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I've been using this for a while, but recently used it to check the New moon times in my location (Melbourne, Australia) and it appears the moon times are incorrect. As of today (8-Feb-2016) Sun Cult is showing the next New Moon as 8/3/2016 10:12:27, whereas my local (Melb. Planetarium) is showing the New Mon at 09-Mar-2016, 11:54. That's more than one whole day out... Which servers does Sun Cult use for it's moon phases/times?

Sun Cult does not use any servers for the moon phases/times.
It calculates everything internally (in Javascript).

However there is known deficiency in that the calculations can generate different values compared to published lists or other reference calculations - seemingly up to 1 day discrepancy.

Unfortunately I don't know where the error(s) is/are in the code, nor do I have access to the reference material for the derivation of the equations.

See this for further information:

https://sourceforge.net/p/suncult/bugs/6/