Universal Gravitation

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Universal Gravitation

• Newtons 4th law

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Universal Gravitation

• Keplers Laws
• Newtons Law of Universal Gravity
• Applying Newtons Law of Universal Gravity

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Universal GravitationKey Terms

• Tyconic system
• Keplers Laws
• Universal Gravity
• Kepler Constant
• Angular Momentum
• Eccentricity of Orbits
• Torsion Balance
• Microgravity
• Geostationary Orbit
• Perturbing Orbits

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Universal Gravitation

• The Tyconic system was named after Tyco Brahe, a
  Danish astronomer who was a mentor to Johannes
  Kepler. In his system, the Earth was at the
  centre of the universe. The sun and moon orbited
  the earth and the other planets revolved about
  the sun.

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Universal Gravitation

• lpc1.clpccd.cc.ca.us/.../ahistlec.htm

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Keplers Laws

• Planets move in elliptical orbits, with the Sun
  at one focus of the ellipse.
• An imaginary line between the Sun and a planet
  sweeps out equal areas in equal time areas.
• The quotient of the mean radius of revolution
  cubed and the square of the period of revolution
  is constant and the same for all planets r3/T2
  k

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Universal Gravity

• Newton reasoned that the attractive force which
  made an apple fall to the ground was the same
  force between the sun and the Earth and the Earth
  and the Moon . He concluded that these were force
  pairs and that every object must attract every
  other object. He summarized

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Universal Gravity

• The force of gravity between any two objects is
  proportional to the product of their masses and
  inversely proportional to the square of the
  distance between their centres.
• F1,2 G (m1 m2 ) / (r1,2)2
• G is the universal gravitational constant
  (determined by Cavendish) as 6.67 x 10-11 Nm2/kg2
• It should not be confused with g 9.81 m/s2

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Reconciling Keplers 3rd with Newtons 4th

• Consider the sun and a planet
• Fgrav G (ms mp) / (r)2
• Suns gravitational force supplies centripetal
  force for planets orbit, so
• G (ms mp) / (r)2 mpv2/r but v 2pr/T
• G ms/ (r)2 (2pr/T)2 and rearranging
• r3/T2 G ms/ (4p)2
• Although this example involves the sun and a
  planet, it applies to all orbital motion

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Finding the mass of the sun without a scale ?

• r3/T2 G ms/ (4p)2 , rearranging,
• ms (4p2 /G)(r3/T2) 1.97 x 1030 kg