General Relativity: An Introduction for Physicists · Problem 5.12

Special relativity revisited — Hobson, Efstathiou & Lasenby

Physics · relativistic-aberration

Problem

An inertial frame

S'

moves with constant velocity

u

along the

x

-axis with respect to frame

S

. A photon in frame

S'

is fired at an angle

\theta'

to the forward direction of motion. Show that the angle

\theta

measured in frame

S

\tan\theta = \frac{\tan\theta'(1-\beta^2)^{1/2}}{1 + \beta\sec\theta'},

where

\beta = u/c