Astro 201 Sept 6 2010 Do on line practice quiz 2 by 9 14 Homework 2 posted on web page due 9 9 Reading Hester Chapters 2 3 Gleiser Sections 3 6 Today Astronomical basis for calendars Why there are seasons Tycho Kepler Newton Forces String Theory Determinism v Chaos Fractals The Astronomical Basis for Calendars The Earth rotates on its axis once a day The Earth orbits the Sun with a period of about 365 242190 days The Moon orbits the Earth such that the period between new moon and new moon is 29 5305 days These periods vary a little bit because of the gravitational forces exerted by the other planets and other factors Every 4 years we take into account the 242190 days by added a leap day February 29 Otherwise we would keep slipping and eventually January would be summer in the northern hemisphere etc Now the thing is that there are NOT an integral number of months 29 5305 days in one 365 242190 year So if for example today is a new moon next year it will not be SEASONS Seasons are a result of the tilt of the Earth s axis with respect to the plane of its orbit Seasons ARE NOT the result of the Earth being closer to the Sun in summer and farther in winter in fact during winter in the northern hemisphere we are closer to the Sun than we are in the summer The Gregorian Calendar Christian one we use is based on the motion of the Earth around the Sun The length and number of months have no connection to the motion of the Moon It is based on the Julian Calendar which was introduced by Julius Caesar in 45 BC He made Jan 1 the start of the Year During the middle ages different groups in Europe adopted different start dates for the new years In 1582 Pope Gregory reformed the calendar which is basically what we use today The French recognized a different pope for a while and had a different calendar The Islamic Calendar is based on the motion of the Moon with no connection to the motion of the Earth around the Sun Hijri Calendar Based on the Qur an Used in many countries around the Gulf e g Saudi Arabia Purely lunar 12 months each with 29 53 days Therefore the Islamic year has 12x29 53 354 36 days The Islamic year is shorter than the time it takes the Earth to go around the Sun Thus a particular Islamic month falls during different times of the year e g Ramadan Years are counted since the Hijra which is is the time that Mohammed emigrated to Medina in AD 622 So AD 2009 is Islamic year 1430 The Jewish and Chinese Calendars combine both so years are linked to the period of the orbit of the Earth around the Sun AND months are linked to the motion of the Moon around the Earth 19 x365 24 an integral number of 29 53 day months Jewish Year A ordinary year has 355 days and 12 months A leap year has 385 days and 13 months The length of a particular month varies from year to year by a day so that if New Year s Day Rosh HaShannah is say a new moon then the first day of every month is a new moon Years are counted since the creation of the world taken to be 3761 BC Thus 1998 is Jewish year 5759 Mayan Calendar The ancient Mayans developed a complex and accurate calendar which was adopted by other people in meso america Aztecs Tolmec Actually had THREE calendars which they used at the same time 1 The Haab Civilian calendar 18 months 20 days each 5 days to make 365 day years The 5 extra days were considered unlucky days of mourning Did not count YEARS in the Haab calendar however 2 The Tzolkin Devine calendar used for divinations two types of weeks one with 13 days the other with 20 days Each year was 260 days Years were not counted Mayan Calendars continued 3 The Long Count Instead of years the Mayan used the Long Count calendar system to keep track of historical events kin 1 day uinal 1 uinal 20 kin 20 days Tun 1 tun 18 uinal 360 days approx 1 year katun 1 katun 20 tun 7 200 days approx 20 years baktun 1 baktun 20 katun 144 000 days approx 394 years pictun 20 baktun 2 880 000 days approx 7885 years calabtun 20 pictun 57 600 000 days approx 158 000 years kinchiltun 20 calabtun 1 152 000 000 days approx 3 million years alautun 20 kinchiltun 23 040 000 000 days approx 63 million years The Mayan calendar started on our August 11 3114 BC With Date 0 0 0 0 0 Then date 13 0 0 0 0 is our December 21 2012 or 12 21 2012 This coincidence has caused some people to claim that the Mayan Calendar predicts the end of the world on December 21 2012 But the Long Count calendar doesn t end on 13 0 0 0 Tycho Brahe 1546 1601 Danish nobleman Got drunk as a college student lost his nose in a duel Built an observatory Uraniborg financed by King Frederic II Made extremely accurate Observations of the planets Astronomi Instaurat Mechanica Tycho s book about his instrumentation Tycho made observations of the positions of the stars and planets that were 15x more accurate than what others had made He beat down the errors by repeating a particular measurement many times and averaging the result Tycho s cosmology Tycho found no parallax for the stars and concluded they are very far away He made measurements which neither the Ptolemaic model nor the simple Copernicus model could explain Earth stationary in center Sun and moon orbit the Earth Other planets orbit the Sun Stars orbit the Earth Johannes Kepler 1564 1630 Worked as Tycho s assistant Took Tycho s observations when Tycho died and spent the next 29 years analyzing them First he wrote Mysterium Cosmographicum The orbits of the 6 known planets were described By 5 Pythagorian polyhedra in spheres Eventually abandoned this model and came up with Kepler s Three Laws of Planetary Motion 1 Planets move in elliptical orbits not circles with the Sun at one focus 2 An imaginary line connecting the Sun to any planet sweeps out equal areas in equal time Planets move faster when near Sun Area 1 Area 2 3 The square of a planet s orbital period is proportional to the cube of its semi major axis P2 years A3 astronomical units 1 Astronomical Unit The Earth Sun Distance The farther out a planet is in the solar system the longer it takes for it to go around the Sun Kepler s Laws are empirical descriptions of the data The don t explain WHY the planets move as they do Isaac Newton 1642 1727 Bubonic Plague 1665 While home for 2 years nothing to do he figured out Laws of motion Gravity with Philosophiae Naturalis Principia Mathematica The …