A star in a distant system approaches the Earth along the line of sight at measured…

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics

Relativity and Gravitation, Ch The postulates and the Lorentz transformation

Problem

A star in a distant system approaches the Earth along the line of sight at 0.300c0.300c measured in the Earth's frame SS, taken as inertial. Along that same line the star ejects a jet of gas towards the Earth at 0.300c0.300c as measured in the star's own frame. The star also shines. A student writes: "The light leaves the star at cc, and the star is coming at 0.300c0.300c, so we receive the light at 1.300c1.300c; likewise the gas arrives at 0.600c0.600c." Take c=2.998×108 m s−1c = 2.998\times10^{8}\ \mathrm{m\,s^{-1}}. ((a)) State which postulate the student's first claim violates, and give the speed of the starlight measured in the Earth's frame, in m s−1\mathrm{m\,s^{-1}}. ((b)) Compute the speed of the gas jet measured in the Earth's frame, in m s−1\mathrm{m\,s^{-1}}, and say by how many per cent of cc the student's 0.600c0.600c is wrong.

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