Opening for today

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Opening for today
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Keplers Laws of Planetary Motion

• Objective Students will explain planetary
  motion using gravitational laws.

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Background

• What is Planetary Motion?
• What makes up planetary motion?
• 365 days refers to?
• 24 hours refers to?

• Refers to how planets, like the Earth, move
  through space.
• All planets orbit a central star, this orbit is
  called its revolution.
• The Earths period (time duration) for 1orbit, or
  revolution, around the Sun.
• The period for 1 rotation of the Earth.

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Kepler the Man
Who is Johannes Kepler? What did he
discover? His 3 Laws of Planetary Motion
German theological student, mathematician,
science fiction writer. Using mentors
observations, and own study of Mars, discovers
elliptical orbits. Law 1 Planets move in an
elliptical orbit Law 2 Planets move faster when
they are closer to the Sun, slower when farther
away. Law 3 Period2 semimajor axis 3 (Period -
the planets period of revolution)
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Keplers Three Laws of Planetary Motion

• 1) Planets orbit the Sun in ellipse pattern
• 2) A line drawn from any planet to the Sun sweeps
  out equal areas over equal time.
• Very complex, but in short, the square of a
  planets period is proportional to the cube of its
  average distance from the Sun.
• (the period squared semimajor axis cubed)

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Demonstration of Law 1
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Notes What in the world is an ellipse???Goal
Take notes over introductory concepts on
planetary motion and elliptical orbits

• An ellipse is a close curve in which the sum of
  the points (foci) inside the ellipse is always
  the same.

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Facts About Law 1

• Ellipse properties
• Eccentricity?
• Is a circle an ellipse?
• Ellipse length
• Ellipse height

• 2 focal points, called foci (plural)
• Refers to flatness of an ellipse. Value
  between 0 and 1.
• Circle has eccentricity of 0.
• Major axis
• Minor axis

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Demonstration of Law 2
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Notes Planets move faster when???Goal Take
notes over introductory concepts on planetary
motion and elliptical orbits

• Suppose that it takes the planet the same amount
  of time to go between positions C and D as it did
  for the planet to go between positions A and B.
  Then the planet must move faster when it is
  closer to the sun and slower when it is farther
  away.

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Facts About Law 2

• Earths orbit around the sun Circle or Ellipse?
• Earths speed around the Sun constant or varies?
• Earths distance from the Sun constant or varies?

• Earth, and all planets, but in an ellipse
  pattern.
• The speed is not constant.
• Distance varies slightly.

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Brief Tutorial

• Period of ANY planet is calculated in years.
• The semi-major axis is a planets average distance
  from the SUN.
• Pperiod of revolution
• Aaverage distance measured in AU

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Notes Period, axis Can we say LOST???Hang in
therewe will get through this!Goal Take notes
over introductory concepts on planetary motion
and elliptical orbits

• Lets do a little practice problem
• P2a3
• P is the period of revolution and a is the
  semimajor axis of the orbiting planet
• If Mars period of revolution is 1.88 years what
  is its semimajor axis?
• First, we cube 1.88 years for the P2 ?
• 3.53 sound about right???

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Notes Period, axis Can we say LOST???Hang in
therewe will get through this!Goal Take notes
over introductory concepts on planetary motion
and elliptical orbits

• Lets do a little practice problem
• First, we cube 1.88 years for the P2 ?
• 3.53 sound about right???
• Now, we take this value, 3.53, and we equate it
  to the cube of the semi-major axis. So a3 3.53
• To find the AU, we have to take the CUBE root of
  3.53.
• 1.52 AU sound about right? Check page

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Notes Period, axis Can we say LOST???Hang in
therewe will get through this!Goal Take notes
over introductory concepts on planetary motion
and elliptical orbits

• Lets do a little practice problem
• P2a3
• P is the period of revolution and a is the
  semimajor axis of the orbiting planet
• If Mars period of revolution is 1.88 years what
  is its semimajor axis?
• P21.8823.53
• P2a3 therefore a33.53
• So a 3v3.53 1.523
• Now you try one. What is the semimajor axis of
  Mercury if its period of revolution is 88 days?

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Vocabulary to Remember

• Orbit
• Ellipse
• Eccentricity
• Period

• How a planet moves around a central star.
• Circle that is somewhat flattened.
• Value from 0 to 1, circle is 0.
• How much time an orbit takes.

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Lets Look At The Lab!

• Write in the purpose for this lab
• Students will explain planetary motion using
  gravitational laws.
• Write in Keplers 3 Laws
• All planets move in the shape of an ellipse
  around the sun.
• A line drawn from the planet to the sun sweeps
  out equal areas over equal time.
• The square of a planets period of revolution is
  proportional to the cube of the planets mean
  distance.