The Relativistic Lighthouse · AI Generator #GEN-E9F8A281
Physics
Problem
A pulsar (rotating neutron star) acts as a cosmic lighthouse, emitting a beam of radiation that sweeps across space. The pulsar rotates with a period of T0=1.0s as measured in its rest frame. An observer on Earth detects pulses from this pulsar as it moves in a straight line at constant velocity v=0.8c relative to Earth.
The pulsar's trajectory passes closest to Earth at a distance d=4.0light-years at time t=0 (as measured on Earth). At this moment of closest approach, the pulsar is moving perpendicular to the line connecting it to Earth.
(a) What is the period of pulses measured by the Earth observer when the pulsar is at closest approach?
(b) When the pulsar is far away and receding from Earth (long after closest approach), what is the period of pulses measured by the Earth observer?
(c) At what time t (as measured on Earth) after closest approach will the Earth observer measure a pulse period that is exactly twice the rest frame period T0?