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3. (25 marks) The center of our Milky Way galaxy is about 23000 ly away. (a) To eight significant figures, at what constant speed parameter ? (? v/c) would you need to travel exactly 23000 ly (measured in the Galaxy rest frame) in exactly 30 year (measured in your frame)? (b) Measured in your frame and in light-years, what length of the Galaxy would pass by during your trip? [Note: 1 ly (light-year) = the distance traveled by light in one year.] 4. (25 marks) An astronaut Alice in a spaceship leaves earth at a speed of 3c/5. When a clock on the spaceship says 1 year has elapsed, Alice sends a light signal back to earth. (a) According to Earth's reference frame, when was the signal sent? (b) According to Earth's reference frame, how long after the spaceship left did the signal arrive on earth? (c) An observer Bob on earth will reply by sending a light signal back to the spaceship when he receives Alice's signal. According to Alice, how much time after sending her signal will elapse before she receives the reply from Bob? 5. (No need to hand in this question) A train of proper length L0 is moving at velocity v relative to the ground. Two light beams are emitted at the midpoint inside the train at time t = 0 according to both train and ground based clocks. One of the light beams is moving in the same direction as v and towards the front door, while the other beam is moving in the opposite direction towards the back door. (a) The velocity of both light beams is c relative to an observer on the train. According to Newtonian physics, what are the velocities of the light

          3. (25 marks) The center of our Milky Way galaxy is about 23000 ly away. (a) To eight significant figures, at what constant speed parameter ? (? v/c) would you need to travel exactly 23000 ly (measured in the Galaxy rest frame) in exactly 30 year (measured in your frame)? (b) Measured in your frame and in light-years, what length of the Galaxy would pass by during your trip? [Note: 1 ly (light-year) = the distance traveled by light in one year.]

4. (25 marks) An astronaut Alice in a spaceship leaves earth at a speed of 3c/5. When a clock on the spaceship says 1 year has elapsed, Alice sends a light signal back to earth. (a) According to Earth's reference frame, when was the signal sent? (b) According to Earth's reference frame, how long after the spaceship left did the signal arrive on earth? (c) An observer Bob on earth will reply by sending a light signal back to the spaceship when he receives Alice's signal. According to Alice, how much time after sending her signal will elapse before she receives the reply from Bob?

5. (No need to hand in this question) A train of proper length L0 is moving at velocity v relative to the ground. Two light beams are emitted at the midpoint inside the train at time t = 0 according to both train and ground based clocks. One of the light beams is moving in the same direction as v and towards the front door, while the other beam is moving in the opposite direction towards the back door. (a) The velocity of both light beams is c relative to an observer on the train. According to Newtonian physics, what are the velocities of the light

3. (25 marks) The center of our Milky Way galaxy is about 23000 ly away. (a) To eight significant figures, at what constant speed parameter ? (? v/c) would you need to travel exactly 23000 ly (measured in the Galaxy rest frame) in exactly 30 year (measured in your frame)? (b) Measured in your frame and in light-years, what length of the Galaxy would pass by during your trip? [Note: 1 ly (light-year) = the distance traveled by light in one year.]

4. (25 marks) An astronaut Alice in a spaceship leaves earth at a speed of 3c/5. When a clock on the spaceship says 1 year has elapsed, Alice sends a light signal back to earth. (a) According to Earth's reference frame, when was the signal sent? (b) According to Earth's reference frame, how long after the spaceship left did the signal arrive on earth? (c) An observer Bob on earth will reply by sending a light signal back to the spaceship when he receives Alice's signal. According to Alice, how much time after sending her signal will elapse before she receives the reply from Bob?

5. (No need to hand in this question) A train of proper length L0 is moving at velocity v relative to the ground. Two light beams are emitted at the midpoint inside the train at time t = 0 according to both train and ground based clocks. One of the light beams is moving in the same direction as v and towards the front door, while the other beam is moving in the opposite direction towards the back door. (a) The velocity of both light beams is c relative to an observer on the train. According to Newtonian physics, what are the velocities of the light

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