34.5 lsaac Newton and the Law of Gravity Isaac Newton was born
in
5
1642, the same year Galileo died. Newton
became a brilliant scientist and mathematician. His greatest discovery
m
lnspiration for new ideas and discov-
was the law of gravity.
th
eries often comes when the ordinary
In later life, Newton told a story about his discovery. He was trying to figure out what kept the moon traveling in its orbit around Earth. Since the moon was in motion, why didn't it fly off into space in a straight line? Then Newton saw an apple fall from a tree. He wondered if the same force that pulled the apple to the ground was tugging on the moon. The difference was that the moon was far away, and Newton reasoned that the force was weaker there. It was just strong enough
is seen in a new way. lsaac Newton gained insight into the laws of nature
after observing an apple fall to the ground.
to bend the moon's motion into
a
mr
plt be de
lot sai
tol
uni
nearly circular path around Earth. This was Newton's great insight. A single force explained a
falling apple on Earth and the
tim vati
movements of heavenly bodies
well. Newton called this force gravity. as
Newton stated the law of gravity in a simple formula. All physical objects, he said, had a force of attraction between them. The strength of the force depend-
amount of matter in
an object
2.'
I J.
t
4. 1
rl
worl
the ground.
sam€
5.
ir
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and
(Principles). The book presented the law of gravity. It also described three laws of motion. Newton's laws provided a physical explanation for what earlier scientists had discovered. For example, others had
that I
Newton's laws dramatically changed people's picture of the universe. Many people began to see the universe as a beautifully designed machine. Some compared it to a well-built clock. The same mathematical laws applied everywhere. All people had to do was discover them.
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a tou
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In thi In
planets traveling around the sun.
Chapter 34
1
1687, Newton published a book known as the Principia
In
shown that the planets moved around the sun. Newton's laws explained why. Just as gravity kept the moon traveling around Earth, it kept the
394
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masses of the objects and the distance between them. For example, the moon and Earth tugged on each other. At a certain point in space, these "tugs" canceled each other out. The result was that the moon was trapped in its orbit around Earth. In contrast, an apple had a small mass and was very close to Earth, so gravity dragged it to ed on the
Then Newton saw an apple fall from a tree. He wondered. if the same force that pulled the apple to the ground was tugging on the. moon. The difference was that ...
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ABSTRACT. A formula of Matsuo Oka [9] expresses the Milnor number of a germ of a complex analytic map with a generic principal part in terms of the Newton polyhedra of the components of the map. In this paper this formula is generalized to the case o
a description of the Newton polyhedra of a multidimensional resultant, generalizing results in [2] and [3]. In order to state the result, we need to define a 'relative' ...
Indeed, by definition, the Newton polyhedron of a germ. â aâZm caxa ..... Theorem 1.19. If Bi,j, i = 1,...,n, j = 1,...,k, are bounded integer polyhedra or bounded.
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