**Astronaut Billbarr's Journey to Alpha Centauri: A Physics Exploration**In this scenario, Astronaut Billbarr travels from Earth to Alpha Centauri in a spaceship moving at a constant velocity. The distance between Earth and Alpha Centauri, according to the fixed-star reference frame, is 4.4 light years.**(a)** *Calculating the Speed for a 20-Year Earth Trip:*To determine the necessary speed for the trip to take 20 years as measured on Earth, we use the formula:\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]Given that the distance is 4.4 light years and the time is 20 years, the speed will be:\[ \frac{4.4 \text{ light years}}{20 \text{ years}} = 0.22c \]where \( c \) is the speed of light.**(b)** *Trip Duration According to Billbarr's Clock:*The time experienced by Billbarr, also known as proper time, accounts for relativistic effects. This time can be calculated using time dilation:\[ t' = t \sqrt{1 - \frac{v^2}{c^2}} \]where \( t \) is the time measured on Earth, \( v \) is the spaceship's speed, and \( c \) is the speed of light. Substituting \( v = 0.22c \) and \( t = 20 \) years, compute \( t' \).**(c)** *Explosions and Light Flashes:*In this hypothetical extension, Earth is destroyed by OrangeDonald and Alpha Centauri by BlackdripRudy. Both events emit light visible to Billbarr as he reaches the midpoint of his journey, suggesting simultaneous observation. The question explores the sequence and timing of these explosions from the frame of reference of the stars, using concepts of simultaneity and light travel time.This exercise highlights how relativity affects measurements of time and simultaneity, crucial for understanding high-speed space travel.

(a) Given: The Earth and Alpha Centauri are separated in the star frame by 4.4 light years. The time…

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