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You can change the date shown and get phases of the moon for any
date you choose. However no checks are currently made as to the
validity of whatever you enter, so make sure you don't enter silly
dates, or you will get surprising answers. The Julian date mechanism
is quite robust, and will correctly extend both far into the future
and way back into antiquity, but the moon algorithm may not be valid
for more than a few hundred years ahead or behind the present.
Note that there is no such thing as the year zero (the Romans hadn't grasped the concept of zero) so you will get an error if you try to enter such a year. The sequence goes ..., 2BC, 1BC, 1AD, 2AD, ..., with no 0AD in the middle, but the program will correct for this by adding one to negative years. Because of changes to the calendar when things got out of step a few hundred years ago, some days don't exist at all, so you may see some surprising gaps between moon phases if you explore these periods.
If you are West of the Greenwich Meridian, then your offset will be a negative value (it is earlier in the day in your timezone), whereas if you are East of it then your offset will be positive (it is later in the day in your timezone). Daylight savings time should be taken into account if it is in effect, by adding one or two hours to the offset.
The correct value is the one which, when added to GMT, gives your local time. Eg, EST would be Minus 5, BST would be Plus 1, for Nepal it would be Plus 5.75. All fractions are rounded to the nearest 15 minutes.