ps

• Eratosthenes's calculation of the Earth's circumference


  It solidifies ancient Greeks' belief of a spherical Earth
• Eratosthenes's method


  • He used vertical poles to observe the shadow cast on two different cities
  • He assumed that the light rays from the Sun are parallel when they reach Earth
  • He observed the shadows cast on two different cities during the summer solstice
  • He determined the value of the distance between the two cities from a complete circle

  
• Difference in the angle of shadows cast in Syene and Alexandria at noon during a summer solstice


  It is caused by the curvature of the Earth's surface

  
• Long before Ferdinand Magellan made his circumnavigation of the world, the ancient Greeks had figured out more than 2,300 years ago that the Earth is round
• Pythagoras's belief


  • Circles and spheres were the most perfect shapes
  • The earth and all the heavenly bodies must be spherical
• Aristotle's observations


  • The round shadow cast by the Earth on the Moon during a lunar eclipse
  • The varying positions of the North Star (Polaris) as one changes latitude
  • The disappearance of sailing ships over the horizon

  
• Eratosthenes's calculation of the Earth's circumference

  1. Observed the shadow cast by a vertical pole in Alexandria

  2. Knew that in Syene, the sun was directly overhead at noon on the summer solstice

  3. Assumed the Sun's rays are parallel when they reach Earth

  4. Reasoned that the difference in the angle of the shadows was due to the curvature of the Earth's surface

  5. Calculated the circumference of the Earth by multiplying the distance between Alexandria and Syene by 50

  
• Tycho Brahe


  Danish astronomer who conducted precise observations of the positions of the planets during his time

  
• Tycho Brahe


  • Invented different astronomical instruments with the help of his assistants
  • Made an extensive study of the solar system
  • Determined the position of 777 fixed stars accurately

  
• The Earth is not a perfect sphere but an oblate spheroid with a slight bulge around the equator and flatter poles
• First instruments created by Tycho Brahe


  • Brass Azimuthal Quadrant (1576)
  • Great Globe (1580)
  • Armillary Sphere (1581)
  • Triangular Sextant (1582)

  
• Pieces of evidence supporting ancient Greeks' belief of a spherical Earth


  • Aristotle's observation of the round shadow cast by the Earth on the Moon during a lunar eclipse
  • Aristotle's observation of the varying positions of the North Star (Polaris) and constellations as one changes latitude
  • Aristotle's observation of the gradual disappearance of sailing ships over the horizon
  • Eratosthenes's calculation of the Earth's circumference using the difference in shadow angles between Syene and Alexandria

  
• Johannes Kepler


  • Became Brahe's successor after the latter's death in 1601
  • Was given access to a vast collection of observations of Mars and continued Brahe's unfinished work
• Kepler's laws of planetary motion


  • The planet's path around the sun is elliptical in nature where the sun is the center and located at one focus
  • There is an imaginary line from the center of the sun to the planet and this sweep out equal areas within equal time intervals
  • The ratio of squares of the periods between any two planets will always be equal to the ratio of the cubes of its distances from the sun

  
• Kepler's first law (law of ellipses)


  1. Planets are moving around the sun by following an ellipse path

  2. An ellipse is a special curve where the sum of the distances from any point within the curve to two other points is always constant

  3. The other two points are termed as the foci of the ellipse

  4. The closer these points are, the more similar an ellipse to the shape of a circle

  5. The shape of a circle is a special case of an ellipse where the two foci are located in the same position

  
• Ellipse


  A shape with two focus points (foci) that lie on the major or longest axis, spaced equally on each side of the center
• Kepler's First Law


  • All planets revolve around the Sun in elliptical orbits, with the Sun at one of the foci
• Kepler's second law (law of equal areas)


  1. The speed of the planet within the space is always changing

  2. A planet moves faster when it is closer to the sun and slower if it is furthest

  3. If there is an imaginary line starting its point at the center of the planet and goes to the center of the sun, the line would sweep out the same area within equal periods of time

  4. The areas formed if Earth is closest to the sun is approximated as a wide short triangle, while the areas formed when Earth is most distant to the sun is approximated as a narrow long triangle

  5. Despite the difference in shape, these areas tend to be of the same size
• Kepler's Second Law


  The radius vector (line from Sun to planet) sweeps out equal areas in equal intervals of time
• Kepler's third law (law of harmonies)

  1. Compares the orbital period and radius of the orbit of one planet to other planets

  2. The ratio of the squares of the periods to the cubes of their average distances to the sun will be the same for every single planet

  
• Semi-major axis


  Half the distance of the major axis of an elliptical orbit
• Kepler's Third Law


  • The square of the time period of revolution of a planet is directly proportional to the cube of its semi-major axis
• Kepler's third law of planetary motion gives an accurate description for the time and distance for each planet's movement around the sun

  
• Johannes Kepler was born prematurely, was a feeble child with weak vision, and at age 6 was sent to school but soon taken out to earn money for the family by working as a waiter in a hotel
• The T2/R3 ratio for the planets' orbits to the sun is also applicable to the T2/R3 ratio of the moon or any satellite orbiting the around any planet

  
• Motion


  The movement or change in location or position of an object at a certain time
• Vertical Motion


  The upward or downward movement of a particular object along a straight line

  
• Horizontal Motion


  The motion parallel to the surface of the ground

  
• Mass


  The measure of the amount of matter in an object
• Friction


  Resistance offered by the surfaces that are in contact when they move past each other
• Air Resistance


  A kind of friction (a force that opposes motion) which occurs between air and another object
• The upward or downward movement of a particular object along a straight line

  
• The measure of the amount of matter in an object
• Resistance offered by the surfaces that are in contact when they move past each other
• The motion parallel to the surface of the ground
• A kind of friction (a force that opposes motion) which occurs between air and another object
• The movement or change in location or position of an object at a certain time
• Aristotle's views on motion


  • Every object has a proper place in the universe
  • There are natural and violent motion

  
• Galileo's views on motion

  • An object can move freely in the absence of Friction

  
• Gravity is a key factor in contour farming. By planting along the contours, Lumad farmers take advantage of gravity's pull