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According to Bob, an observer on Earth, a rocket carrying Martha from Earth directly to the planet Zorg travels at a speed of 0.80 c and takes 30 years to reach Zorg. Zorg is at rest relative to the Earth. a) What is the distance between Earth and Zorg, according to Bob? Express this distance in light-years. b) How long does Martha, the observer on the rocket, think the trip takes? c) What is the distance between Earth and Zorg, according to Martha? Express this distance in light-years. d) Although Bob and Martha disagree about distances and times, they do agree on the value of what is called the space-time interval between the events of Martha passing Earth and Martha reaching Zorg. In fact, every observer agrees on the value of this interval, defined as: |(cat)² – (Ax)² (e) A third observer, Ralph, thinks that the two events of Martha passing Earth and Martha reaching Zorg occur 25 years apart. In Ralph's reference frame, what is the spatial distance Ax between these two events? Ralph's relative velocity relative to Earth does not change.

According to Bob, an observer on Earth, a rocket carrying Martha from Earth directly to the planet Zorg travels at a speed of 0.80 c and takes 30 years to reach Zorg. Zorg is at rest relative to the Earth. a) What is the distance between Earth and Zorg, according to Bob? Express this distance in light-years. b) How long does Martha, the observer on the rocket, think the trip takes? c) What is the distance between Earth and Zorg, according to Martha? Express this distance in light-years. d) Although Bob and Martha disagree about distances and times, they do agree on the value of what is called the space-time interval between the events of Martha passing Earth and Martha reaching Zorg. In fact, every observer agrees on the value of this interval, defined as: |(cat)² – (Ax)² (e) A third observer, Ralph, thinks that the two events of Martha passing Earth and Martha reaching Zorg occur 25 years apart. In Ralph's reference frame, what is the spatial distance Ax between these two events? Ralph's relative velocity relative to Earth does not change.

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Exercise 1 According to Bob, an observer on Earth, a rocket carrying Martha from Earth directly to the planet Zorg travels at a speed of 0.80 c and takes 30 years to reach Zorg. Zorg is at rest relative to the Earth. a) What is the distance between Earth and Zorg, according to Bob? Express this distance in light-years. b) How long does Martha, the observer on the rocket, think the trip takes? c) What is the distance between Earth and Zorg, according to Martha? Express this distance in light-years. d) Although Bob and Martha disagree about distances and times, they do agree on the value of what is called the space-time interval between the events of Martha passing Earth and Martha reaching Zorg. In fact, every observer agrees on the value of this interval, defined as: (cAt)² – (Ax)² (e) A third observer, Ralph, thinks that the two events of Martha passing Earth and Martha reaching Zorg occur 25 years apart. In Ralph's reference frame, what is the spatial distance Ar between these two events? Ralph's relative velocity relative to Earth does not change.
Transcribed Image Text:Exercise 1 According to Bob, an observer on Earth, a rocket carrying Martha from Earth directly to the planet Zorg travels at a speed of 0.80 c and takes 30 years to reach Zorg. Zorg is at rest relative to the Earth. a) What is the distance between Earth and Zorg, according to Bob? Express this distance in light-years. b) How long does Martha, the observer on the rocket, think the trip takes? c) What is the distance between Earth and Zorg, according to Martha? Express this distance in light-years. d) Although Bob and Martha disagree about distances and times, they do agree on the value of what is called the space-time interval between the events of Martha passing Earth and Martha reaching Zorg. In fact, every observer agrees on the value of this interval, defined as: (cAt)² – (Ax)² (e) A third observer, Ralph, thinks that the two events of Martha passing Earth and Martha reaching Zorg occur 25 years apart. In Ralph's reference frame, what is the spatial distance Ar between these two events? Ralph's relative velocity relative to Earth does not change.
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