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Newtons law of universal

gravitationLiz Fox

2-16-06

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A little review

Law 1: The orbit of a planet/comet about the Sunis an ellipse with the Sun's center of mass at onefocus.

Law 2: A line joining a planet/comet and the Sunsweeps out equal areas in equal intervals oftime

Law 3: The ratio of the squares of therevolutionary periods for two planets is equal tothe ratio of the cubes of their semimajor axes

http://www.edumedia.fr/m185_l2-newton-laws.html

http://www.edumedia.fr/m185_l2-newton-laws.htmlhttp://www.edumedia.fr/m185_l2-newton-laws.htmlhttp://www.edumedia.fr/m185_l2-newton-laws.htmlhttp://www.edumedia.fr/m185_l2-newton-laws.htmlhttp://www.edumedia.fr/m185_l2-newton-laws.htmlhttp://www.edumedia.fr/m185_l2-newton-laws.html

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Some background

Copernicus- De revolutionibus orbiumcoelestium 1543

Kepler- Astronimia Nova 1609

Galileo- Sedereus Nuncius - 1610

http://en.wikipedia.org/wiki/De_revolutionibus_orbium_coelestiumhttp://en.wikipedia.org/wiki/De_revolutionibus_orbium_coelestiumhttp://en.wikipedia.org/wiki/De_revolutionibus_orbium_coelestiumhttp://en.wikipedia.org/wiki/De_revolutionibus_orbium_coelestium

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Newtons Principia

Mathematical Principles of NaturalPhilosophy

Published in 1687

Uses Keplers Laws to prove elliptical

orbits

Explains behavior of tides, precession ofthe equinoxes, and the irregularities in themoons orbit

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Newtons Astronomical Data and

Deductions

The planets orbiting Jupiter (Saturn)describe areas proportional to the times ofdescriptions; and their periodic times are

as the 3/2th power of their distances fromits center.

The periodic times of the five primary

planets are as the 3/2th power of theirmean distances from the sun.

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The nature of the forces

The forces by which the primary planetsare continually drawn off from rectilinearmotions, and retained in their proper

orbits, tend to the sun; and are inverselyas the squares of the distances of theplaces of those planets from the suns

center.

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An Inverse-Square Law

Centripetal vs. centrifugal

Huygens- Horologium Oscillatorium (On PendulumClocks) - 1673

When 2 identical bodies move with the samevelocity on unequal circumferences, their[centripetal] forces are in the inverse proportionto their diameters

When identical bodies move on unequalcircumferences with unequal velocities the[centripetal] force of the faster is to that of theslower as the square of their velocities

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Newtons take

The centripetal forces of bodies tend to thecenters of the same circles; and are toeach other as the squares of the arcs

described in equal times dividedrespectively by the radii of the circles.

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The Moons Centripetal

Acceleration

The moon gravitates towards the earth,and by the force of gravity is continuallydrawn off from a rectilinear motion, and

retained in its orbit.

It is solely the gravity of the earth thatkeeps the moon in orbit.

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The Law of Gravitation for PointMasses

Law of universal gravitation- there is apower 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 sphericalshell, a point mass experiences no netgravitational force

Next, if a point mass is placed outside theshell, it is attracted to the exact center as ifall of its mass were concentrated at a point

Same for solid sphere of uniform density

Teachers' Domain: String Theory: Newton'sEmbarrassing Secret

http://www.teachersdomain.org/9-12/sci/phys/mfw/newtonsecret/index.htmlhttp://www.teachersdomain.org/9-12/sci/phys/mfw/newtonsecret/index.htmlhttp://www.teachersdomain.org/9-12/sci/phys/mfw/newtonsecret/index.htmlhttp://www.teachersdomain.org/9-12/sci/phys/mfw/newtonsecret/index.html

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Inertial and Gravitational Masses

Inertial vs. Gravitational mass

Inertial mass vs. weightThe mass isknown by the weight of each body, for it isproportional to the weight, as I have foundby experiments on pendulums.

Keplers 3rd Law

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A Final Thought

Nature and natures laws lay hid in night;

God said Let Newton be! and all was

light.