A shuttle moves along the axis of the station frame at
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
A shuttle moves along the +x axis of the station frame S at 0.500c. When it passes the station it launches a probe forwards, along the same axis, at 0.500c as measured in the shuttle's rest frame. All frames are inertial, all motion is along the common x axis, and light travels in vacuum.
((a)) Find the probe's speed relative to the station, and its rapidity ψ relative to S. (Get the speed from the velocity addition rule and the rapidity from the fact that rapidities add.)
((b)) In S, the launch is at x=0, t=0 and the probe passes a distant buoy at x=1.199×109m, t=5.00s. Compute Δs2, classify the separation, and state the proper time recorded by the probe's own clock between these two events.
((c)) The probe transmits at 1.500GHz in its own rest frame while moving directly away from the station along the line of sight. What frequency is received at the station?