Lecture 7: Newton and Kepler

"Don't sit under the apple tree, with anyone else but me."

Glenn Miller

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    • Date: September 20, 1994
    Reading Assignment: pp. 48-61

    Description : Kepler's laws, Newton's Laws, universal gravitation.

    Objectives

  • be able to list the three laws of planetary motion and understand what each of these laws mean.
  • be able to list Newton's laws of motion and understand what they mean.
  • be able to understand Newton's law of gravity
  • understand how changing mass and distance affect gravity
  • \be able to list the contributions of Tycho, Kepler and Newton

    • Lecture Outline

    Slide # 1: Lecture 7: Newton and Kepler, the Dudes and their Laws

  • Click here for subtitle
  • Tycho
  • Kepler
  • Newton
    • Slide # 2: Thursday: Exam #1
  • Bring
  • Scantron sheet
  • #2 pencil
  • calculator (if you like)
  • 45 questions
  • Sample test is on the Mosaic server
  • http://astro.gmu.edu/
    • Slide # 3: Lecture 6: The Copernican Revolution
  • Copernicus
  • Galileo
  • (Tycho)
  • (Kepler)
  • (Newton)
    • Slide # 4: The Geocentric Model Slide # 5: No Epicycles!?
  • are all the epicycles gone?
    • Slide # 6: Copernican Epicycles
  • some epicycles are still needed
  • a simplier model for the solar system
    • Slide # 7: Galileo's Big Observations
  • mountains on the Moon
  • phases of Venus
  • moons around Jupiter
  • spots on the Sun
  • stars not seen without a telescope
    • Slide # 8: Galileo's Books
  • "Dialogue Concerning the Two Chief World Systems"
  • Described why a Geocentric Model would not work.
  • The Starry Messenger
  • an observational log
    • Slide # 9: Things are looking bad for the Revolution
  • Galileo arrested 1633 and placed under house arrest
  • Epicycles are still being used
  • No reason why things orbit around the Sun
    • Slide # 10: Tycho (Brahe)
  • 1546-1601
    • Slide # 11: Tycho- an Astronomer who could Party
  • Kidnapped by his Uncle at age two
  • Lost his nose in a duel over Mathematics
  • Established best naked-eye observatory
  • Kicked out of Denmark
  • Died because he was trying to be polite
    • Slide # 12: Why didn't the Church bother Tycho, Kepler and Newton? Slide # 13: Tychos observations
  • created a table of planetary positions
  • very accurate data
  • did NOT use a telescope
    • Slide # 14: Kepler
  • Hired by Tycho
  • Mathematician from Austria
  • Inherited Tycho's Observations and Job
  • 1571-1630
    • Slide # 15: Kepler's Laws of Planetary Motion
  • analyzed Tycho's observations
  • determined HOW planets move around the Sun
  • developed Three Laws of Planetary Motion
    • Slide # 16: Kepler's 1st Laws
  • The orbital path of planets are elliptical, with the Sun at one focus.
    • Slide # 17: What is an Ellipse?
  • A Special Type of Elongated Circle
    • Slide # 18: Parts of an Ellipse
  • Foci
    • Slide # 19: Parts of an Ellipse
  • The Major Axis
    • Slide # 20: Parts of an Ellipse
  • Semi-Major Axis
    • Slide # 21: Kepler's 2nd Law
  • An imaginary line connecting the Sun to any planet sweeps out equal areas in e
    • Slide # 22: Kepler's 2nd Law- Equal Areas in Equal Times
  • A Planet moves faster when it is near the Sun
    • Slide # 23: Kepler's 3rd Law
  • The square of a planet's orbital period is proportional to the cube of its orb
    • Slide # 24: Kepler's 3rd Law
  • We can calculate how LONG it takes for a planet to orbit if we know its Semi-M
    • Slide # 25: The AU is
  • an Astronomical Unit
  • the average distance between the Earth and Sun
  • about 1.5 x 108 km
  • about 9.3 x 107 miles
    • Slide # 26: Kepler's Third Law- Example #1
  • What is the orbital period of Earth?
    • Slide # 27: Kepler's 3rd Law- Example #2
  • What is the orbital period of an object at 5 AU's?
    • Slide # 28: Kepler's Laws
  • orbital paths are ellipses with the Sun at one focus
  • equal areas in equal times
  • P2= a3
    • Slide # 29: Kepler's Laws
  • No Epicycles
  • an accurate description of Planetary Motion
    • Slide # 30: How were the Laws Derived?
  • Analysis of Tycho's Observations
    • Slide # 31: Measuring the AU
  • Kepler could measure distance in AU's
  • He could not calculate miles/AU
  • Measuring the AU is done using radar
    • Slide # 32: Newton
  • 1642-1727
    • Slide # 33: Newton's Contributions
  • 3 laws of motion
  • Universal Gravitation
  • Calculus
  • (also optics, the wave theory of light and a nice cookie)
    • Slide # 34: Newton's Laws of Motion
  • Three Laws which describe motion
  • Same laws apply to planets and people
    • Slide # 35: Some Terms:
  • Speed = how fast something moves
  • Velocity = speed + direction of motion
  • Acceleration = a change in the velocity
  • change in the speed
  • change in the direction of motion
    • Slide # 36: Newton's 1st Law
  • Every body stays at rest or continue in uniform motion in a straight line unle
    • Slide # 37: Inertia
  • the tendency of objects not to change velocity
    • Slide # 38: Newton's 1st Law
  • Why don't we observe this?
  • Objects do not continue in uniform motion in a straight line
  • Friction and gravity are both forces
    • Slide # 39: Newton's 2nd Law
  • Force = Mass x Acceleration
  • Acceleration = Force / Mass
  • Acceleration is proportional to Force (if the mass is constant)
    • Slide # 40: Newton's 2nd Law
  • if you triple the force, the acceleration will triple
  • the mass will not change
    • Slide # 41: Mass
  • a property of matter
  • does not change due to acceleration or velocity
    • Slide # 42: Newton's 3rd Law
  • Every action has an equal and opposite reaction
    • Slide # 43: Newton's Law of Gravity
  • inverse square law
    • Slide # 44: Newtonian Gravity
  • doubling the distance decreases the force by 4
  • tripling the distance decreases the force by 9
  • halving the distance increases the force by 4
    • Slide # 45: Newton's Gravity
  • Newton went home from Cambridge in 1665
  • Halley visited Newton in 1684
  • Published Principia
    • Slide # 46: Newtonian Gravity
  • the force of gravity never goes to zero
    • Slide # 47: Newtonian Gravity
  • doubling the mass of object #1 increases the force by two
  • tripling the mass of object #1 increases the force by three
    • Slide # 48: Newton's Laws and Planetary Motion
  • orbits are due to gravity
  • Sun and planet have a gravitational force
  • the force causes an acceleration
  • the acceleration causes the planet to go in an ellipse
    • Slide # 49: The Copernican Revolution
  • Copernicus 1473-1543
  • Galileo 1564-1642
  • Tycho 1546-1601
  • Kepler 1571-1630
  • Newton 1642-1727