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The Twins Communicate, Quantitative—Problem 1
Gracie heads off into space at $v = {99 \over 101} c$ and, according to George who remains back on Earth, she travels 99 light-years away, turns around and heads back home at $v = {99 \over 101} c$. During the entire journey, George sends out a flash toward Gracie once every year and Gracie sends out a flash toward George once a year.
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Question 1 of 8
1. Question
According to George's clock, how often does he receive flashes that Gracie sends during her outbound journey?
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Question 2 of 8
2. Question
According to Gracie's clock, how often does she receive flashes during her outbound journey?
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Question 3 of 8
3. Question
According to George's clock, how often does he receive flashes that Gracie sends during her inbound journey?
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Question 4 of 8
4. Question
According to Gracie's clock, how often does she receive flashes during her inbound journey?
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Question 5 of 8
5. Question
According to George's clock, how many years after Gracie's departure does he receive the first flash that she sent after the outbound portion of her journey concluded? That is, according to George, how many years after Gracie's departure does he begin to receive flashes from her at the higher rate?
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Question 6 of 8
6. Question
According to George's clock, for how long does he receive flashes at the rate calculated in part (a), and for how long does he receive the flashes calculated in part (c)?
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Question 7 of 8
7. Question
According to Gracie's clock, for how long does she receive flashes at the rate calculated in part (b), and for how long does she receive the flashes calculated in part (d)?
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Question 8 of 8
8. Question
In total, then, how many years has George aged during this episode. How many years has Gracie aged? That is, how many flashes does Gracie receive (indicating George's aging) and how many flashes does George receive (indicating Gracie's aging)?
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