BRADLEY AND ABERRATION
Living at Kew in London early in the 18th century was an enthusiastic
young astronomer, James Bradley. He is famous chiefly for his accurate
observations of star places which have been invaluable to astronomers of
later epochs in ascertaining the proper motions of stars.
The latitude of Bradley's house in Kew was very nearly the same as the
declination of the bright star Gamma Draconis, so that it passed through
his zenith once every day. Bradley had a zenith sector, and with this he
observed with the greatest care the zenith distance of Gamma Draconis at
every possible opportunity. This he did by pointing the telescope on the
star and then recording the small angle of its inclination to a fine
plumb line. So accurate were his measures that he was probably certain
of the star's position to the nearest second of arc.
What he hoped to find was the star's motion round a very slight orbit
once each year, and due to the earth's motion in its orbit round the
sun. In other words, he sought to find the star's parallax if it turned
out to be a measurable quantity.
It is just as well now that his method of observation proved
insufficiently delicate to reveal the parallax of Gamma Draconis; but
his assiduity in observation led him to an unexpected discovery of
greater moment at that time. What he really found was that the star had
a regular annual orbit; but wholly different from what he expected, and
very much larger in amount. This result was most puzzling to Bradley.
The law of relative motion would require that the star's motion in its
expected orbit should be opposite to that of the earth in its annual
orbit; instead of which the star was all the time at right angles to the
earth's motion.
Bradley was a frequent traveler by boat on the Thames, and the apparent
change in the direction of the wind when the boat was in motion is said
to have suggested to him what caused the displacement of Gamma Draconis.
The progressive motion of light had been roughly ascertained by Roemer:
let that be the velocity of the wind. And the earth's motion in its
orbit round the sun, let that be the speed of the boat. Then as the wind
(to an observer on the moving boat) always seems to come from a point in
advance of the point it actually proceeds from (to an observer at rest),
so the star should be constantly thrown forward by an angle given by the
relation of the velocity of light to the speed of the earth in orbital
revolution round the sun.
The apparent places of all stars are affected in this manner, and this
displacement is called the aberration of light. Astronomers since
Bradley's discovery of aberration in 1726 have devoted a great deal of
attention to this astronomical constant, as it is called, and the arc
value of it is very nearly 20".5. This means that light travels more
than ten thousand times as fast as the earth in its orbit (186,330 miles
per second as against the earth's 18.5). And we can ascertain the sun's
distance by aberration also because the exact values of the velocity of
light and of the constant of aberration when properly combined give the
exact orbital speed of the earth; and this furnishes directly by
geometry the radius of the earth's orbit, that is the distance of the
sun.
In fact, this is one of the more accurate modern methods of ascertaining
the distance of the sun. As early as 1880 it enabled the writer to
calculate the sun's parallax equal to 8".80, a value absolutely
identical with that adopted by the Paris Conference of 1896, and now
universally accepted as the standard.
In whatever part of the sky we observe, every star is affected by
aberration. At the poles of the ecliptic, 23-1/2 degrees from the
earth's poles, the annual aberration orbits of the stars are very small
circles, 41" in diameter. Toward the ecliptic the aberration orbits
become more and more oval, ellipses in fact of greater and greater
eccentricity, but with their major axes all of the same length, until we
reach the ecliptic itself; and then the ellipse is flattened into a
straight line 41" in length, in which the star travels forth and back
once a year. Exact correspondence of the aberration ellipses of the
stars with the annual motion of the earth round the sun affords
indisputable proof of this motion, and as every star partakes of the
movement, this proof of our motion round the sun becomes many
million-fold.
Indeed, if we were to push a little farther the refinement of our
analysis of the effect of aberration on stellar positions, we could
prove also the rotation of the earth on its axis, because that motion is
swift enough to bear an appreciable ratio to the velocity of light.
Diurnal aberration is the term applied to this slight effect, and as
every star partakes of it, demonstration of the earth's turning round on
its axis becomes many million-fold also.