The Astronomy Book

70

system. This breakthrough
intrigued Halley so much that he
went on to calculate the orbits of
24 other comets, and to prove that
one comet (Halley’s comet) returned
to the sun around every 76 years.
Perhaps more importantly, Halley
was so impressed by Newton’s
work that he strongly encouraged
him to publish his findings. This
resulted in the book Philosophiae
Naturalis Principia Mathematica,
published in Latin on July 5, 1687,
in which Newton describes his
laws of motion, his gravitational
theory, the proof of Kepler’s three
laws, and the method he used to
calculate a comet’s orbit.

In his book, Newton stressed that

his law was universal—gravity

affects everything in the universe,

regardless of distance. It explained

how an apple fell on his head in the

orchard of Woolsthorpe where his

mother lived, the tides in the seas,

the moon orbiting Earth, Jupiter

orbiting the sun, and even the

elliptical orbit of a comet. The

physical law that made the apple

fall in his yard was exactly the

same as the one that shaped the

solar system, and would later be

discovered at work between stars

and distant galaxies. Evidence

was all around that Newton’s law

of gravitation worked. It not only

explained where planets had been,

but also made it possible to predict

where they would go in the future.

Constant of proportionality

Newton’s law of gravitation states

that the size of the gravitational

force is proportional to the masses

of the two bodies (m 1 and m 2 )

multiplied together and divided

by the square of the distance, r,

between them (see left). It always

draws masses together and acts

along a straight line between them. If

the object in question is spherically

symmetrical, like Earth, then its

gravitational pull can be treated as

if it were coming from a point at its

GRAVITATIONAL THEORY

center. One final value is needed

to calculate the force—the constant

of proportionality, a number that

gives the strength of the force:

the gravitational constant (G).

Measuring G

Gravity is a weak force, and this

means that the gravitational

constant is rather difficult to

measure accurately. The first

laboratory test of Newton’s theory

was made by the English aristocrat

scientist Henry Cavendish in 1798,

71 years after Newton’s death. He

copied an experimental system

proposed by the geophysicist John

Michell and successfully measured

the gravitational force between

two lead balls, of diameters 2 and

Newton’s law of universal
gravitation shows how the force
produced depends on the mass of
the two objects and the square
of the distance between them.

The force
of attraction
between the
bodies (F)

The masses of

the two bodies

(m 1 and m 2 )

The distance between

the bodies (r)

F =

Gm 1 m 2

r^2

The gravitational
constant (G)

Gravity explains

the motions of the

planets, but does not

explain what sets

them in motion.

This force is

universal and applies

to all bodies with

mass at all distances.

The planets’ elliptical orbits are explained

by an attractive force that reduces at a rate of

the square of the distance between objects.

Nature and Nature’s

laws lay hid in night:

God said, “Let Newton

be!” and all was light.

Alexander Pope