12 AUSTRALIAN SKY & TELESCOPE May | June 2017
DISCOVERIES by David Ellyard
Newton, Halley and the universe
A scientific masterpiece would have remained unpublished if not for a colleague’s encouragement.
AT A MEETING ON JUNE 2, 1686,
the Royal Society in London made a
profound decision. It decided to arrange
for the publication of a new book by one
its leading members, Isaac Newton. Its
Latin title when translated into English
was to be the Mathematical Principles
of Natural Philosophy. According to the
minutes of the meeting, the astronomer
Edmond Halley was to “undertake the
business of looking after it and printing
it at his own charge”.
The Principia, as it is more
conveniently called, is arguably the
most powerful and profound product
yet of human intelligence. Drawing
together in one system the physics of
the Earth and the cosmos, it is the
supreme expression of the ‘mechanistic’
view of the world — nature like a
machine, both reliable and intelligible.
But the Principia may never have
been written but for the intervention
of Halley, later best known for ‘his’
comet but in fact one of the most
versatile scientists of his time. In
August 1684, Halley visited Professor
Newton at Cambridge to discuss a
nagging problem; what is the nature of
the law that defines the strength of the
gravitational attraction between, say,
the Earth and the Sun, or the Sun and
the Moon? Most people believed that
the force of ‘gravity’ depended on the
distance between the two objects, and
many argued the relationship followed
an ‘inverse square’ rule. Halve the
separation and the attraction increased
four-fold; double it and the attraction
fell to a quarter of its original value.
There was another issue. Johannes
Kepler had shown in 1609 that the
planets moved in elliptical orbits
around the Sun. Did these two things
go together? Did an inverse square law
decree elliptical orbits, and vice versa?
Halley and others suspected so, but did
not have the mathematical skills toprove it. Newton did, and in fact had,
nearly 20 years before. He promised to
show Halley the calculations.
Halley wanted more. He urged
Newton to write down all that he
knew about the problem to show the
Royal Society, and then for publication.
Reluctant at first, Newton set to work
with increasing intensity. Halley kept
him at it, encouraging him, checking
the proofs and ultimately paying for
the printing. When the grand synthesis
appeared in 1687, after 18 months of
prodigious effort, it was Newton’s work
but also Halley’s achievement.The Principia is tough reading. Even
when translated from the original Latin,
the prose is dense and long-winded, the
geometrical arguments complex, the
diagrams daunting. Yet it is a triumph, a
treasure house of wondrous insights, as
Newton strove to apply the burgeoning
power of mathematics to what we now
call ‘physics’.
Much of the early pages of the
book are concerned with the laws of
motion, but astronomers were most
taken with the third section, which
Newton called ‘The System of the
World’. It was an audacious title.Newton planned to show not only
how the larger cosmos moved but
why. His explanation involved a new
understanding of gravity, which he
saw as a force of attraction between all
objects everywhere. That insight unites
the fall of an apple to the ground with
the progress of the distant planets.
As Newton laid it out, the pull of
gravity depended firstly on the amount
of ‘stuff’ in objects. The more massive
a pair of objects, the more fiercely they
tugged at one another. A large and
a small object attracted each other
equally, but the larger object resisted
more and moved less. The Sun’s vast
mass allowed it to hold its place at
the centre and require the Earth and
the other planets to go round it. So
Nicholas Copernicus was vindicated.
The other factor was distance. As
many before him had suspected, gravity
followed an ‘inverse square’ law. In a
striking result, Newton showed that
only mass and separation mattered,
not size. Symmetrical objects, however
vast, behaved as if all their mass was
concentrated at a single point at the
heart of each.
Thus empowered, Newton could
prove that celestial objects moving
freely under the attraction of the Sun
traced explicable paths; ellipses if the
orbits were closed, parabolas if the
ends did not meet. The planets, moons
and comets held their courses because
gravity exactly balanced their tendency
to fly onward in a straight line, and so
pulled them into predictable orbits.
Universal gravity explained in detail
much else; the ocean tides raised by the
pulls of Sun and Moon, the shape of the
Earth, the Moon’s complex motions, the
precession of the equinoxes. All these
and more were elements of ‘The System
of the World’. On one point only did
Newton admit ignorance. He could not
explain gravity itself. That simply was.Isaac Newton laboured
to produce a theory of gravity.