Environmental Engineering Reference
In-Depth Information
c
a + d
V
+
u
Figure 5.5 The velocity of starlight relative to the Earth at point A in its orbit around the
Sun (denoted by the big arrow).
Note that if
V
0. When the Earth is at the point A, if
we suppose an ether wind is blowing at a speed
V
=
0 it would follow that
α
=
u
(in the opposite direction
to the direction of motion of the Earth) then adding the velocities of the ether and
the velocity of the starlight relative to the ether we can obtain the velocity of the
starlight relative to the Earth
4
. The addition of velocities is illustrated in Figure 5.5.
From the figure, we can determine that
+
V
+
u
tan
(α
+
δ)
=
α
+
δ
(5.7)
c
and we assume all angles are small (which sounds reasonable since
c
is presumably
much larger than
V
). Similarly, at positions B and D the apparent position of the
star is given by
V
c
tan
α
=
α.
(5.8)
From these two equations it follows that
δ
u/c
. So, the star moves backwards
and forwards in the night sky over the course of 1 year reaching its extreme
positions when the Earth is at points A and C in its orbit. The angular size of this
oscillation is just 2
δ
=
2
u/c
which is independent of the Sun's velocity. If the star
were not in the ecliptic then it would appear to move in an ellipse. In any case,
direct observation of these stellar aberrations led Bradley to conclude that the ratio
of 'the Velocity of Light to the Velocity of the Eye (which in this Case may be
supposed the same as the Velocity of the Earth's annual Motion in its Orbit) as
10210 to One.'
5
30 km/s
which is precisely the speed one expects given that the Earth travels around the
Sun once every 365 days. In their time, Bradley's measurements had an additional
significance: they provided a direct verification of Copernicus' claim that the Earth
rotates around the Sun.
Substituting for the known velocity of light gives
u
4
More correctly it is the velocity of the light captured by the observer's telescope relative to the
telescope.
5
Letter to Edmond Halley published in Philosophical Transactions of the Royal Society of London,
Vol. 35 (1727).
