Physical science

• Tycho Brahe was the most important observational astronomer until the invention of the telescope in 1608
• Tycho Brahe


  • He built his first astronomical and alchemical laboratory named "Uraniborg" in Ven, an island between Denmark and Sweden
  • He created several devices which he used in observing the various objects in the sky
• Instruments created by Tycho Brahe


  • Brass Azimuthal Quadrant (1576)
  • Great Globe (1580)
  • Armillary Sphere (1581)
  • Triangular Sextant (1582)
• Tycho Brahe's contributions in astronomy

  • He made the most precise observations by devising the best instruments available
  • He compiled extensive data on the position of planet Mars which later proved crucial to Kepler
  • He made careful observations of a supernova in 1572 and a comet in 1577
  • He made the best measurements that had yet been made in the search for stellar parallax
  • He was the first astronomer to make corrections for atmospheric refraction
  • He proposed the Tychonic Planetary Model (geoheliocentric)
• Tycho Brahe hired Johannes Kepler as a "research assistant" to do mathematical calculations that he hoped would be useful in proving his geoheliocentric model
• Johannes Kepler accepted the job offer of Brahe partly because he needed Brahe's observational data for his mathematical analyses in proving his version of the heliocentric model
• Kepler's Three Laws of Planetary Motion

  • Law of ellipses (1609)
  • Law of equal areas (1609)
  • Law of periods (1619)
• Law of ellipses


  Planets move in an elliptical orbit with the sun as one of the foci
• Law of equal areas


  The line joining the sun and the planet sweeps equal areas in equal times as the planet revolves around the sun
• Law of periods


  The planet's period of revolution and its average distance from the sun are related by two-thirds power
• Brahe's and Kepler's models including the dominant Ptolemaic and Copernican models were incorrect. Only the heliocentric idea of the sun being the center of the solar system was proven correct.

  
• Brahe's and Kepler's models including the dominant Ptolemaic and Copernican models were incorrect. Only the heliocentric idea of the sun being the center of the solar system was proven correct

  
• Ellipse


  A closed curve surrounding two fixed points (foci), such that for all points on the curve, the sum of the two distances to the focal points is a constant

  
• Ellipse


  • Has a major axis (longest diameter)
  • Has a minor axis (shortest diameter)
  • Has semi-major axes (half of major axis)
  • Has semi-minor axes (half of minor axis)
• Kepler's Law of Ellipses

  1. Orbit of each planet is an ellipse

  2. Planet is sometimes closer to the sun (perihelion)

  3. Planet is sometimes farther from the sun (aphelion)

  
• Kepler's Law of Equal Areas

  • Planets cover equal areas of the ellipse over equal time intervals
  • Caused by the variation in the gravitational pull of the sun to the planet
• Kepler's Second Law is a consequence of the conservation of angular momentum
• Kepler's Law of Periods


  The square of the orbital period (T^2) is proportional to the cube of the semi-major axis of its orbit (R^3)
• Data Illustrating Kepler's Third Law of Planetary Motion for the Solar System

  • Planet
  • Period (T) (Earth years)
  • Distance (R) (in AU)
  • T^2/R^3 Ratio

  
• The T^2/R^3 ratio would be the same value regardless of the planet's mass. If the period is expressed in Earth's years while the distance is in AU, the ratio will be 1
• Activity 1: Matching Type

  Match the law of planetary motion to its correct statement/description and illustration/table
• Activity 2: The Law of Ellipses

  1. Construct an ellipse using pencil, ruler, 2 thumbtacks, 30cm string, 2 short bond paper, cardboard

  2. Observe and compare the results with different distances between the tacks
• An ellipse is a closed curve surrounding two fixed points (foci), such that for all points on the curve, the sum of the two distances to the focal points is a constant

  
• The two thumbtacks and the pencil represent the foci and the path of the planet in Kepler's first law of planetary motion
• The distance between the two tacks affects the shape of the output. The closer the tacks, the more elongated the ellipse
• When analysing markets, a range of assumptions are made about the rationality of economic agents involved in the transactions
• The Wealth of Nations was written

  1776
• Rational


  (in classical economic theory) economic agents are able to consider the outcome of their choices and recognise the net benefits of each one
• Consumers act rationally by


  Maximising their utility
• Producers act rationally by


  Selling goods/services in a way that maximises their profits
• Workers act rationally by


  Balancing welfare at work with consideration of both pay and benefits
• Governments act rationally by


  Placing the interests of the people they serve first in order to maximise their welfare
• Rationality in classical economic theory is a flawed assumption as people usually don't act rationally
• Marginal utility


  The additional utility (satisfaction) gained from the consumption of an additional product
• If you add up marginal utility for each unit you get total utility