Two Chapter 6

• Galileo presented strong support for the Copernican model and published a book defending it.
  • He discovered.
    • Four moons of Jupiter
    • That there were many more stars than previously thought
    • The moon was of irregular shape
      • had mountains
      • had craters
    • The sun had spot.
• Galileo was tried before the inquisition because of his ideas. The result was house arrest for the rest of his life.
• After the inquisition, he wrote "Dialogue Concerning Two New Sciences" which presented
  • a new way of science writing.
  • the scientific method which included observing, analyzing, hypothesizing, experimenting, etc.
  • his idea of gravity, uniform motion, and acceleration.
    • These formed the basis for Newton's work.

• Newton made major contributions to physics.
  • He worked out the binomial theorem in mathematics.
  • Newton developed calculus.
  • He developed his universal law of gravity.
    • Developed by speculating whether the same force that causes the moon to orbit, also causes an apple to fall.
• The universal law of gravity shows that gravitational force is inversely proportional to distance squared.
• Newton used this to predict the acceleration due to the earth's gravity at the moons surface.

• Measurements of the moon's orbit show the moon's centripetal acceleration is nearly 2.7 X 10^-3 m/s².
• Newton essentially proved that:

• Edmund Halley plotted the motion of Halley's comet.
• Newton suggested that if force is inversely proportional to the square of the distance, then planets would move in ellipses.
• Newton showed by calculations, that his suggestion was correct. To do this he used new astronomical data (like Halley's) to show that the prediction matched observations.
• For planets in circular orbits traveling with uniform speed we have;

• Kepler's third law states:

• Newton felt that K varied for different planets according to:

• The mass of the Earth is 5.98 X 10²⁴ kg and the radius is 6.38 X 10⁶ m.
• Cavendish (Henry) used a device to measure G in 1798.
• The results of Newton's work are:
  • Many thinkers thought there was an exact law of existence.
  • The age of reason began.
  • The laws of the universe could be used to predict almost anything.
• By the 20th Century, this deterministic view had to be tempered.
• We should recall that:

• In the above equation, g = -9.81 m/s².

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November 5, 2013