71
12 in (5.1 and 30 cm) (see above).
Many have tried to refine and
repeat the experiment since. This
has led to a slow improvement in
the accuracy of G. Some scientists
suggested that G changed with
time. However, recent analysis of
type 1a supernovae has shown that,
over the last nine billion years, G
has changed by less than one part
in 10 billion, if at all. The light from
distant supernovae was emitted
nine billion years ago, allowing
scientists to study the laws of physics
as they were in the distant past.
Seeking meaning
Like many of the scientists of his
time, Newton was deeply pious
and sought a religious meaning
behind his observations and laws.
The solar system was not regarded
as a random collection of planets,
and the sizes of the specific orbits
were thought to have some specific
meaning. For example, Kepler had
sought meaning with his notion
of “the music of the spheres.”
Building on ideas first put forward
by Pythagoras and Ptolemy, Kepler
suggested that each planet was
responsible for an inaudible
musical note that had a frequency
proportional to the velocity of the
planet along its orbit. The slower
a planet moved, the lower the
note that it emitted. The difference
between the notes produced by
adjacent planets turned out to be
well-known musical intervals such
as major thirds.
There is some scientific merit
behind Kepler’s idea. The solar
system is about 4.6 billion years
old. During its lifetime, the planets
and their satellites have exerted
gravitational influences on eachTHE TELESCOPE REVOLUTION
other and have fallen into resonant
intervals, similar to the way musical
notes resonate. Looking at three of
the moons of Jupiter, for every once
that Ganymede orbits the planet,
Europa goes around twice and Io
four times. Over time, they have
been gravitationally locked into
this resonance.The three-body problem
The solar system as a whole
has fallen into similar resonant
proportions to Jupiter’s moons.
On average, each planet has an
orbit that is about 73 percent larger
than the planet immediately closer
to the sun. Here, however, there
appears a difficult mathematical
problem, and one that Newton had
grappled with. The movement of a
low-mass body under the gravitational
influence of a large-mass body can
be understood, and predicted. But
when three bodies are involved,
the mathematical problem becomes
exceedingly difficult. ❯❯Distant supernovae are seen today
as they were billions of years ago.
Analysis of their structure shows that
the law of gravity operated with the
same value of G then as today.Henry Cavendish measured the gravitational constant using a torsion balance. Two
large balls (M) were fixed in place, while two smaller balls (m) were attached at either end
of a wooden arm suspended from a wire. The gravitational attraction (F) of the small balls
to the large ones caused the balance to rotate slightly, twisting the wire. The rotation
stopped when the gravitational force equaled the torque (twisting force) of the wire.
Knowing the torque for a given angle made it possible to measure the gravitational force.
M
F
F
M
m
m
Large ball Small ballWire twists