Long Trips at Constant Acceleration. Consider a spaceship on a longtrip with a constant

Chapter 13, Problem 55

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Long Trips at Constant Acceleration. Consider a spaceship on a longtrip with a constant acceleration of 1g. Although the derivation isbeyond the scope of this book, it is possible to show that, as longas the ship is gone from Earth for many years, the amount of timethat passes on the spaceship during the trip is approximatelywhere D is the distance to the destination and ln is the naturallogarithm. If D is in meters, andthe answer will be in units of seconds. Use this formula asneeded to answer the following questions. Be sure to convert thedistances from light-years to meters and final answers from secondsto years; useful conversions:.a. Suppose the ship travels to a star that is 500 light-years away.How much time will pass on the ship? Approximately howmuch time will pass on Earth? Explain.b. Suppose the ship travels to the center of the Milky Way Galaxy,about 28,000 light-years away. How much time will passon the ship? Compare this to the amount of time that passeson Earth.c. The Andromeda Galaxy is about 2.2 million light-yearsaway. Suppose you had a spaceship that could constantly accelerate at 1g. Could you go to the Andromeda Galaxy andback within your lifetime? Explain. If you could make thejourney, what would you find when you returned to Earth?