Before we get started on the converstions, let's explain a few things.
The International Date Line split the time zone on the 180 degree of the meridian so that the western half of that time zone was a day ahead of the eastern half of that time zone.
So to go eastwards from the 180 degree meridian, begin at the eastern half of that time zone. The Julian Date would be -0.5 local time there. On the western half of that time zone, the Julian Date would be 0.5 local time there. On the zero degree meridian, it is 0.0 local time. Going eastward from the 180 degree meridian and around the world in 24 time zones, you get these values:
When it is any time at the zero degree meridian, just add the decimal number to that time zone's Julian Period Days to get the local Julian Period day for the area. Note that I included two extra degrees East zones, 195 and 210, for computing local Julian Period Days for those zones that are advanced 13 and 14 hours respectively and west of the International Date line.
Also note that the Julian-1 and Gregorian calendars skip year zero because there was no such Roman numeral zero, so the year after 1 B.C. was 1 A.D.
For the Julian Period Day that matches January 1, 4713 B.C. Gregorian, we have to add 38 days to the Julian Period Day 0.
So, Julian Period Day 38 began at noon on February 8, 4713 B.C. Julian-1, or February 8, -4712 Julian-1 decimalized for mathematical operations. On the Gregorian calendar, Julian Period Day 38 began at noon on January 1, 4713 B.C. Gregorian, or January 1, -4712 Gregorian decimalized for mathematical operations.
The Julian Period Year is simply the Julian Period Day divided by the constant 365.25. Julian Period Day 0.000 in this calendar would be January 1, 0 Julian Period Calendar. In this calendar, there is a year zero. If there was such as thing as a Gregorian Period Calendar, the matching date would look like November 24, -1 Gregorian Period Calendar.
To convert from the Julian Period Day to the Julian Period Year...
Julian Period Day ÷ 365.25
JPY = JPD / 365.25
To convert from the Julian Period Year to the Julian Period Day...
Julian Period Year × 365.25
JPD = JPY * 365.25
To convert from the Julian Period Day to the Julian-1 Year...
(Julian Period Day ÷ 365.25) − 4712
Julian-1-Year = (JPD / 365.25) - 4712
To convert from the Julian-1 Year to the Julian Period Day...
(Julian-1 Year + 4712) × 365.25
JPD = (Julian-1-Year + 4712) * 365.25
To convert from the Julian Period Day to the Gregorian Year...
((Julian Period Day − 38) ÷ 365.24218967) − 4712
Gregorian-Year = ((JPD - 38) / 365.24218967) - 4712
To convert from the Gregorian Year to the Julian Period Day...
((Gregorian Year + 4712) × 365.24218967) + 38
JPD = ((Gregorian-Year + 4712) * 365.24218967) + 38
To convert from the Julian-1 Year to the Gregorian Year...
((((Julian-1 Year + 4712) × 365.25) − 38) ÷ 365.24218967) − 4712
Gregorian-Year = ((((Julian-1-Year + 4712) * 365.25) - 38) / 365.24218967) - 4712
To convert from the Gregorian Year to the Julian-1 Year...
((((Gregorian Year + 4712) × 365.24218967) + 38) ÷ 365.25) − 4712
Julian-1-Year ((((Gregorian-Year + 4712) * 365.24218967) + 38) / 365.25) - 4712
Julian Period Day 1461 began at noon on January 1, -4708 (4709 B.C.)
Julian Period Day 1721058 began at noon on January 1, 0 (1 B.C.)
Julian Period Day 2457402 began at noon on January 1, +2016 (2016 A.D.)
To get the Julian Day Number between two leap years on the Julian-1 (not the Gregorian) calendar:
((higher year) − (lower year)) × 365.25
Note: This formula works only on years that are multiples of four.
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