Let's say a spaceship is approaching Sagittarius A*. How close to this black hole must the spaceship get to experience time twice as slowly?
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- Suppose you are planning a trip in which a spacecraft is to travel at a constant velocity for exactly six months, as measured by a clock on board the spacecraft, and then return home at the same speed. Upon return, the people on earth will have advanced exactly 76 years into the future. According to special relativity, how fast must you travel? (Give your answer with six significant digits as a multiple of c.)Suppose you decide to travel to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How much is that speed?A millonairess was told in 1995 that she had exactly 15 years to live. However if she travels awayfrom the Earth at 0.8c and then returns at the same speed, the last New Year's day the doctors expecther to celebrate is ___________ This is about special relativity : time dilation, please include step by step so i could learn from it.
- Can you prove Newtonian mechanics is a subset of special relativity?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)? As gravity increases the falling object will not suffer any change in appearence or the progression of time. 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.The pilot of a space ship shines a laser pointer from the back of the ship to the front. The laser travels at the speed of light 300,000 km/s with respect to the ship, which is itself moving at 100,000 km/s. What will be the speed of the laser beam according to an observer at rest outside the ship? Express your answer in km/s
- The area of the event Horizon of a black hole is 4tRg². Use the Schwarzschild metric to verify this. (Please answer in detail or skip)Imagine an alien spaceship traveling so fast that it crosses our galaxy (whose rest diameter is 100,000 ly) in only 100 y of spaceship time. Observers at rest in the galaxy would say that this was possible because the ship's speed B was so close to 1 that the proper time it measured between its entry into and departure from the galaxy was much shorter than the galaxy frame coordinate time (~ 100,000 y) between those events. But how does this look to the aliens? To them, their clocks are running normallu, but the galaxy, which moves backward relative to them at speed B~1, is Lorentz-contracted to a bit less than 100 ly across: this is what makes it possible for the whole galaxy to fly by them in only 100 y. Then find the diameter of the galaxy in the aliens' frame, and verify that it is possible for a galaxy moving at speed B with this diameter to passthe aliens' ship completely in 100y. Answer: 0.9999995A 50-year-old astronaut goes off on a long-term mission in a spacecraft that travels at speeds close to that of light. The mission lasts exactly 200 years as measured on Earth. Biologically speaking, at the end of the mission, the astronaut's age would be exactly 25 years none of the above exactly 30 years O less than 50 years the same as before
- Suppose a galaxy is moving away from Earth at a speed of 0.78c. It emits radio waves of 0.680 m. What wavelength would we detect on Earth? with a wavelengthYou pitch a baseball to your friend from the back of a pick-up truck. You know that you pitch at 40 m/s, but your friend reports that he caught the ball going 10 m/s. What is the speed of the truck? (Use Galilean/Newtonian relativity.The special theory of relativity is "special" because it deals only with a certain type of reference frames, inertial reference frames. What are inertial reference frames?