A spacecraft leaves Earth at a constant speed of 0.69c as measured by an observer on Earth. It heads towards a distant star system. The star system is 43.94 lightyears away from Earth, as measured by an observer on Earth. When the spacecraft leaves Earth, the captain of the crew is 24.5 years old. (a) What is the Lorentz γ factor to 3 decimal place precision? (b) What is time taken, in years (to one decimal place precision), to reach the star system as measured by an observer on Earth? (c) What is the distance, in lightyears (to one decimal place precision), the spacecraft travels to reach the star system as measured by the crew of the spacecraft? (d) How old is the captain of the crew when the spacecraft arrives at the star system (use one decimal place precision, and assume the captain can live well beyond normal range of years for a human)? (e) As the spacecraft arrives at the star system, it sends a radio signal back to Earth. Assuming the spacecraft never stops and continues past the star system with the same constant speed as in all parts above, how long does the radio signal take, in years (to one decimal precision), according to the spacecraft’s clock, to reach Earth?
A spacecraft leaves Earth at a constant speed of 0.69c as measured by an observer on Earth. It heads towards a distant star system. The star system is 43.94 lightyears away from Earth, as measured by an observer on Earth. When the spacecraft leaves Earth, the captain of the crew is 24.5 years old.
(a) What is the Lorentz γ factor to 3 decimal place precision?
(b) What is time taken, in years (to one decimal place precision), to reach the star system as measured by an observer on Earth?
(c) What is the distance, in lightyears (to one decimal place precision), the spacecraft travels to reach the star system as measured by the crew of the spacecraft?
(d) How old is the captain of the crew when the spacecraft arrives at the star system (use one decimal place precision, and assume the captain can live well beyond normal range of years for a human)?
(e) As the spacecraft arrives at the star system, it sends a radio signal back to Earth. Assuming the spacecraft never stops and continues past the star system with the same constant speed as in all parts above, how long does the radio signal take, in years (to one decimal precision), according to the spacecraft’s clock, to reach Earth?
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