A survey ship moves at constant speed in a straight line along the axis of the…

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 survey ship moves at constant speed in a straight line along the

+x

axis of the station frame

S

. It flies from marker

M_1

to marker

M_2

, both at rest in

S

. Station clocks (synchronised in

S

) record the crossing as taking

3.00\ \mathrm{s}

; the ship's own clock records

1.80\ \mathrm{s}

between the same two passings. All motion is along the common

x

axis, both frames are inertial, and light travels in vacuum. ((a)) Find the ship's speed as a multiple of

c

, and hence its rapidity

\psi

relative to

S

. ((b)) Two station beacons flash. In

S

, flash

A

is at

x = 0

t = 0

and flash

B

is at

x = 1.20 \times 10^{9}\ \mathrm{m}

t = 3.00\ \mathrm{s}

. Compute

\Delta s^2

for this pair and classify the separation as timelike, spacelike or lightlike. ((c)) The ship's lamp emits light of wavelength

480\ \mathrm{nm}

measured in the ship's rest frame, and the ship is moving directly away from the station receiver along the line of sight. What wavelength is received in

S

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