Is the 60th day of this year February 29th or March 1st?
Dates, days of the week, and year numbers are all different labels for the same day.
When scheduling continuous observations, you might say "starting on the 60th day of the year." However, ordinary years are different from leap years, and the rules for leap years are also different between the Gregorian calendar and the Julian calendar. If you write the rules clearly, you can convert back and forth between dates and serial numbers.
Guess first
Is the 60th day of all years March 1st?
Show answer and explanation
No, it might be February 29th in a leap year — There is an extra day in February in leap years, and the subsequent day sequence correspondence will move.
Then connect experience and science
The first day counting from January 1st
The day sequence is not a program index starting from 0. January 31st is the 31st day, followed by February.
N starts from 1
First decide whether this year is a leap year
There are usually no leap years in the Gregorian calendar unless it is divisible by 400; the Julian calendar treats leaps every four years.
The age may be different in different calendars
Month, day and serial number can be checked each other
First use the year, month and day to calculate N, and then back-calculate the month and day according to the same calendar. It should return to the original position.
Pouplier's formula changes N back to M and D
Weeks go in their own continuous cycle
The week is calculated by a seven-day cycle of consecutive days, and cannot be guessed just based on the day of the month.
week = floor(JD+1.5) mod 7
N is the serial number starting from 1 within the calendar year. Confirm the leap year first, and then accumulate or back-calculate the month and day from the month; the modulo 7 result of the week formula is mapped to the name of the week according to this lesson, and 0 cannot always be understood as Monday.
give it a try
Compare the 60th day of 2023 and 2024, and try 1900 again: it is an ordinary year in the Gregorian calendar, but a leap year in the Julian calendar.
No need to memorize symbols
- N
- Day sequence within the year counting as 1 starting from January 1st
- K
- Take 1 for leap years and 2 for ordinary years.
- weekday
- The 7-day recurring remainder after JD+1.5 rounding
Algorithm, accuracy and scope of application
Implement the day of the week method, day order formula within the year, and Pouplier's reverse month and day algorithm on printed pages 65–66 of Chapter 7. The leap year rules of the Gregorian calendar and the Julian calendar are dealt with separately; this lesson does not mix the 1582 calendar jump date, please use the date/JD lesson for the historical mixed calendar. The year number starts from 1 and is not a zero-based array. The inverse algorithm is not available for clear return of 366 in ordinary years or illegal dates; the week is calculated through continuous JD and does not change due to the selection of month and day display mode. The day sequence reciprocity and independent JD difference verification of each valid day for many centuries are used, and a few calendar screenshots are not used as evidence of the algorithm.
my understanding check
What is the first day of the year?
January 1 — The day order in this lesson starts with 1 instead of 0.
Is 1900 definitely a leap year in both the Gregorian and Julian calendars?
No, the two sets of rules are different — There is no leap year in 1900 in the Gregorian calendar, and there is a leap year in 1900 in the Julian calendar.
What should be done if the 366th day is entered in an ordinary year?
A clear reminder that there is no such day this year — You cannot secretly change the day sequence within an illegal year to another year.
First determine the calendar and leap year, and then turn the "number" back to the month and day; the week will cycle every seven days along the continuous time.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 7 chapter