
Suppose an astronaut travels to a distant star and returns to Earth. Except for brief intervals of time when he is accelerating or decelerating, his spaceship travels at the incredible speed of v = 0.995c relative to the Earth. The star is 46 light-years away. (A light-year is the distance light travels in 1 year.) a. Show that the factor γ for this velocity is approximately equal to 10.
a. How long does the trip to the star and back take as seen by an observer on Earth?
b. How long does the trip take as measured by the astronaut?
c. What is the distance traveled as measured by the astronaut?
d. If the astronaut left a twin brother at home on Earth while he made this trip, how much younger is the astronaut than his twin when he returns?
(a)

To show that the factor
Answer to Problem 3SP
It is shown that the factor
Explanation of Solution
Given info: The velocity of the spaceship is
Write the expression to find the
Here,
Substitute
Conclusion:
Therefore, it is shown that the factor
(b)

The time taken for the travel to the star and back to earth as seen by an observer on earth.
Answer to Problem 3SP
The time taken for the travel to the star and back to earth as seen by an observer on earth is
Explanation of Solution
Write the expression to find the distance travelled in meter.
Write the expression to find the time taken by the spaceship to travel back and forth.
Here,
Substitute
Conclusion:
Therefore, the time taken for the travel to the star and back to earth as seen by an observer on earth is
(c)

The time taken for the travel to the star and back to earth as seen by the astronaut.
Answer to Problem 3SP
The time taken for the travel to the star and back to earth as seen by the astronaut is
Explanation of Solution
Write the expression to find the distance travelled in meter.
Write the expression to find the time taken by the spaceship to travel back and forth as seen by the astronaut.
Here,
Substitute
Conclusion:
Therefore, the time taken for the travel to the star and back to earth as seen by the astronaut is
(d)

The distance travelled as measured by the astronaut.
Answer to Problem 3SP
The distance travelled as measured by the astronaut is
Explanation of Solution
Write the expression to find the distance as measured by the astronaut.
Here,
Substitute
Conclusion:
Therefore, the distance travelled as measured by the astronaut is
(e)

The age difference between the astronaut and his twin after he returns from his space journey.
Answer to Problem 3SP
The age difference between the astronaut and his twin after he returns from his space journey is
Explanation of Solution
Write the expression to find the age difference between the astronaut and his twin.
Here,
Substitute
Conclusion:
Therefore, the age difference between the astronaut and his twin after he returns from his space journey is
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Chapter 20 Solutions
Physics of Everyday Phenomena
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