c²r The time dilation a distance r from Earth's center is 3 = due to the speed of a satellite + dilation due to gravity exactly equal the dilation experienced by a person at Earth's surface where 3 = two clocks run at the same rate? 2GM. The speed of a satellite in a stable circular orbit is v= GM. At what height above Earth's surface will the dilation ? In other words, at what height will the 2GM Ve² RE
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- B3The center of our Milky Way galaxy is about 23000 ly away. (a) To eight significant figures, at what constant speed parameter would you need to travel exactly 23000 ly (measured in the Galaxy frame) in exactly 25 y (measured in your frame)? (b) Measured in your frame and in lightyears, what length of the Galaxy would pass by you during the trip? (a) Number (b) Number I Units Units1 2. Preparations are under way for a spacecraft visit to the Alpha Centauri star system, 4.30- lightyears away Provisions are placed on board to allow for a trip of 8 years. a. What minimum speed must the spacecraft travel relative to Earth if the provisions are to last?
- The Minkowski interval between Alice’s birth and Alice’s death is −144yrs . How long did Alice live? Will other observers agree or disagree with that judgement?A particle has a rest mass of 6.35 × 10¯ kg and a momentum of 5.39 × 10-¹8 kg.m/s. Determine the total relativistic energy E of the particle. 1.67 ×10-⁹ E = Incorrect Find the ratio of the particle's relativistic kinetic energy K to its rest energy Erest. K 1.93 Erest || IncorrectAs a spaceship is moving toward Earth, an Earthling measures its length to be 403 m, while the captain on board radios that her spaceship's length is 624 m. Calculate the spaceship's speed relative to earth and supply the missing numerical factor below. __)c
- How fast is a rocket going it its passengers measure its length to be 25.5 but the people on earth watching it go by measure its length to be 18.8? Please give your answer as a fraction of c. For example, if v=1.5*10^ 8 m/s,use V/c=0.5 .A star is 16.6 light-years from Earth. Part A How long would it take a spacecraft traveling 0.950c to reach that star as measured by observer on Earth? tEarth 17.5 years Submit ✓ Part B Correct How long would it take a spacecraft traveling 0.950c to reach that star as measured by observer on the spacecraft? t = 5.46 years Submit ✓ Previous Answers Part C Correct Submit What is the distance traveled according to observers on the spacecraft? 15.18 light-years Previous Answers Part D Correct Previous Answers v= 5.18 What will the spacecraft occupants compute their speed to be from the results of part B and part C? IT| ΑΣΦ Submit Previous Answers Request Answer ? X Incorrect; Try Again; 3 attempts remaining .CA severely injured Peter can only live for the next 3.5 hours. Before dying, he wants to go back to Earth which is 5 light-hours away. What should be the minimum cruise speed of the Peter's spaceship so that at least he can make it before he runs out of time? HINT: The answer is NOT 4.29x108 m/s. Wrong answers will be downvoted. Thank you.
- You are now in 20 years old. You are disappointed with the current situation. So, you decide to leave to the future of Earth. You plan a space journey for 5 years(go in 2.5 years and back in 2.5 years.) with a constant speed v relative to Earth. If you wish to reach the Earth after 100 years when you are 25 years old, how fast the speed, v you need to set for your spaceship? (Give your answer in 5 significant figures)Particles called ?-mesons are created by accelerator beams. If these particles travel at 2.40 ✕ 108 m/s and live 3.00 ✕ 10−8 s when at rest relative to an observer, how long (in seconds) do they live as viewed in the laboratory?1. If a subatomic particle moves close to the speed of light. Its decay would occur ___? 2. A space explorer travels between asteroids that are 100 000 m apart. His/her space probe travels with constant speed of 0.8c=2.4x108 m/s. What is the time of the trip between asteroids measured by observer on one of the asteroids? Write your answer rounded to 2 decimal places in ms