Earth-bound
observer. How far apart are the Earth and Alpha Centauri as measured by the astronaut? (b) In terms of c, what is her velocity
relative to the Earth? You may neglect the motion of the Earth relative to the Sun. (See Figure 28.11.)
At
Alpha
Centauri
Earth
Lo
v =
Δt
(а)
At,
At,
Alpha
Centauri
(b)
Figure 28.11 (a) The Earth-bound observer measures the proper distance between the Earth and the Alpha Centauri. (b) The astronaut
observes a length contraction, since the Earth and the Alpha Centauri move relative to her ship. She can travel this shorter distance in a
smaller time (her proper time) without exceeding the speed of light.
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