Michale is decided to buy a ticket to go to space. After meticulously planning his journey, he travel his vessel at speed 7/10c from Earth to the nearby planet, Alfa-0, 20 light-years away (as measure the common rest frame of Earth and Alfa-0). He spends a year (as measured in Earth- Alfa-0 frame this foreign planet sharing stories of human history to aliens. Finally, he is ready to head home. His hosts, charmed by his friendliness and the stories of his wonderful home, give him their best space ship for the return voyage. In this new ship, he travels at speed 95/100 c. Let W be Michael's departure from Earth (which we can set as the origin of the reference frame), X his arival to the Alfa-0, Y his departure from the Alfa-0, and Z his arrival back to Earth. a. Draw the spacetime diagram from the rest frame of the Earth Alfa-0 system, indicating Michale's worldline, and the events, W, X, Y, Z. (A rough sketch will suffice - do not worry about the angles.
Michale is decided to buy a ticket to go to space. After meticulously planning his journey, he travel his vessel at speed 7/10c from Earth to the nearby planet, Alfa-0, 20 light-years away (as measure the common rest frame of Earth and Alfa-0). He spends a year (as measured in Earth- Alfa-0 frame this foreign planet sharing stories of human history to aliens. Finally, he is ready to head home. His hosts, charmed by his friendliness and the stories of his wonderful home, give him their best space ship for the return voyage. In this new ship, he travels at speed 95/100 c. Let W be Michael's departure from Earth (which we can set as the origin of the reference frame), X his arival to the Alfa-0, Y his departure from the Alfa-0, and Z his arrival back to Earth. a. Draw the spacetime diagram from the rest frame of the Earth Alfa-0 system, indicating Michale's worldline, and the events, W, X, Y, Z. (A rough sketch will suffice - do not worry about the angles.
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Transcribed Image Text:Michale is decided to buy a ticket to go to space. After meticulously planning his journey, he travels in
his vessel at speed 7/10c from Earth to the nearby planet, Alfa-0 , 20 light-years away (as measured in
the common rest frame of Earth and Alfa-0). He spends a year (as measured in Earth- Alfa-0 frame) on
this foreign planet sharing stories of human history to aliens. Finally, he is ready
to head home. His hosts, charmed by his friendliness and the stories of his wonderful
home, give him their best space ship for the return voyage. In this new ship, he travels
at speed 95/100 c. Let W be Michael's departure from Earth (which we can set as the origin of
the reference frame), X his arrival to the Alfa-0, Y his departure from the Alfa-0,
and Z his arrival back to Earth.
a. Draw the spacetime diagram from the rest frame of the Earth - Alfa-0
system, indicating Michale's worldline, and the events, W, X, Y, Z. (A rough sketch will
suffice - do not worry about the angles.
b. Find the distance, and the time interval between events W, and X in
Earth-Sun rest frame. Find the distance, and the time interval between events Y , and Z
in Earth-Sun rest frame. How long did Michale's trip take, from perspective of his mother
bear, back on Earth? What are their (x, çt) coordinates of events W, X, Y, Z in this frame?
c. Find the time interval between events W and X in Michale's first rest frame,
using Lorentz transformations
Expert Solution
Step 1
World Line of the trip.
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