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For a general discussion of Julian day numbers see Julian Day Numbers, and in particular the explanation of the difference between astronomical and chronological Julian day numbers given in Section 4 and in Section 5.
To put it briefly, astronomical Julian days correspond to 24-hour periods which begin at noon GMT, with 0 AJD beginning at noon on -4712-01-01 in the Julian Calendar, whereas chronological Julian days correspond to 24-hour periods which begin at midnight GMT at the start of -4712-01-01 Julian. (But see the exception discussed at the end of this section.) A Julian date is a Julian day number with a fractional component representing the time within the day. Thus the astronomical Julian date 1.25 AJD corresponds to 18:00 GMT on -4712-01-02 JC, whereas the chronological Julian date 1.25 CJD corresponds to 06:00 GMT on -4712-01-02 JC. Chronological Julian dates relative to the prime meridian (0 degrees longitude) are always 0.5 greater than the corresponding astronomical Julian dates (since 0.5 days = 12 hours).
An astronomical Julian date is independent of location on the Earth, since it is always relative to the prime meridian of zero degrees. A chronological Julian date, however, is longitude-dependent. A chronological Julian day begins at midnight local time, not midnight GMT. (However, when the concept is used without reference to any particular location then by default the prime meridian of zero degrees is assumed.)
In this software, when local time is set to GMT then CJD exceeds AJD by exactly 0.5 (corresponding to the 12-hour difference in the start of the day). In this case, switching between GMT and local time does not change CJD.
When local time differs from GMT then AJD and CJD will differ by 0.5 plus or minus some quantity (<= 0.5) which depends on the offset of local time from GMT. E.g., if local time is GMT plus six hours (0.25 days) then CJD will exceed AJD by 0.5 + 0.25 = 0.75. In this case, switching between GMT and local time changes CJD (and may change the dates displayed, as in the example of Thursday the 10th given above).
In a calendar whose days (nucthemerons) are divided into 24 hours and 60 minutes a chronological Julian day is the period from one 00:00 to the next. Normally 00:00 occurs at midnight local time (or midnight at some given meridian of longitude for a particular timezone). However in the Hermetic Lunar Week Calendar 00:00 occurs six hours after midnight, so a chronological Julian day in this calendar runs from approximately dawn to the next dawn. This means that chronological Julian dates, when used with respect to the Hermetic Lunar Week Calendar take their fractional component from the time elapsed from six hours after midnight, not midnight itself. So, for example, noon at Greenwich on 2007-01-01 is Julian date 2,454,102.5 for calendars whose days begin at midnight, but is 2,454,102.25 for the Hermetic Lunar Week Calendar. The display of the chronological Julian date in this software always assumes days beginning at midnight, even when the Date/time box shows a HLW date.
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