A futuristic trip from Earth to Alpha Centauri is taking place. The travellers start on Earth, from position (t, x) = (0, 0). They must travel from Earth (considered stationary) to Alpha Centauri, a distance of L = 4.37 light years away, such that they arrive at Alpha Centauri at Earth time of T = 10 years. a) Team A travels with a constant acceleration so that their worldline can be parametrized by the proper time Tau as t(Tau) = a-1sinh(a*Tau) x(Tau) = a-1(cosh(a*Tau) - 1) for a constant 'a.' They blast off at (t, x) = (0, 0) and travel with this constant acceleration until they reach Alpha Centauri at Earth time of 10 years. What proper time does Team A measure (in years)?
A futuristic trip from Earth to Alpha Centauri is taking place. The travellers start on Earth, from position (t, x) = (0, 0). They must travel from Earth (considered stationary) to Alpha Centauri, a distance of L = 4.37 light years away, such that they arrive at Alpha Centauri at Earth time of T = 10 years. a) Team A travels with a constant acceleration so that their worldline can be parametrized by the proper time Tau as t(Tau) = a-1sinh(a*Tau) x(Tau) = a-1(cosh(a*Tau) - 1) for a constant 'a.' They blast off at (t, x) = (0, 0) and travel with this constant acceleration until they reach Alpha Centauri at Earth time of 10 years. What proper time does Team A measure (in years)?
Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter1: Relativity I
Section: Chapter Questions
Problem 28P
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Setup: A futuristic trip from Earth to Alpha Centauri is taking place. The travellers start on Earth, from position (t, x) = (0, 0). They must travel from Earth (considered stationary) to Alpha Centauri, a distance of L = 4.37 light years away, such that they arrive at Alpha Centauri at Earth time of T = 10 years.
a) Team A travels with a constant acceleration so that their worldline can be parametrized by the proper time Tau as
t(Tau) = a-1sinh(a*Tau)
x(Tau) = a-1(cosh(a*Tau) - 1)
for a constant 'a.' They blast off at (t, x) = (0, 0) and travel with this constant acceleration until they reach Alpha Centauri at Earth time of 10 years. What proper time does Team A measure (in years)?
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