Suppose we want to send an astronaut on a round trip to visit a star that is 200 light-years distant and at rest with respect to Earth. The life support systems on the spacecraft enable the astronaut to survive at most 20 years. At what speed must the astronaut travel to make the round trip in 20 years of spacecraft time?
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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.)The star Epsilon Eridani is 10.4 light-years from Earth. Imagine a spaceship that travels from Earth to Epsilon Eridani at a constant speed of 0.921c. On Earth, we would measure the time it takes for the ship to reach the star to be (10.4ly/0.921c)= 11.2 years. (a) How much time (in years) would it take the ship to travel from the Earth to the star as measured by a passenger aboard the ship? years (b) What is the distance to the star (in light years) as measured by a passenger aboard the ship?Michale is decided to buy a ticket to go to space. After meticulously planning his journey, he travels in his vessel at speed 7/10c from Earth to the nearby planet, Alfa-0 , 20 light-years away (as measured in the common rest frame of Earth and Alfa-0). He spends a year (as measured in Earth- Alfa-0 frame) on this foreign planet sharing stories of human history to aliens. Finally, he is ready to head home. His hosts, charmed by his friendliness and the stories of his wonderful home, give him their best space ship for the return voyage. In this new ship, he travels at speed 95/100 c. Let W be Michael's departure from Earth (which we can set as the origin of the reference frame), X his arrival to the Alfa-0, Y his departure from the Alfa-0, and Z his arrival back to Earth. a. Draw the spacetime diagram from the rest frame of the Earth - Alfa-0 system, indicating Michale's worldline, and the events, W, X, Y, Z. (A rough sketch will suffice - do not worry about the angles. b. Find the…
- A spaceship has proper length L_p and passes by a person standing on Earth. The personstanding on Earth measures that it takes time delta_t for the spaceship to pass a fixed point on theEarth. What is the speed (v) of the spaceship, according the person standing on Earth? Giveyour answer for v in terms of L_p, delta_t, and c (the speed of light).A cosmic ray particle is released from an exploding star that is 2600 Light Years from Earth. If the particle traveled at 98% the speed of light, how far did it travel in its own frame of reference before hitting Earth?Your clocks and calendars are synchronized with the clocks and calendars in a star system exactly 10 ly from earth that is at rest relative to the earth. You receive a TV transmission from the star system that shows a date and time display. The date it shows is June 17, 2050. When you glance over at your own wall calendar, what date does it show?
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