Newton

1
Newtons law of universal gravitation

• Liz Fox
• 2-16-06

2
A little review

• 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
3
Some background

• Copernicus- De revolutionibus orbium coelestium
  1543
• Kepler- Astronimia Nova 1609
• Galileo- Sedereus Nuncius - 1610

4
Newtons Principia

• Mathematical Principles of Natural Philosophy
• Published in 1687
• Uses Keplers Laws to prove elliptical orbits
• Explains behavior of tides, precession of the
  equinoxes, and the irregularities in the moons
  orbit

5
Newtons 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.

6
The nature of the forces

• 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
  suns center.

7
An Inverse-Square Law

• Centripetal vs. centrifugal
• Huygens- Horologium Oscillatorium (On Pendulum
  Clocks) - 1673

• 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

8
Newtons take

• 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.

9
The Moons 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.

10
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

11
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

Teachers' Domain String Theory Newton's
Embarrassing Secret
12
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.
• Keplers 3rd Law

13
A Final Thought

• Nature and natures laws lay hid in night God
  said Let Newton be! and all was light.