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Keplers

Laws of Planetary Motion

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Contents

Biography of Johannes KeplerKeplers Laws of Planetary MotionData proving Keplers 3rd Law

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Objectives:State Keplers Laws of Planetary

Motion

Identify the importance of motion

of the planetsKeplers achievements on the solar

system and planetary orbits

Draw the solar system, showingthe position of the different planetsand the shape of the planets orbits.

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History: Explanations of Planetary

Motion

Aristotle, Plato (4th century BCE)

natural places for things, with Earth at center of

Universe.

could not account for retrograde motion of planets asseen from Earth

Ptolemy (Alexandria, 100-200 CE)

geocentric epicycles (circles on circles) for motions ofeverything

Alamagest held sway for 1400 years, modeled

retrograde motion

no dynamics, just a numerical fit

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Copernicus (Polish monk) 1543deathbed publication

heliocentric picture, still with epicyclesto gain accuracy, no dynamics

Tycho Brahe, (1546-1601) Danishobserver, nobleman, duelist,philanderer,

built greatest observatory (1570-97, notelescopes yet)

wrong theory: planets revolve around Sun,but Sun revolves around Earth

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Johannes Kepler (B. 1571 - 1630)

German mathematician and astrologer

planetary orbits fit the 5 nested regular(perfect) solids (1596) proving that there

can be only 6 planets (mysticism, wrong!)

works with Tycho (1600-27), inherits hisdata, develops radical 3 laws of planetary

motion, improves prediction accuracy 100-

fold

derived and generalized Keplers 3 lawsfrom his own theoretical work

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Galileo Galilei (Italy, 1564-1632) Radical

approach: do experiments & use math

dynamics pioneer ag same for all masses kinematics + inertia (Newtons first law)

invented the telescope, discovered the moons

of Jupiter Copernican, persecuted by the Church

Isaac Newton (B. 1632) published the Principia

(1687)

invented calculus, dynamics (laws of motion),

law of gravitation

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Johannes Kepler (1571-1630)

1571/12/271630/11/15

German astronomer

Believer in Heliocentrism mathematics teacher assistant

to Tycho Brahe

Kepler was appointed to be

Brahes successor

Famous of his laws of

planetary motion

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Keplers achievements Keplers Laws of

Planetary Motion

Cosmographicum (Sacred

Mystery of the Cosmos)

His first book to support

Copernicus

Harmony of the World

Including the proofs of

Keplers 3rdLaw

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Relations with Newtons Laws of Motion

Newton combine the law ofuniversal gravitation withcircular motion

Keplers Law of HarmoniesSame as Keplers 3rd Lawk = 2.97 x 10-19 s2/m3 =(T2)/(R3)

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Keplers 1stLaw

The orbit of every planet is an ellipse

with the sun at one of the foci.

Law of Ellipses

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Keplers 2ndLaw

A line joining a planet and the sun sweeps out

equal areas during equal intervals of time.

Law of Areas

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Keplers 3rdLaw The squares of the orbital periods of planets

are directly proportional to the cubes of thesemi-major axis of the orbits. or the revolution

of a planet is proportional to the 3/2

Law of Periods

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T2 = 4 2 x R3

GMT2 = k R3

T = kR3/2

Where:T = period

M = mass of the central body

R = orbital radiusG = gravitational constant

= pi

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Data proving Keplers 3rdLaw

Planet t (yr) r (AU) t^2 r^3 RatioMercury 0.241 0.387 0.058 0.058 1:1

Venus 0.615 0.723 0.378 0.378 1:1

Earth 1 1 1 1 1:1

Mars 1.881 1.524 3.538 3.54 1:1

Jupiter 11.862 5.203 140.707 140.852 1:1

Saturn 29.448 9.537 867.185 867.432 1:1

Uranus 84.07 19.191 7067.765 7067.939 1:1

Neptune 164.878 30.069 27184.755 27186.729 1:1

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How is Newtons Law of

Universal Gravitation related

to Keplers Law of PlanetaryMotion

NEWTON SHOWED THAT GRAVITATION HOLDSTHE COSMOS TOGETHER

- DERIVED KEPLERS LAWS FROM HIS LAW OF

GRAVITATION -

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Benefits of understanding Astronomy

Know more about the basics of the

solar system

Learn how the orbits affecting

Earth

Provide evidences leading to

another space phenomenon

Physics Calculate the velocity and gravity

between planets

Understand Newtons Laws

http://en.wikipedia.org/wiki/Image:GodfreyKneller-IsaacNewton-1689.jpghttp://upload.wikimedia.org/wikipedia/commons/9/97/The_Earth_seen_from_Apollo_17.jpg

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The EndThank you for watching!