An ice-mining tug moves inertially directly away from an observatory at the constant…
PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics
Relativity and Gravitation, Ch Minkowski spacetime, four-vectors and causal structure
Problem
An ice-mining tug moves inertially directly away from an observatory at the constant speed 0.250c in the observatory frame S. In the tug's own rest frame its hull lamp fires twice from the same point of the hull, the two flashes being 40.0μs apart as read by a clock at rest in the tug. The tug also carries a lamp emitting a spectral line of wavelength 486.1 nm as measured in the tug's rest frame. Everything happens in vacuum and gravity is ignored.
((a)) Calculate Δs2 between the two flashes, in m2, and hence predict whether any inertial observer could record the second flash before the first.
((b)) Calculate the wavelength of the spectral line received at the observatory.
((c)) Calculate the redshift z of that line.