Astronomy Principles and Practice Fourth Edition.pdf

136 The reduction of positional observations: II
Figure 11.2. The effect of aberration.
took light to cross the diameter of the Earth’s orbit. Roemer, from a rough knowledge of this distance
and the time interval, calculated the velocity of light, obtaining a value not far removed from the
modern value of 299 792·5kms −1 .
11.4 The angle of aberration
Bradley remembered this work of Roemer, neglected for half a century. He also knew that the velocity
of the Earth in its heliocentric orbit was about 30 km s −1 in a direction always at right angles to its
radius vector (assuming the Earth’s orbit to be circular). He now had all the information required to
explain the phenomena he had observed and produce a formula to predict them.
In everyday life we are familiar with a number of examples embodying the principle involved. For
instance, in a stationary car on a rainy day we see the raindrops stream downwards. But when the car
moves, the raindrops’ paths slant so that they appear to be coming from a direction between directly
overhead and the direction in which the car is travelling.
In figure 11.2, let light from a star X enter a telescope at A so that the observer sees the star in the
middle of the field of view. The telescope, because of the Earth’s orbital velocity v km s −1 ,ismoving
in the direction EE 1 . By the time the light travelling with velocity c km s −1 (c = 299 792·5 kms −1 )
has reached the foot of the telescope, the telescope has moved into the position E 1 B. To the observer,
the star appears to lie in the direction E 1 B because the telescope has had to be tilted slightly away from
the true direction of the star towards the instantaneous direction in which the observer is moving.
The angle of aberration, θ, is obtained by considering △AEE 1 in which the distances EE 1
and AE 1 are proportional to v and c respectively. If we take AE 1 D = θ and AED = θ 1 ,then
sin AEE 1
AE 1
= sin EAE 1
EE 1