66 ISAAC NEWTON
It also shows that the
acceleration depends on the mass
of a body.
For a given force, a body with a
small mass will accelerate faster
than one with a larger mass.
The Third Law is stated as
“For every action there is an equal
and opposite reaction.” It means
that all forces exist in pairs: if
one object exerts a force on a
second object, then the second
object simultaneously exerts a force
on the first object, and both forces
are equal and opposite. In spite of
the term “action,” movement is not
required for this to be true. This
is linked to Newton’s ideas about
gravity, since one example of his
Third Law is the gravitational
attraction between bodies. Not
only is Earth pulling on the Moon,
but the Moon is pulling on Earth
with the same force.
Universal attraction
Newton started thinking about
gravity in the late 1660s, when he
retired to the village of Woolsthorpe
for a couple of years to avoid
the plague that was ravaging
Cambridge. At that time, several
people had suggested that there
was an attractive force from the
Sun, and that the size of this force
was inversely proportional to the
square of the distance. In other
words, if the distance between
the Sun and another body is
doubled, the force between them
is only one quarter of the original
force. However, it was not thought
that this rule could be applied
close to the surface of a largeI have not been able to
discover the cause of these
properties of gravity from
phenomena, and I frame
no hypotheses.
Isaac Newtonbody such as Earth.
Newton, seeing an apple fall from a
tree, reasoned that Earth must be
attracting the apple and, since the
apple always fell perpendicular to
the ground, its direction of fall was
directed to the center of Earth. So
the attractive force between Earth
and the apple must act as if it
originated in the center of Earth.
These ideas opened the way to
treating the Sun and planets as
small points with large masses,
which made calculations much
easier by measuring from their
centers. Newton saw no reason
to think that the force that made
an apple fall was any different from
the forces that kept the planets in
their orbits. Gravity, then, was a
universal force.
If Newton’s theory of gravity is
applied to falling bodies, M 1 is the
mass of Earth and M 2 is the mass
of the falling object. So the greater
the mass of an object, the greater
the force pulling it downward.
However, Newton’s Second Law
tells us that a larger mass does not
accelerate as quickly as a smaller
one if the force is the same. So
the greater force is needed to
accelerate the greater mass, and all
objects fall at the same speed, as
long as there are no other forces
such as air resistance to complicate
matters. With no air resistance, a
hammer and a feather will fall at
the same speed—a fact finally
demonstrated in 1971 by astronaut
Dave Scott, who carried out the
experiment on the surface of the
Moon during the Apollo 15 mission.
Newton described a thought
experiment to explain orbits in
an early draft of the Philosophiae
Naturalis Principia Mathematica.
He imagined a cannon on a very
high mountain, firing cannon balls
horizontally at higher and higher
speeds. The higher the speed atNewton’s Law of Gravity produces the equation below,
which 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
two masses (F).The masses of the
two bodies (M).The distance
between them (r).F =
GM 1 M 2
r^2
The gravitational
constant (G).