Models of the Universe

• The model of the solar system today traces its history back to the ancient Greek astronomy
• Celestial sphere


  Coordinate system used to map the positions of celestial objects in the sky

  
• Celestial sphere

  • Equivalent to the Earth's north pole
  • Equivalent to the Earth's south pole
  • Equivalent to the Earth's latitude (north-south location)
  • Equivalent to the Earth's longitude (east-west location)
  • Path which the sun appears to take
  • Point where the ecliptic intersects with the celestial equator

  
• Even before Plato, the Greeks deduced that the Earth is spherical
• The Greeks were able to measure the diameter of the Earth
• The Greeks noted that the stars are viewed differently as they travel north and south
• Eratosthenes' method to measure the Earth's circumference

  1. No vertical shadow cast in Syene

  2. Shadow cast at an angle of 7.2° in Alexandria

  3. Distance between Syene and Alexandria was 5000 stadia

  4. Calculated the Earth's circumference as 250,000 stadia

  
• The sense of symmetry by Greeks demands a spherical Earth located at the center of the sphere of heavens

  
• Astronomical events known before telescopes


  • Length of the year known by Babylonians, Assyrians, Egyptians
  • Egyptians tracked the yearly cycle of the star Sirius
  • Early Chinese civilizations tracked comets, meteors, and dark spots of the Sun
  • Mayans developed a calendar based on the movements of Venus
  • Polynesians used stars for navigation
• Diurnal motion


  Apparent daily motion of stars and celestial bodies across the sky due to Earth's rotation

  
• Fixed stars


  Stars whose movements seem fixed in the sky

  
• Wandering stars


  Stars whose movements deviate from the fixed stars (Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn)
• Annual motion

  Apparent yearly motion of stars and celestial bodies across the sky due to Earth's revolution
• Ecliptic


  Path the Sun appears to take in the celestial sphere

  
• Zodiac


  Band of 13 constellations visible in the ecliptic
• Equinoxes

  Two days in a year when the Sun crosses the celestial equator
• Solstices


  Two days in a year when the Sun is at the farthest declination (north or south) from the celestial equator
• Precession


  Slow 'wobbling' of Earth's axis of rotation due to the gravitational pull of the Moon and Sun
• Solar eclipse


  Occurs when the Moon passes between the Earth and Sun, with the Moon casting a shadow on the Earth's surface
• Lunar eclipse


  Occurs when the Earth is directly aligned between the Sun and Moon, with the Earth casting a shadow on the Moon
• Models of the universe


  • Ptolemaic system
  • Copernican system
  • Tychonic system
• Ptolemaic system


  • Earth is the center of the universe
  • All other celestial bodies revolve around the Earth
  • Stars are fixed in the outermost celestial sphere
  • Used epicycles and deferents to explain retrograde motion

  
• Copernican system


  • Sun is the center of the universe
  • All planets including Earth revolve around the Sun
  • Only the Moon revolves around the Earth
  • Stars are fixed in the outermost celestial sphere
  • Differences in orbital speeds explain retrograde motion

  
• Tychonic system


  • Earth is the center of the universe
  • Moon and Sun revolve around Earth
  • All other planets revolve around the Sun
  • Stars are fixed in the outermost celestial sphere
  • Same explanation for retrograde motion as Copernican system

  
• Planets usually rise from east to west as seen in the celestial sphere

  
• Retrograde motion of planets is due to the difference in the period of revolution of the planets around the Sun
• Ptolemy used epicycles and deferents to explain retrograde motion
• Tycho Brahe


  Danish astronomer who precisely recorded the positions of the Sun, Moon, and planets for over 20 years
• Johannes Kepler


  Analyzed Tycho Brahe's data and formulated the three laws of planetary motion

  
• Kepler's 1st Law (Law of Ellipse)


  • Orbits of all planets are elliptical with the Sun at one focus

  
• Kepler's 2nd Law (Law of Equal Areas)


  • A line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time
• Kepler's 3rd Law (Law of Harmony)


  • The square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit
• Areas


  1. A line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time

  2. A planet moves fastest when it is nearest to the sun

  
• Law of Harmony

  • The square of a planet's orbital period (years) is proportional to the cube of the semimajor axis of its orbit (in astronomical units or AU) or P^2 = a^3
  • The larger the orbit's size, the longer it takes to orbit the sun