cweston - 2 months ago 29

C# Question

I need to convert from a standard **Gregorian** date to a **Julian** day number.

I've seen nothing documented in C# to do this directly, but I have found many posts (while Googling) suggesting the use of ToOADate.

The documentation on ToOADate does not suggest this as a valid conversion method for Julian dates.

Can anyone clarify if this function will perform conversion accurately, or perhaps a more appropriate method to convert DateTime to a Julian formatted string.

This provides me with the expected number when validated against Wikipedia's Julian Day page

`public static long ConvertToJulian(DateTime Date)`

{

int Month = Date.Month;

int Day = Date.Day;

int Year = Date.Year;

if (Month < 3)

{

Month = Month + 12;

Year = Year - 1;

}

long JulianDay = Day + (153 * Month - 457) / 5 + 365 * Year + (Year / 4) - (Year / 100) + (Year / 400) + 1721119;

return JulianDay;

}

However, this is without an understanding of the magic numbers being used.

Thanks

Answer

OADate is similar to Julian Dates, but uses a different starting point (December 30, 1899 vs. January 1, 4713 BC), and a different 'new day' point. Julian Dates consider noon to be the beginning of a new day, OADates use the modern definition, midnight.

The Julian Date of midnight, December 30, 1899 is 2415018.5. This method should give you the proper values:

```
public static double ToJulianDate(this DateTime date)
{
return date.ToOADate() + 2415018.5;
}
```

As for the algorithm:

`if (Month < 3) ...`

: To make the magic numbers work our right, they're putting February at the 'end' of the year.`(153 * Month - 457) / 5`

: Wow, that's some serious magic numbers.- Normally, the number of days in each month is 31 28 31 30 31 30 31 31 30 31 30 31, but after that adjustment in the if statement, it becomes 31 30 31 30 31 31 30 31 30 31 31 28. Or, subtract 30 and you end up with 1 0 1 0 1 1 0 1 0 1 1 -2. They're creating that pattern of 1s and 0s by doing that division in integer space.
- Re-written to floating point, it would be
`(int)(30.6 * Month - 91.4)`

. 30.6 is the average number of days per month, excluding February (30.63 repeating, to be exact). 91.4 is almost the number of days in 3 average non-February months. (30.6 * 3 is 91.8). - So, let's remove the 30, and just focus on that 0.6 days. If we multiply it by the number of months, and then truncate to an integer, we'll get a pattern of 0s and 1s.
- 0.6 * 0 = 0.0 -> 0
- 0.6 * 1 = 0.6 -> 0 (difference of 0)
- 0.6 * 2 = 1.2 -> 1 (difference of 1)
- 0.6 * 3 = 1.8 -> 1 (difference of 0)
- 0.6 * 4 = 2.4 -> 2 (difference of 1)
- 0.6 * 5 = 3.0 -> 3 (difference of 1)
- 0.6 * 6 = 3.6 -> 3 (difference of 0)
- 0.6 * 7 = 4.2 -> 4 (difference of 1)
- 0.6 * 8 = 4.8 -> 4 (difference of 0)

- See that pattern of differences in the right? That's the same pattern in the list above, the number of days in each month minus 30. The subtraction of 91.8 would compensate for the number of days in the first three months, that were moved to the 'end' of the year, and adjusting it by 0.4 moves the successive differences of 1 (0.6 * 4 and 0.6 * 5 in the above table) to align with the adjacent months that are 31 days.
- Since February is now at the 'end' of the year, we don't need to deal with its length. It could be 45 days long (46 on a leap year), and the only thing that would have to change is the constant for the number of days in a year, 365.
- Note that this relies on the pattern of 30 and 31 month days. If we had two months in a row that were 30 days, this would not be possible.

`365 * Year`

: Days per year`(Year / 4) - (Year / 100) + (Year / 400)`

: Plus one leap day every 4 years, minus one every 100, plus one every 400.`+ 1721119`

: This is the Julian Date of March 2nd, 1 BC. Since we moved the 'start' of the calendar from January to March, we use this as our offset, rather than January 1st. Since there is no year zero, 1 BC gets the integer value 0. As for why March 2nd instead of March 1st, I'm guessing that's because that whole month calculation was still a little off at the end. If the original writer had used`- 462`

instead of`- 457`

(`- 92.4`

instead of`- 91.4`

in floating point math), then the offset would have been to March 1st.