Download Fox on Newton`s Law of Universal Gravitation

Newton’s law of universal
gravitation
Liz Fox
2-16-06
A little review…
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Law 1: The orbit of a planet/comet about the Sun
is an ellipse with the Sun's center of mass at one
focus.
Law 2: A line joining a planet/comet and the Sun
sweeps out equal areas in equal intervals of
time
Law 3: The ratio of the squares of the
revolutionary periods for two planets is equal to
the ratio of the cubes of their semimajor axes
http://www.edumedia.fr/m185_l2-newton-laws.html
Some background
Copernicus- De revolutionibus orbium
coelestium – 1543
 Kepler- Astronimia Nova – 1609
 Galileo- Sedereus Nuncius - 1610
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Newton’s Principia
Mathematical Principles of Natural
Philosophy
 Published in 1687
 Uses Kepler’s Laws to prove elliptical
orbits
 Explains behavior of tides, precession of
the equinoxes, and the irregularities in the
moon’s orbit

Newton’s Astronomical Data and
Deductions
The planets orbiting Jupiter (Saturn)
describe areas proportional to the times of
descriptions; and their periodic times are
as the 3/2th power of their distances from
its center.
 The periodic times of the five primary
planets are as the 3/2th power of their
mean distances from the sun.
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“The nature of the forces”
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The forces by which the primary planets
are continually drawn off from rectilinear
motions, and retained in their proper
orbits, tend to the sun; and are inversely
as the squares of the distances of the
places of those planets from the sun’s
center.
An Inverse-Square Law
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Centripetal vs. centrifugal
Huygens- Horologium Oscillatorium (On Pendulum
Clocks) - 1673
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When 2 identical bodies move with the same
velocity on unequal circumferences, their
[centripetal] forces are in the inverse proportion
to their diameters
When identical bodies move on unequal
circumferences with unequal velocities the
[centripetal] force of the faster is to that of the
slower as the square of their velocities
Newton’s take
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The centripetal forces of bodies tend to the
centers of the same circles; and are to
each other as the squares of the arcs
described in equal times divided
respectively by the radii of the circles.
The Moon’s Centripetal
Acceleration
The moon gravitates towards the earth,
and by the force of gravity is continually
drawn off from a rectilinear motion, and
retained in its orbit.
 It is solely the gravity of the earth that
keeps the moon in orbit.
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The Law of Gravitation for Point
Masses
Law of universal gravitation- there is a
power of gravity pertaining to all bodies,
proportional to the several quantities of
matter which they contain.
 Henry Cavendish (1731-1810)
 Hypotheses non fingo
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Gravitation for Extended Bodies
Inside a homogeneous hollow spherical
shell, a point mass experiences no net
gravitational force
 Next, if a point mass is placed outside the
shell, it is attracted to the exact center as if
all of its mass were concentrated at a point
 Same for solid sphere of uniform density
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Teachers' Domain: String Theory: Newton's
Embarrassing Secret
Inertial and Gravitational Masses
Inertial vs. Gravitational mass
 Inertial mass vs. weight – “The mass is
known by the weight of each body, for it is
proportional to the weight, as I have found
by experiments on pendulums.”
 Kepler’s 3rd Law
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A Final Thought
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“Nature and nature’s laws lay hid in night;
God said ‘Let Newton be!’ and all was
light.”