Environmental Engineering Reference
In-Depth Information
14.5 In 1959, Pound and Rebka studied 14.4 keV photons (emitted as a result of
the radioactive decay of
57
Fe) as they travelled the 22.6m from the roof
of their laboratory down to the basement. They observed a frequency in the
basement of
(
1
10
−
15
and
f
0
is the emitted
frequency. Confirm that this blue shift is consistent with relativity theory.
14.6 (a) Consider a clock moving (not too fast) at an altitude
h
in the vicinity of
the Earth's surface. If a time
τ
elapses on the clock, convince yourself that
+
z)f
0
where
z
=
(
2
.
57
±
0
.
26
)
×
1
d
t,
v(t)
2
2
c
2
gh
c
2
τ
≈
+
−
where
v(t)
is the speed of the clock at a time
t
as measured in an inertial
frame at rest relative to the centre of the Earth.
(b) An airplane departs from an airport and travels eastwards above the equa-
tor with a constant ground-speed of 1000 km/h and at an altitude of 10 km.
After completing one lap of the Earth it returns to the same airport. How does
the time registered on a clock on the airplane differ from that registered on
a clock in the airport at the end of the journey given that they were initially
synchronized? Note that you cannot neglect the rotation of the Earth.
14.7 Two pointlike spacecraft are at rest in an inertial frame
S
and they are attached
by a length of rope which is just taut. Simultaneously in
S
the spacecraft turn
on their identical engines whence they being to accelerate away in the same
direction, parallel to the length of rope. What happens to the rope?
