Universal Gravitation and Keplers Laws

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Universal Gravitation and Keplers Laws

• How do the all the objects in the solar system
  move?

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Newtons Law of Universal Gravitation Applies to
Everything!

• F G m1 m2 / d2
• If one of the masses doubles the force doubles
• If the distance doubles the force decreases to
  1/4

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What does the gravitational force look like as a
function of distance?
Different curves correspond to different
masses The force increases rapidly as you get
closer
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Keplers Laws

• How can we describe how all the objects in the
  solar system move?

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Johannes Kepler

• 1571-1630
• Made many observations of the motions Mars
• Supported Galileo
• Kepler didnt know why his Laws workeda law
  summarizes observations

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Drawing an ellipse

• The black line is a piece of string
• The thumb tacks are the foci of the ellipse

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Keplers First Law

• All objects travel in elliptical orbits about the
  sun
• The sun is at one foci of the ellipse
• e is the eccentricity of the ellipse (how oval it
  is)

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Orbits in the Solar System

• Most of the planets have nearly circular orbits
• Icarus, an asteroid, has a very elliptical orbit
• Comets have the most elliptical orbits

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Halleys comet
Motion is way out of the ecliptic plane Rotates
in opposite direction (retrograde motion) Planets
are not scaled to size
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An edge on view of the solar system
Clearly Pluto and Halleys comet have orbits
tipped way Out of the plane of the orbits of the
rest of the planets!
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Keplers Second Law

• The planets sweep out equal areas in equal times
• The planets move faster on the side of the orbit
  closer to the sun

http//images.google.com/imgres?imgurlhttp//onli
ne.physics.uiuc.edu/courses/phys150/fall03/links/s
mall_images/kepler_smc.gifimgrefurlhttp//online
.physics.uiuc.edu/courses/phys150/fall03/links/lin
ks.htmlh107w150sz10tbnid1IUln7RdqYDvxMtb
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Keplers Third Law
 

• The tighter your orbit around the sun, the faster
  you go
• The square of the period of the rotation is
  proportional to the cube of the semi-major axis
  of the ellipse

http//www.ac.wwu.edu/stephan/ Astronomy/planets.
html

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Keplers Third Law
Asteroid
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Does Keplers 3rd Law Work?

• Astronomical unit A.u. average distance
  between the earth and the sun
• 1 year period of Earths orbit
• T2 CR3 if T is in years and R is in A.u. (C 1
  year2/au3)

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Does Keplers 3rd Law Work? T2 CR3
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So What?

• Kepler didnt know why his laws worked! Remember
  a law just describes a relationship, it doesnt
  tell you why.
• Newton was able to show that he could derive
  Keplers Laws from Newtons three laws and the
  Theory of Universal Gravitation

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Asteroid Belt
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Meet Asteroid Ida
http//news.nationalgeographic.com/kids/2003/12/im
ages/asteroid-big.jpg
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Asteroid Eros
http//images.google.com/imgres?imgurlhttp//scie
nce.nasa.gov/headlines/images/eros/orbits.gifimgr
efurlhttp//science.nasa.gov/headlines/y2000/ast2
1jun_1_ada.htmh312w342sz11tbnidtPr0eo5LZuy
rJMtbnh104tbnw115hlenstart54prev/images
3Fq3Dasteroid26start3D4026svnum3D1026hl3De
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Comet Hyakutake
http//www.astronomy.com/asy/objects/images/asy-20
010724-01335-orig-lg.jpg
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Anatomy of a Comet
http//www22.homepage.villanova.edu/rex.saffer/Obs
night/comets.html
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When Comets Get Near Planets
http//www22.homepage.villanova.edu/rex.saffer/Obs
night/comets.html
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Pieces of Comet Shoemaker-Levy Collide with
Jupiter
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When Comets Get Near Planets
Earth-sized spot On Jupiter Caused by a Piece of
the Shoemaker-Levy comet
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Meet a Comet

• Images of Comet Tempel 1
• ½ the size of Manhattan
• Ice detected by NASA Deep Impact Mission

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Crashing into a CometImages 0.84 s apart during
impact
http//deepimpact.jpl.nasa.gov/gallery/T1_Ejecta_D
evel.html