Days of the week: - named after 7 Power (moving) objects in the sky (Sun, Moon, 5 planets) Models of the Universe:
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1 Motions of the Planets ( Wanderers ) Planets move on celestial sphere - change RA, Dec each night - five are visible to naked eye Mercury, Venus, Mars, Jupiter, Saturn Days of the week: - named after 7 Power (moving) objects in the sky (Sun, Moon, 5 planets) English Spanish French Roman/Latin Germanic/ Origin Norse Origin Sunday Domingo Dimanche Sun Sun Monday Lunes Lundi Luna (Moon) Moon Tuesday Martes Mardi Mars Tyr Wednesday Miercoles Mercredi Mercury Wodan Thursday Jueves Jeudi Jupiter (Jove) Thor Friday Viernes Vendredi Venus Frigg Saturday Sabado Samedi Saturn Saturn Motion of the planets: - move near ecliptic (through zodiac) - most of the time, move eastward Prograde Motion - occasionally: change direction and move westward Retrograde Motion Models of the Universe: Aristotle: philosophy of Idealism ( 2000 years ago) - circles and spheres are ideal shapes structure of universe based on circles and spheres Geocentric Cosmology - Earth is at center, stationary - Sun, Moon, 5 known planets revolve around Earth on concentric circles - Earth at center of rotating Celestial Sphere
2 Ptolemaic Model - orbit of planet around Earth - Deferent - planets are fixed to smaller circles - Epicycles Planets revolve on epicycles while epicycles revolve on deferent Claudius Ptolemy (137 A.D.) - most accurate model of planetary motion at the time based on Geocentric Cosmology Link: Ptolemaic System - used for over 1300 years - over time, needed adjustments
3 Eventually, model had 234 epicycles to describe the motion of 5 planets!! Orbit of Mercury Nicholas Copernicus ( ) - developed an accurate Sun centered ( Heliocentric ) model Heliocentric Cosmology - Earth is a planet, orbiting around the sun - other planets on larger or smaller orbits explains retrograde motion in simple way: - Earth passes by outer planets - gives appearance that other planets change direction Copernicus - used simple geometry to find distances to planets - close to modern values! - but, still used circular orbits - not entirely accurate Tycho Brahe ( ) Greatest Observational Genius of the Age - very accurate & precise observations before telescope - accuracy of 0.1 o (or 6') - near limit of human eye - measured positions of planets Johannes Kepler ( ) Greatest Theoretician of the Age - assistant to Tycho Brahe - used data to describe planetary orbits (after Tycho s death) - tried to find correct geometrical shape: - found that orbits are Ellipses!!
4 Kepler s First Law: Orbits of planets: - are ellipses - with the sun at one focus Eccentricity: - measure of how round/flat the ellipse is - ranges from 0 (circle) to 1.0 (flat line) Properties of an Ellipse: b a focus focus a - semimajor axis b - semiminor axis Kepler s Second Law: Kepler studied motion of a planet: the speed of the planet changes - planets move faster when closer to sun (closest point: Perihelion) - planets move slower when farther from sun (furthest point: Aphelion) A line joining a planet and the sun: - sweeps out equal areas in equal times Kepler s Third Law: When Kepler studied other planets, found: - a planet with a larger orbit - takes longer to orbit the sun and moves slower! The squares of the periods are proportional to the cubes of the semimajor axes Definition: For Earth s orbit Semimajor axis = 1 Astronomical Unit For any planet, P 2 = a 3 Mercury: P = yrs a = A.U. P 2 = yrs 2 a 3 = A.U. 3 Jupiter: P = yrs a = 5.20 A.U. P 2 = yrs 2 a 3 = A.U. 3 Example: An object that orbits 4 A.U. from Sun a = 4 AU: a 3 = 4 3 = 64 P = a 3 = 64 = 8 yrs Object will take 8 years to orbit Sun
5 Galileo Galilei ( ) - first person to use telescope to study sky Astronomical Observations: Surface of the Moon - normal geological features like mountains, craters, valleys similar to Earth Surface of the Sun - saw spots on surface ( blemishes! ) could measure rotation Moons of Jupiter - four moons in orbit around Jupiter - obeyed Kepler s Laws - Earth not only center of revolution Venus - goes through same phases as Moon - becomes larger when dimmer, smaller when brighter Previous Observations -Mercury, Venus always close to sun Geocentric (Earth-centered) Model: - their orbits around the Earth must be linked to sun
6 Heliocentric Model: - their orbits are smaller than Earth, cannot move far away from sun If Venus has all the phases of Moon: Venus must orbit sun! Observations cannot be explained by Geocentric Cosmology! Isaac Newton ( ) - described what causes motion FORCE - a force is a push or a pull Newton s Three Laws of Motion: First Law (Law of Inertia) if no net force, an object: - will be at rest - or moves at a constant speed, in straight line, forever Second Law (F = ma) If a net force acts on an object: - it changes its motion (accelerates) - speeds up, slows down, or turns - depends on mass of object - more mass, harder to accelerate Third Law ( action action-reaction reaction ) If two objects apply forces on each other: - the forces are exactly the same strength, but opposite in direction Planets move on elliptical orbits - change direction, speed due to force on planets! Newton: Universal Law of Gravity F G = G m 1 m 2 r 2 G - gravitational constant = 6.67 x m 3 /kg s 2 - proportional to masses (m 1, m 2 ) - inversely proportional to square of distance (r)
7 Mass versus Weight Mass - amount of matter Weight - force of gravity on matter If you weighed 150 lbs on Earth: Mass Weight Sun 68 kg 4000 lbs Jupiter 68 kg 400 lbs Mars 68 kg 60 lbs Moon 68 kg 25 lbs Asteroid 68 kg 1/2 oz.
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