Calendars

1. Calendars • Year not even number of days (or months) • Problem: • Calendar year too short • Spring (vernal equinox) occurs later and later • Solution: • Add leap days (or months); lengthen average year • want average length = sidereal year (365.2422 days)

2. Early Calendar • Sumerians & Babylonians • Year 360 days (actual value = 365.24) • Divide Circle into 360 degrees • Each degree divided into 60 minutes of arc • Each minute divided into 60 seconds of arc • 12 months per year (actual value = 12.37) • Origin of 12 Zodiacal signs (sun in each for 1 month) • Month begins at first appearance of crescent moon • Month is 29 or 30 days (modern value = 29.53) • Leap months • added every few years • lengthen year, so average = 12.37 months • Named after common activities (planting, harvest, etc.) • Day divided into 12 hours • Egyptians later adopt 24 hour day Base 60 numbers

3. The Week • Originally, time between market days • Sumerian & Babylonian: 4-8 days • Differed by city / region • Greeks (& Egyptians): 10 day week • Romans 8 days (market week) • Egyptians: 7 days (planet worship) • Romans abroad bring home • 7 day week permitted by Caesar Augustus • Officially adopted by Emperor Constantine • Days named after planets

4. Solar Calendars • Solar Calendars • Months ignore phase of moon • Leap days maintain synchronization with seasons • Example: Gregorian Calendar (our calendar)

5. Modern Calendar • Julian Calendar (adopted by Julius Caesar) • Normal year = 365 days • Add leap day (Feb 29) every 4 years • Average length of year = 365.25 days • Months at given time of year • not linked to moon phase • 30 or 31 days (except February)

6. Modern Calendar • Gregorian Calendar (adopted by Pope Gregory) • 10 day error accumulated by 1582 • 10 days eliminated from calendar • October 4, 1582 followed by October 15, 1582 • Modified leap day rules • Remove one leap day every hundred years (i.e., no leap year in century years, e.g., 1800, 1900…) • Average length of year = 365.24 days • Except every 400 years (so 2000 was a leap year!) • Average length of year = 365.2425 days

7. Beginnings of Astrology • Babylonians believed: • Location of planets influence destiny of kings • Greeks: • Adopted Babylonian astrology • Believed individuals (personality/destiny) affected by planets • “Horoscope” - chart of planet locations • “Natal signs” - zodiacal location of sun/planets at birth • “House” - location in the sky

8. Science vs. Astrology • Astrology: “planets exert force at birth” • Science: “gravity only known planetary force” • Doctor produces larger effect than planet! • Astrology: “planets affect personality” • people born in given month share similar personalities • Science: • people w/ similar traits have birthdates distributed equally through year There is NO scientific support for astrology!!

9. Rise of Science • Greek Philosophy - Rational Thought • The Universe is knowable • The Universe is understandable • Observe the Universe • Think about it • Hypothesize / Explain • Test

10. Models of Universe • Must Explain • Night & Day • Motion of Sun • Motion and Phases of Moon • Motion of Planets • Inferior planets (Mecury & Venus) • always close to sun • never at opposition • Superior planets (Mars, Jupiter & Saturn) • Seen both near sun & at opposition • Retrograde motion • Superior planets: only near opposition

11. Greek Cosmology • Geocentric Model • Earth at center of Universe • Philosophy • Spheres / Circles simplest objects • Motion of planets on circles • Rate of motion is uniform • Fastest objects are closest • Ptolemy • Greek Astronomer • Alexandria, Egypt

12. Ptolemaic System • Start with circular path - deferent • Does not produce retrograde motion • Add epicycle - circle on deferent • Planet moves backward on inside of epicyle

13. Epicyclic Motion

14. Birth of Modern Astronomy • Copernicus • Ptolemaic system too complicated • Suggested Heliocentric model • Sun at center • Planets orbit sun • Orbits are circles • Planets in order • Mercury, Venus, Earth, Mars, Jupiter, Saturn

15. Copernican Model

16. Copernicus & Retrograde Motion

17. You observe Mars and find that it is undergoing retrograde motion. What time does it transit? • 6 am • Noon • 6pm • Midnight Opposition At highest point Where is the Sun?

18. Testing - the key to science • Greeks • Rational thought was sufficient • Inconsistencies blamed on faulty perception • Modern Science • Models make predictions • Verification provides support for model • A “Theory” is a generally accepted model

19. Geocentric vs. Heliocentric Predicted Phases of Venus • Geocentric: only crescent phases • Heliocentric: both full and crescent phases Observations show both!

20. Galileo • Built Telescope • Observed: the Moon, Jupiter, Jovian moons, Saturn, and Venus. • Saw: • Sunspots • Sun not perfect • Mountains, Craters, and Valleys on Moon • Moon not perfect • Moons orbiting Jupiter • Objects can orbit other bodies, not Earth! • Phases: Venus had both crescent and gibbous • Verified Heliocentric model predictions

21. Galileo - Sunspot Observations

22. Galileo ObservesMoons ofJupiter

23. Tycho Brahe • Danish Astronomer • Accurately measured positions • Mars • Enabled Quantitative Testing

24. Kepler • Worked for Tycho (in Prague) • Believed Heliocentric model (Copernicus) • To match Tycho’s data, model needed modification • Kepler’s Laws • Orbit is Ellipse • Sun at focus • Planet sweeps out equal areas in equal times • Period (P) - size (a = semi-major axis) relationship P2 = a3 P in years a in astronomical units (AU) (1 AU = size of earth’s orbit)

25. Ellipse focus focus a a = length of semi-major axis

26. Kepler’s 2nd Law time from 1 to 2 = time from 3 to 4 area 1-2-S = area 3-4-S

27. Kepler’s 2nd Law

28. Kepler’s 2nd Law • Equal area law implies that planets move: • Faster when closer to sun • Perihelion = planet closest to sun • Slower when farther from sun • Aphelion = planet farthest from sun

29. Kepler’s Model

30. Kepler’s 3rd Law P2 = a3 Relation between period of orbit and distance from Sun The farther a planet is from the Sun, the longer it takes to go around its orbit.