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5) A manned space ship is to explore the solar system of Alpha Centauri, which is a triple star system 4.365 light-years (cy) from earth. a) Calculate how fast on average the ship must go in order for the crew to get there in 18 months (.e. they age 1.5 y during the trip)? Express your answer as x ratio to the speed of light. v/c. Hint. Consider how velocity times time relates to distance and gamma: solve for velocity. b) according to relativity, how is it possible for the astronauts to get there in less time than it takes light to travel there? c) How long does it take the ship to get there according to people on earth? d) As soon as the astronauts arrive, they send a radio message back to earth. How much time passes on earth between when the astronauts leave earth and when the message is received? e) If the mass of the space ship is to kg calculate the kinetic energy of the ship traveling at the speed of part (a). Express the result as a ratio of kinetic energy to rest energy calculate how much H mass (fuel) in kg is required to propel the ship to the velocity calculated in parts Calex Express the result as a multiple of the mass of the ship. Hint: The ship uses a nuclear ramjet engine, which converts interstellar H into kinetic energy by using the same fusion reaction as occurs in the sun H He + 26.7 MeV. This reaction converts 0.711% of the hydrogen mass into kinetic energy