A rocket carries Rindler coordinates with tail at and

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

The Geometry of Gravity, Ch Accelerated observers, Rindler coordinates and the equivalence principle

Problem

A rocket carries Rindler coordinates (η,ξ)(\eta,\xi) with tail at ξ=0\xi=0 and g00=−(1+aξ/c2)2g_{00}=-(1+a\xi/c^2)^2, where x0=cηx^0=c\eta. A recorder at the nose, a height ℓ=250 m\ell = 250\,\mathrm{m} above the tail, reads g00=−(1+2.72×10−14)2g_{00} = -(1+2.72\times10^{-14})^2. ((a)) Find the rocket's proper acceleration aa. ((b)) Using the equivalence principle, predict the acceleration a dropped object would appear to have relative to the nose platform, for a stationary laboratory of the same field strength. ((c)) Find the distance behind the tail at which g00=0g_{00}=0.

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