By Nga Lai Wong Chelsea Lin Chan Chi Wai Aletheia Mohn

The Gregorian calendar The Gregorian calendar the reform of Julian calendar the reform of Julian calendar the reform Roman calendar the reform Roman calendar designed from the orbital period that the Earth surrounds the sun designed from the orbital period that the Earth surrounds the sun one orbital period = one year (approximately 365 days)‏ one orbital period = one year (approximately 365 days)‏ also called solar calendar also called solar calendar

The Leap Year Rule The Leap Year Rule Every year that is exactly divisible by four is a leap year Every year that is exactly divisible by four is a leap year years that are exactly divisible by 100are still leap years when the centurial years that are exactly divisible by 400. For example, the year 1900 was not a leap year; the year 2000 was a leap year. years that are exactly divisible by 100are still leap years when the centurial years that are exactly divisible by 400. For example, the year 1900 was not a leap year; the year 2000 was a leap year.

Tropical year – 365days 5hrs 48min 46s Tropical year – 365days 5hrs 48min 46s No. of days in 400 years = 365 × = No. of days in 400 years = 365 × = Average no. of days in a year = ÷ 400 = Average no. of days in a year = ÷ 400 = No. of days in one tropical year = No. of days in one tropical year = Error = = Error = =

Falls behind the seasons because the slowing down of the Earth's rotation makes each day slightly longer over time In the year 4000, the calendar will fall behind by at least 0.8 but less than 1.1 days I In the year 12,000 the calendar would fall behind at least 8, but less than 12 days Error (due to Calendar seasonal error):

Chinese Calendars

The Relationship 1. Metonic cycle - a period of 19 tropical years = 235 synodic months - Mathematical basis : 19 tropical years = days 235 synodic months = days - - Application in traditional calendars : predict eclipses other uses : flight planning for lunar spacecraft missions.

Enrichment Prediction of ellipse Prediction of ellipse Sky maps Sky maps Stellar Magnitudes Stellar Magnitudes Trigonometry Trigonometry

Advantages and disadvantages of different calendars 1. Advantages and disadvantages of different calendars - lunar calendar : simple format based on the shape of the moon ; no fixed date for the 1st day of the year - solar calendar : fixed no. of days in different months ; no relationship with the moon - combined calendar : both the advantages of the above calendars ; too complicated in calculation

Differences in Chinese & Western astronomy: I. names of stars or constellations II. 'division' of the sky for observation III. use of celestial coordinate system IV. degrees of the earth V. concept about the sky VI. methods of calculation