Chapter 7 Gravitation

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Chapter 7 Gravitation

•  
• In this chapter you will
•  
• Learn the nature of gravitational force.
• Relate Keplers laws of planetary motion to
  Newton's laws of motion.
• Describe the orbits of planets and satellites
  using the law of universal gravitation.

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Chapter 7 Sections

• Section 7.1 Planetary Motion and Gravitation
• Section 7.2 Using the Law of Universal
  Gravitation

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SECTION 7.1 PLANETARY MOTION AND GRAVITATION

• Objectives
• Relate Keplers laws to the law of universal
  gravitation.
• Calculate orbital speeds and periods.
• Describe the importance of Cavendishs experiment.

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INTRODUCTION

• Nicholas Copernicus a Polish astronomer, that
  observed the movements of the planets revolved
  around the Sun, his book was published in 1543.
• Tycho Brahe a Dutch astronomer. At the age of
  14 saw an eclipse of the sun and vowed to become
  an astronomer. He believed the moon and Sun
  revolved around Earth and all other planets
  revolve around the Sun.

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KEPLERS LAWS

• Johannes Kepler a German astronomer. He was an
  assistant of Brahe. When Brahe died he inherited
  30 years worth of observations and from this
  data he was able to develop 3 laws of planetary
  motion. He believed in a Sun centered universe.
•  
• Keplers First Law states that the paths of the
  planets are ellipses with the Sun at one focus.
•  
• Comets are divided into 2 groups.
• Long Period Comets (Orbital Period over 200
  years.)
• Short Period Comets (Orbital Period under 200
  years. Halleys)
• Kepler noticed that the planets move faster when
  they are closer to the sun and slower when they
  are farther away from the sun.

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KEPLERS LAWS

• Keplers Second Law states that an imaginary
  line from the Sun to a planet sweeps out equal
  areas in equal time intervals. (Fig. 7.3)
• Keplers Third Law states that the square ratio
  of the periods of any 2 planets is equal to the
  cube of the ratio of their average distances from
  the sun.
• (TA / TB)2 (rA / rB)3
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• Table 7.1 p. 173 will be used throughout this
  chapter.

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KEPLERS LAWS

• Do Example Problem 1 p. 174
• (TC / TI)2 (rC / rI)3
• (16.7 / 1.8)2 (rC / 4.2)3
• (9.28)2 rC3 / 74.088
• 86.1184(74.088) rC3
• 6380.34 rC3
• 18.55 units rC
• Do Practice Problems p. 174 1-5

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NEWTONS LAW OF UNIVERSAL GRAVITATION

• Sir Isaac Newton started studying planetary
  motion in 1666. He found that the Force varies
  inversely with the square of the distance between
  the centers of the planet and the sun. Force (F)
  is proportional to 1 / r2.
•  
• Gravitational Force the attractive force
  between 2 objects that is directly proportional
  to the mass of the objects.
•  

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NEWTONS LAW OF UNIVERSAL GRAVITATION

• Newtons Law of Universal Gravitation states
  that objects attract other objects with a force
  that is proportional to the product of their
  masses and inversely proportional to the square
  of the distance between them. The Gravitational
  Force is equal to the Universal Gravitational
  Constant, times the mass of object 1, times the
  mass of object 2 divided by the distance between
  the centers of the objects squared.
• F G(m1m2 )
•   r2
• Go over the Connecting Math to Physics Table at
  bottom of p. 175.

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UNIVERSAL GRAVITATION AND KEPLERs THIRD LAW

• Period of a Planet Orbiting the Sun equals 2?
  times the square root of the orbital radius cubed
  divided by the product of the universal
  gravitational constant and the mass of the Sun.
• ______________
• T 2? v (r3 / (G ms) )

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MEASURING THE UNIVERSAL GRAVITATIONAL CONSTANT

• Henry Cavendish an Englishman that calculated
  the attractive force between 2 objects (G). He
  found the value for G by substituting into the
  Law of Universal Gravitation. His experiment is
  called Weighing Earth because it helped
  determine Earths mass.
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• The value of G is 6.67 x 10-11 Nm2/kg2 if you use
  m1 and m2 measured in kg and r in meters and F in
  Newtons.
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• Read through p. 178 and go over example.
• Do 7.1 Section Review p. 178 6-11