Scientific Revolution

  • Democritus, Empedocles, and other Pre-Socratics developed proto-scientific theories unable to make precise, testable predictions. Things changed in the 17th century.
  • The Scientific Revolution began in 1543 with the publication of Copernicus’ heliocentric theory of the solar system.
    • Copernicus’s system postulated circular orbits for the planets. Deferents and epicycles were used to explain their retrograde motion.
  • Beginning in the 17th century, scientific theories were formulated mathematically, yielding testable predictions.
    • Johannes Kepler’s Three Laws of Planetary Motion (1609-1618)
      • Ellipses: the orbit of each planet is an ellipse with the Sun at one focus.
      • Equal Areas: an imaginary line drawn from a planet to the Sun sweeps out equal areas in equal times.
      • Harmony: (the orbital period of a planet)2 is directly proportional to (the average distance of the planet to the sun)3.
    • Galileo’s Laws of Falling Bodies and Projectiles (1609)
      • Falling Bodies: the (distance a body falls) is directly proportional to (elapsed time)2 
      • Projectile Motion: the trajectory of a projectile is a parabola
    • Isaac Newton’s Theory of Gravitation (1687)
      • Using the magic of differential equations (F=MA), Newton’s theory predicted, second to second, the motion of falling bodies and the orbits of the planets
  • Galileo in 1623:
    • The laws of Nature are written in the language of mathematics.
  • A scientific theory is an axiom system:
    • designed to explain certain kinds of phenomena
    • defined by its postulates
    • supported or disproved by its predictions
Newton’s Theory of Gravitation
Equation of Motion as a Differential Equation