For an ancient observation date, would it be wrong to change it to consecutive days?
The same year, month and day may not be the same day if the calendar is different; choose the rule first and then check both ways.
History records a date, but modern programs require JD. In addition to the year, month and day, you also need to know whether it uses the Gregorian calendar or the Julian calendar, whether it crosses the local calendar change, and how to enter the year number of "BC". The conversion is not to directly apply a calendar for today.
Guess first
Knowing the words "October 10, 1582", can we determine which day it must be?
Show answer and explanation
You also need to know the calendar and regional rules — Extended Gregorian/Julian calendars may have this tag, while some 1582 mixed calendar rules skip it.
Then connect experience and science
First write the calendar next to the date
The same string of year, month and day is not necessarily the same day in the Gregorian calendar and the Julian calendar. The program first clarifies the rules and rejects non-existent dates.
date + calendar → unique number of consecutive days
Use consecutive days to cross the calendar
In the Roman rules, October 4th is followed by October 15th. The date label jumps ten digits, but only one day has passed.
1582-10-04 → JD2299159.5; the next day JD2299160.5
Convert JD back to calendar
The inverse algorithm first adds 0.5, uses midnight as the boundary between integer days and decimals within the day, and then finds the year, month and day.
Z=floor(JD+0.5), F is the remaining decimal
The meaning of negative years and MJD should also be explained
The astronomical year has 0 years; MJD just subtracts 2,400,000.5 from JD. The starting point is different, and the time described does not change.
MJD = JD − 2400000.5
Expand the calculation
若 M≤2：Y←Y−1，M←M+12 A = floor(Y/100) BGregorian calendar = 2 − A + floor(A/4)；BJulian calendar = 0 JD = floor(365.25(Y+4716)) + floor(30.6001(M+1)) + D + B − 1524.5
D contains intraday decimals. floor is rounded to negative infinity and cannot be replaced by truncated decimals; select the calendar first, and then calculate the correction B.
give it a try
After entering the expanded date, you can change the year, month and day. First compare before and after the 1582 calendar change, and then use "check date from JD" to check back; the two conversions should point to the same day.
No need to memorize symbols
- JD / MJD
- Number of consecutive days / JD−2400000.5
- Astronomical Year 0
- Corresponding to the historical year 1 BC
- extended calendar
- Extending the same arithmetic rules to the past or future does not mean adopting them in local history.
- Roman Calendar Rules
- Specific mixing rules for 1582-10-04 followed by 1582-10-15
Algorithm, accuracy and scope of application
Supplementary Chapter 7 Date to JD, JD back to date, astronomical negative year, calendar selection and MJD. Forwardly reuse the verified Astro.jd, first independently verify the month length and leap year; reversely use the Z/F and A/B/C/D/E integer steps of Printed Page 63, and select the Gregorian or Julian calendar in explicit mode. The Roman 1582 hybrid model excludes October 5–14; does not claim a worldwide same-date calendar change. The forward direction supports astronomical years from −4712 to 3000, and the reverse direction supports JD0 to 3000000. Negative JD is not processed; year 0 is not written as "0 BC". 24h is regarded as 0h of the next day, and it will still advance according to the continuous JD when changing the calendar. MJD midnight is an integer and JD noon is an integer. This lesson only does calendar arithmetic, conversion within the same time scale, and does not mix in UT1/TT differences or time zones.
my understanding check
Year 0 in the astronomical calendar corresponds to which year in the ordinary historical calendar?
1 BC — Astronomical year numbers retain 0, and historical BC/AD years usually do not have 0 years.
How much should JD be increased from October 4 to 15, 1582 in Rome?
1 day — In this blending rule, they are adjacent dates.
What does MJD=0 correspond to?
JD=2400000.5 — MJD changed the zero point; the two are not the same number.
The continuous time did not jump due to the calendar change; what changed was the date label. The calendar, year number and time scale must be written clearly.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 7 chapter