Which of the following statements best describes the behaviour of an object falling towards the Event Horizon of a Black Hole (according to an observer a long way from it)? O As gravity increases the falling object will not suffer any change in appearence or the progression of time. O As gravity increases the object's light will be compressed, leading to it looking bluer, with time appearing to passing more slowly for it. The falling object will appear to experience an increase in the rate of time, and it's colour will appear evermore red. As the falling object experiences ever stronger gravity, it will become redder and time will appear to pass more slowly for it.
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- One day, an astronomer is looking through a telescope and observes three spaceships having an interstellar battle in the vacuum of space (see diagram below). The astronomer sees a Century Hawk traveling at 0.92c. In front of the Century Hawk and traveling in the same direction is an O-Wing Fighter going 0.5c. Behind the Century Hawk and traveling in the opposite direction is a Borg Box going 0.6c. The Century Hawk fires its rear lasers at the Borg Box and fires its forward lasers at the O-Wing Fighter. (DISCLAIMER: The diagram below is not to scale & no spaceships were harmed during the making of this problem.) How fast will the photons emitted from the FORWARD lasers be moving relative to the ASTRONOMER?? ×c How fast will the photons emitted from the REAR lasers be moving relative to the CENTURY HAWK?? ×cA muon is created 60 km above the surface of the earth. In the earth’s frame, the muon is traveling directly downward at 0.9999c.a. In the earth’s frame of reference, how much time elapses between the muon’s creation and the time it reaches the surface?b. Use time dilation to determine, in the muon’s frame, how much time elapses between the muon’s creation and the time it reaches the surface.c. In the muon’s frame of reference, length contraction reduces the distance between the point at which it is created and the surface of the earth. What is this distance?d. The ratio of the distance you calculated in part c and the time you calculated in part b is a speed. Calculate this speed; what do you notice?The star Proxima Centauri is 4.24 light-years from Earth. Imagine a spaceship that travels from Earth to Proxima Centauri at a constant speed of 0.925c. On Earth, we would measure the time it takes for the ship to reach the star to be (4.24ly/0/925c)=4.58 years How much time (in years) would it take the ship to travel from the Earth to the star as measured by an astronaut aboard the ship? ______ years What is the distance to the star (in light years) as measured by an astronaut aboard the ship? _______ ly
- Alice is moving with a velocity of 0.7c away from Bob in the positive x-direction. Bob observes two events at ad = (1, 0, 2, 3) and b = (5, 0, 0, 2) of a particle's worldline (measured in flat spacetime, %3D using Cartesian coordinates). i) If Alice observes the same two events, what components does she measure? ii) Calculate the proper time between these two events.As you pilot your space utility vehicle at a constant speed toward the moon, a race pilot flies past you in her spaceracer at a constant speed of 0.830c, relative to you. At the instant the space-racer passes you, both of you start timers at zero. At the instant when you measure that the spaceracer has traveled 1.13 × 10°m past you, what does the race pilot read on her timer?mh.2 A pursuit spacecraft from the planet Tatooine is attempting to catch up with a Trade Federation cruiser. As measured by an observer on Tatooine, the cruiser is traveling away from the planet at 0.600c. The pursuit ship is traveling at 0.800c relative to Tatooine, in the same direction as the cruiser. What is the speed of the cruiser relative to the pursuit ship?
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