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Newton’s Successors

Posted on July 23rd, 2007 by Admin.
Categories: Uncategorized.

Edmund Halley succeeded Flamsteed as Second Astronomer Royal in
1721. Although he did not contribute directly to the mathematical
proofs of Newton’s theory, yet his name is closely associated with
some of its greatest successes.

He was the first to detect the acceleration of the moon’s mean
motion. Hipparchus, having compared his own observations with those of
more ancient astronomers, supplied an accurate value of the moon’s
mean motion in his time. Halley similarly deduced a value for modern
times, and found it sensibly greater. He announced this in 1693, but
it was not until 1749 that Dunthorne used modern lunar tables to
compute a lunar eclipse observed in Babylon 721 B.C., another at
Alexandria 201 B.C., a solar eclipse observed by Theon 360 A.D., and
two later ones up to the tenth century. He found that to explain
these eclipses Halley’s suggestion must be adopted, the acceleration
being 10″ in one century. In 1757 Lalande again fixed it at 10.”

The Paris Academy, in 1770, offered their prize for an investigation
to see if this could be explained by the theory of gravitation. Euler
won the prize, but failed to explain the effect, and said: “It appears
to be established by indisputable evidence that the secular inequality
of the moon’s mean motion cannot be produced by the forces of
gravitation.”

The same subject was again proposed for a prize which was shared by
Lagrange [1] and Euler, neither finding a solution, while the latter
asserted the existence of a resisting medium in space.

Again, in 1774, the Academy submitted the same subject, a third time,
for the prize; and again Lagrange failed to detect a cause in
gravitation.

Laplace [2] now took the matter in hand. He tried the effect of a
non-instantaneous action of gravity, to no purpose. But in 1787 he
gave the true explanation. The principal effect of the sun on the
moon’s orbit is to diminish the earth’s influence, thus lengthening
the period to a new value generally taken as constant. But Laplace’s
calculations showed the new value to depend upon the excentricity of
the earth’s orbit, which, according; to theory, has a periodical
variation of enormous period, and has been continually diminishing for
thousands of years. Thus the solar influence has been diminishing, and
the moon’s mean motion increased. Laplace computed the amount at 10″
in one century, agreeing with observation. (Later on Adams showed that
Laplace’s calculation was wrong, and that the value he found was too
large; so, part of the acceleration is now attributed by some
astronomers to a lengthening of the day by tidal friction.)

Another contribution by Halley to the verification of Newton’s law was
made when he went to St. Helena to catalogue the southern stars. He
measured the change in length of the second’s pendulum in different
latitudes due to the changes in gravity foretold by Newton.

Furthermore, he discovered the long inequality of Jupiter and Saturn,
whose period is 929 years. For an investigation of this also the
Academy of Sciences offered their prize. This led Euler to write a
valuable essay disclosing a new method of computing perturbations,
called the instantaneous ellipse with variable elements. The method
was much developed by Lagrange.

But again it was Laplace who solved the problem of the inequalities of
Jupiter and Saturn by the theory of gravitation, reducing the errors
of the tables from 20′ down to 12″, thus abolishing the use of
empirical corrections to the planetary tables, and providing another
glorious triumph for the law of gravitation. As Laplace justly said:
“These inequalities appeared formerly to be inexplicable by the law of
gravitation–they now form one of its most striking proofs.”

Let us take one more discovery of Halley, furnishing directly a new
triumph for the theory. He noticed that Newton ascribed parabolic
orbits to the comets which he studied, so that they come from
infinity, sweep round the sun, and go off to infinity for ever, after
having been visible a few weeks or months. He collected all the
reliable observations of comets he could find, to the number of
twenty-four, and computed their parabolic orbits by the rules laid
down by Newton. His object was to find out if any of them really
travelled in elongated ellipses, practically undistinguishable, in the
visible part of their paths, from parabolae, in which case they would
be seen more than once. He found two old comets whose orbits, in shape
and position, resembled the orbit of a comet observed by himself in
1682. Apian observed one in 1531; Kepler the other in 1607. The
intervals between these appearances is seventy-five or seventy-six
years. He then examined and found old records of similar appearance in
1456, 1380, and 1305. It is true, he noticed, that the intervals
varied by a year and a-half, and the inclination of the orbit to the
ecliptic diminished with successive apparitions. But he knew from
previous calculations that this might easily be due to planetary
perturbations. Finally, he arrived at the conclusion that all of these
comets were identical, travelling in an ellipse so elongated that the
part where the comet was seen seemed to be part of a parabolic
orbit. He then predicted its return at the end of 1758 or beginning of
1759, when he should be dead; but, as he said, “if it should return,
according to our prediction, about the year 1758, impartial posterity
will not refuse to acknowledge that this was first discovered by an
Englishman.”[3] [_Synopsis Astronomiae Cometicae_, 1749.]

Once again Halley’s suggestion became an inspiration for the
mathematical astronomer. Clairaut, assisted by Lalande, found that
Saturn would retard the comet 100 days, Jupiter 518 days, and
predicted its return to perihelion on April 13th, 1759. In his
communication to the French Academy, he said that a comet travelling
into such distant regions might be exposed to the influence of forces
totally unknown, and “even of some planet too far removed from the sun
to be ever perceived.”

The excitement of astronomers towards the end of 1758 became intense;
and the honour of first catching sight of the traveller fell to an
amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached
perihelion on March 13th, 1759.

This fact was a startling confirmation of the Newtonian theory,
because it was a new kind of calculation of perturbations, and also it
added a new member to the solar system, and gave a prospect of adding
many more.

When Halley’s comet reappeared in 1835, Pontecoulant’s computations
for the date of perihelion passage were very exact, and afterwards he
showed that, with more exact values of the masses of Jupiter and
Saturn, his prediction was correct within two days, after an invisible
voyage of seventy-five years!

Hind afterwards searched out many old appearances of this comet, going
back to 11 B.C., and most of these have been identified as being
really Halley’s comet by the calculations of Cowell and Cromellin[4]
(of Greenwich Observatory), who have also predicted its next
perihelion passage for April 8th to 16th, 1910, and have traced back
its history still farther, to 240 B.C.

Already, in November, 1907, the Astronomer Royal was trying to catch
it by the aid of photography.

FOOTNOTES:

[1] Born 1736; died 1813.

[2] Born 1749; died 1827.

[3] This sentence does not appear in the original memoir communicated
to the Royal Society, but was first published in a posthumous reprint.

[4] _R. A. S. Monthly Notices_, 1907-8