In the frame of a space station two navigation buoys are at rest on the axis

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

In the frame

S

of a space station two navigation buoys are at rest on the

x

axis. Event

A

: at

t = 0

the buoy at

x = 3.00\times10^{8}

m transmits a pulse. Event

B

: at

t = 1.50

s the buoy at

x = 9.00\times10^{8}

m transmits a pulse. All coordinates and times are those of

S

; the buoys and the station are at rest in

S

, and everything happens in vacuum with gravity ignored. At the same time a cargo hauler is moving inertially directly away from the station along

+x

0.600c

. Its beacon emits light of frequency

450

THz as measured in the hauler's own rest frame. ((a)) Predict, and then decide by calculating

\Delta s^2

(in

\mathrm{m^2}

), whether the pulse transmitted at

A

could have triggered the transmission at

B

. ((b)) Calculate the beacon frequency received by the station.

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