A probe leaves a space station from rest and its engine holds a constant proper…

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · The equivalence principle and gravity as geometry · The equivalence principle and gravity as geometry

Relativity and Gravitation, Ch Accelerated observers, hyperbolic motion and the equivalence principle

Problem

A probe leaves a space station from rest and its engine holds a constant proper acceleration a=15.0 m s−2a = 15.0\ \mathrm{m\,s^{-2}} (the reading of an accelerometer carried on board) along the +x+x direction. The station frame SS is inertial, with the probe at x=0x = 0 at t=0t = 0. Take c=2.998×108 m s−1c = 2.998\times10^{8}\ \mathrm{m\,s^{-1}}. Ignore all gravitational fields and treat the motion as one-dimensional. ((a)) How much proper time τ\tau does the probe's own clock record before its speed in SS reaches 0.600c0.600c? ((b)) How much time tt has passed in SS at that moment? ((c)) How far has the probe travelled in SS? ((d)) The Newtonian estimate xN=12aτ2x_{\rm N} = \tfrac{1}{2}a\tau^{2} uses the ship's own clock. By what percentage of the correct distance does it fall short?

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