A rocket has engines that give it a constant acceleration of 1 g (9...

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A rocket has engines that give it a constant acceleration of 1 g (9.81 m/s²) relative to its instantaneous inertial frame.
(a) If the rocket starts from rest near Earth, how far from the Earth (as measured in the Earth's frame) will the rocket be in 40 years as measured on Earth? How far after 40 years as measured in the rocket?
(b) Compute the proper time for the occupants of a rocket ship to travel 30,000 light years from the Earth to the center of the galaxy. Assume they maintain an acceleration of 1 g for half the trip and decelerate at 1g for the remaining half.
(c) Give the expressions for x and t as functions of proper time for the entire trip in part (b).

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