Astronomy Principles and Practice Fourth Edition.pdf

The velocity of light 135
Table 11.1. The discovery of stellar aberration.
Date December 21st March 21st June 21st September 21st
Expected declination δ − q δ δ + q δ
Measured declination δ δ − q 1 δ δ + q 1
40 seconds of arc and the time-tables of these stellar shifts were always three months out of step with
the parallactic motion Bradley sought to detect.
It is said that Bradley hit upon the correct interpretation of these results during a pleasure trip
on the river Thames. The sailing boat Bradley and his friends were in tacked to and fro. Bradley’s
attention was caught by the pennant at the masthead and by the way its direction changed every time
the boat tacked. The crew told him that the pennant’s direction was due to a combination of wind
velocity and the boat’s velocity at that moment.
Bradley realized the significance of the sailors’ remarks.
Replace the wind by light coming from a star; replace the boat by the Earth moving around the
Sun, the shifting course of the boat being now the continually changing direction of motion of the
Earth in its circular orbit. Then the pennant indicates the apparent direction in which the star is seen, a
direction dependent upon the velocity of light from the star and the velocity of the Earth in its orbit.
Bradley’s own words are instructive:
At last I conjectured that all the phenomena hitherto mentioned proceeded from the
progressive motion of light and the Earth’s annual motion in its orbit. For I perceived that,
if light was propagated in time, the apparent place of a fixed object would not be the same
when the eye is at rest, as when it is moving in any other direction than that of the line
passing through the eye and object; and that when the eye is moving in different directions,
the apparent place of the object would be different.
The fact that light travelled with a finite speed was known to Bradley and he also knew its
approximate speed.
11.3 The velocity of light
In 1675, the Danish astronomer Roemer had measured the velocity of light by noting variations in
the times of eclipses of Jupiter’s satellites. Galileo himself had observed on many occasions that
the satellites he had discovered disappear into the shadow cast by Jupiter and had suggested that, by
constructing tables of the eclipse times, they could be used as astronomical clocks for finding ships’
longitudes at sea. The disappearance or reappearance of a satellite could be looked upon as a light
signal. If the velocity of light was infinitely large, these light signals would occur at regular intervals
since the orbits of the satellites about Jupiter were very nearly circular.
Roemer found that the eclipses did not take place at absolutely regular time intervals. All four
satellites’ eclipses were sometimes early and sometimes late. He also noticed that the amounts by
which they were early or late depended upon the positions of Jupiter and the Earth: eclipses were
earliest when Jupiter was nearest the Earth and latest when Jupiter and the Earth were on opposite
sides of the Sun. Roemer concluded correctly that the discrepancies were due to the velocity of light
being finite, so that the light signal indicating the beginning or end of an eclipse took time to cross
space from the vicinity of Jupiter to the Earth. This time varied because of the changing Earth–Jupiter
distance. The maximum discrepancy between the earliest and latest eclipse times was then the time it