Physics 53
Gravity
Nature and Nature's law lay hid in night:
God said, "Let Newton be!" and all was light.
— Alexander Pope
Kepler’s laws
Explanations of the motion of the celestial bodies — sun, moon, planets and stars — are
among the oldest scientiFc theories. The apparent rotation of these bodies around the
earth every day was attributed by the ancients to their place in "celestial spheres" which
revolved daily around the stationary earth, assumed to be at the center of the universe.
The wandering of the planets against the background of stars presented a challenge to
this earth-centered (“geocentric”) model. Their peculiar motions were explained in
terms of smaller spheres rolling on larger ones. As observations became more accurate
these explanations became more intricately complicated.
The sun-centered (“heliocentric”) model of Copernicus (about 1540) was simpler, but it
made the earth merely one of the planets orbiting the sun. This provoked outrage, since
it challenged the central importance of
homo sapiens
in the universe.
In the late 1500’s the Danish astronomer Tycho Brahe carried out a careful and
systematic set of observations of the night sky, especially of the motions of the planets.
His assistant Johannes Kepler inherited the voluminous data he had accumulated;
Kepler subjected them to careful numerical analysis, and in the early years of the next
century he was able to discern in the data three regularities:
Kepler’s laws of planetary motion
1.
The orbits of planets are ellipses, with
the sun at one focus.
2.
As the planet moves, the line from the
sun to a planet sweeps out equal areas
in equal times.
3.
The ratio
T
2
/
a
3
is the same for all
planets, where
T
is the period and
a
is
the semi-major axis of the orbit.
PHY 53
1
Gravity

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*How to explain these three laws (the "Kepler problem") was a major concern of the
scientists of the 17th century, among whom was Isaac Newton.
Universal gravitation
Newton's analysis of gravity was partly motivated by the Kepler problem, but more by
the idea that the moon in its orbit is continually “falling” toward the earth, much as
objects near the surface of the earth — including the famous apple? — fall to the
ground. He proposed that the solution to both problems lay in a universal law:
Law of universal gravitation
Every pair of point masses
m
1
and
m
2
attract with a force given by
F
=
G
m
1
m
2
r
2
,
where
r
is the distance between the masses
and
G
is a universal constant.
Because of its simplicity, elegance and its universality — note that it applies to
every
pair
of point masses in the universe — this has served over the centuries as a model for what
a general law of nature ought to be like.
The value of

This is the end of the preview.
Sign up
to
access the rest of the document.