Chapter 19
Aberration
We will in this chapter leave our crystal and turn to the physics of our ‘outside’
space for which the Einsteinian Special Theory of Relativity with its specific critical
velocity, the speed of light c L , is valid.
We consider the case of the light emitted from a star S , which in o is observed
as a plane wave propagating along negative y-axis, cf. Figure 19.1. The star is seen,
if the rays arriving at A(t 1 ) and B(t 1 ) respectively, meet at O
.
Let us now consider an inertial system
, which is moving along negative x-axis
of o at a velocity of amount v . A telescope resting in
has the linear dimension
2L . We ask for the angle α
of inclination, which is measured in
for the telescope
if the star is observed there. This angle α
of inclination is defined by the condition
that the peripheral rays meet in the middle.
1 Obviously, if the telescope would not
be inclined, but positioned parallel to x
-direction of
, the star could not be seen,
since both rays would not meet at O
, cf. Fig. 19.2.
For calculating the angle α
of aberration measured in
, we will make use of
the postulate (112) of Lorentz contraction measured in o , solely,
L
= L o
1 −
v 2
c
2
L
.
(112)
This is sufficient for the calculation of the exact relativistic angle of aberration.
We have the projections,
a
= L cos α
, b
= L sin α
.
(241)
The telescope is resting in
. Applying the postulate (112) with a
and a for L o
and L
we measure in o ,
1 This definition also applies to modern very long baseline interferometry.
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https://doi.org/10.1007/978-981-15-3168-2_19
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