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AST 822: Electromagnetic Radiation
Problem Set 5: due Wednesday, November 9
1) An observer in the inertial frame of reference
K
sees a particle
moving in the
xy
plane, with velocity
u
x
=
u
cos
θ
and
u
y
=
u
sin
θ
. The inertial frame of reference
K
0
is moving relative to
the frame
K
at a velocity
v
=
βc
along the
x
axis.
In the
K
0
frame, the particle’s velocity is
u
0
x
=
u
0
cos
θ
0
and
u
0
y
=
u
0
sin
θ
0
.
a) If the particle being viewed is a photon, what are sin
θ
and
cos
θ
in terms of
θ
0
and
β
?
b) What is the
aberration angle
Δ
θ
≡
θ
0

θ
in the limit
β
¿
1?
c) If the Earth is moving on a circular orbit with a velocity
v
= 30 km s

1
, what is the maximum aberration you expect in
the position of stars over the course of a year?
(This eFect is
the “aberration of starlight”, ±rst measured by James Bradley
in AD 1728.)
2 a) In an inertial frame
K
0
, a neutron is at rest, and thus
has a lifetime
t
≈
10
3
s.
In an inertial frame
K
, the neutron
is highly relativistic, and has an energy
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 Fall '05
 RYDEN

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