The Cosmic Mirror Observatory · AI Generator #GEN-FC3BB683
Physics
Problem
A revolutionary space-based observatory consists of two identical spacecraft: a laser source and a mirror reflector, separated by a proper distance of L0=1.50×108m in their common rest frame. The system moves as a rigid body with velocity v=0.800c relative to Earth in the direction perpendicular to the line connecting the spacecraft.
The laser spacecraft emits a short pulse toward the mirror at t=0 (in the Earth frame), when the laser is at position (0,0) and the mirror is at position (L0/γ,0), where γ is the Lorentz factor. The mirror reflects the pulse back to the laser.
From Earth's perspective, what is the total time T elapsed from when the laser emits the pulse until it receives the reflected pulse back? Express your answer in terms of L0, c, and the given numerical values.
Note: The spacecraft velocity is perpendicular to the laser beam direction, and you may assume the mirror reflects the light pulse perfectly back along its incident path in the mirror's rest frame.