Astronomical Clocks ~ 1 day ~ 1 hour
Calendar A calendar is just a really slow clock ticks = days Assign some names/ patterns to days Allow predictions of future Question: How do you check the performance of a calendar?
Phases of the Moon
Important Dates (Northern Hemisphere) Summer solstice (~June 21): Pole most directly toward sun Longest day of year Sun rises at northernmost point Winter solstice (~December 21): Pole most directly away from sun Shortest day of year Sun rises at southernmost point Equinoxes (~March 21 and ~September 21): Pole tilt perpendicular to line between Earth and Sun Day and night have equal length
Problem Synodic period : 29.53 days (full-moon to full-moon) Tropical year : 365.24219 days (solstice to solstice)
Problem Moon phases provide good short-term cycle for marking time Can know place in cycle to within ~1 day by looking at sky Year is crucial cycle for agriculture: plant in spring, harvest in fall Can know place in seasonal cycle from sunrise/ sunset location Want calendar system that combines these Problem: 365.24219 29.538 = 12.368 Not nice numbers
Calendar Synchronization How to keep lunar calendar in synch with solar year? 1) Don t just allow months to drift with respect to seasons Modern example: Islamic calendar strictly lunar (based on sighting of crescent moon) ~11 days shorter than tropical year 2) Intercalation of months Modern example: Jewish calendar Variable length 12-month year: 353, 354, or 355 days Occasional 13-month leap years: 383, 384, or 385 days Adjust as needed to start w/ new moon, avoid having certain holidays fall on Sabbath days
Calendar Synchronization How to keep in synch with solar year, roughly with lunar? 3) Extra-calendrical days 12 30-day months = 360 days; 5 additional holidays Used by ancient Egyptians 10-12 strictly lunar months, starting after some significant date early Romans: reference to equinox, ~60 extra days Trobriand islands: reference to spawning of marine worm
Calendar Synchronization How to keep in synch with solar year, roughly with lunar? 4) Western system: lunar-derived months, not synched to moon 12 fixed-length months (28, 30,or 31 days) Occasional intercalated days leap years Base year: 365 days Leap year: 366 days Keeps seasonal milestones more or less fixed Not at all synchronized with moon Usually 1 full moon/month, sometimes 2
History Origin of leap-year system: ancient Rome After ~450 BCE, Rome used 12- month, 355 day calendar Well short of tropical year, needed occasional intercalated months Decision to add month made by pontifex maximus political office Intercalations motivated by politics Add month to keep allies in office longer Omit month to shorter rivals terms
Julian Calendar Calendar reformed by Julius Caesar in 46BC Fixed months at current lengths Leap year adding day to February every fourth year Required adding two months to re-synch calendar with equinoxes 46 BC had 445 days Initially implemented slightly incorrectly, refined by Augustus in 8AD
Gregorian Calendar Tropical year: 365.24219 days Julian year: 365.25 days pretty good, but still drifts Reform needed by 16 th century to keep Christian holidays in season Gregorian Calendar: Pope Gregory XIII assembled experts Astronomers, theologians Goals: 1) Fix position of equinoxes/ solstices in year 2) Determine formula for date of Easter
Gregorian Calendar New rules, still in use today: Leap year if: 1) divisible by 4 2) not a century year 3) unless divisible by 400 Gregorian year length: 365.2425 days 3300 years to lose 1 day Required dropping 10 days October 5 October 15, 1582 Delayed in non-catholic countries Britain (and American colonies): 1752 (drop 11 days) Russia/USSR: 1918 (after revolution) (drop 13 days)
World Calendar As always, an elegant alternative exists (that no-one will agree to) Worked out in 1963 12 months alternate 30, 31 days Extracalendrical December W Leap day June W Advantages Equal quarters of 91 days Jan 1 always a Sunday Disadvantage: Inertia Can t get US on metric system