# How to calculate geocentric conjunction time and moon altitude at a given time

Umm al-Qura calendar of Saudi Arabia determine the new moon if these criteria meet at 29th day:

• The geocentric conjunction occurs before sunset.
• The moon sets after the sun.

I've got the formula to calculate when the sun (seen by the observer) sets, considering observer's latitude, longitude, height (altitude from sea level), and the date (Julian Day). I would like to ask the formula to calculate:

1. When (the time) geocentric conjunction happens.
2. How much (the angle) the altitude of the moon (seen by the observer) at a given time is.

Thank you

• There's a famous scientist quote (maybe Newton?) that says that if the orbit of the Moon were any more complicated it'd make people give up trying to get to the bottom of it and it was just hard enough to give work for thousands of years of the best minds (like Hipparchos, Ptolomy, Muslims, Kepler and Newton) (I don't remember the exact words). If you want a formula that's any good it's going to be a lot more complicated.. Jun 10 '15 at 5:21
• I am curious how KACST calculate it. Jun 10 '15 at 21:38
• I don't know. I'd be interested to see too. But such a calendar would often be earlier than the traditional Islamic calendar. You can't code that, however, only look for the Moon. There must be mathematical Islamic calendar more accurate than that one, though. It seems like they made the calendar as simple as possible so people could get the new month from the western newspaper's weather page or something like that. I think there's one where the Moon has to be a x altitude when the Sun is at y altitude and at least this elongation apart, numbers chosen with observation. I like that one better. Jun 11 '15 at 2:27
• I assume you're familiar with ssd.jpl.nasa.gov/?horizons and things like naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/planets/… which can calculate geocentric lunar position to the best known approximations?
– user21
Jun 11 '15 at 14:09