Equation relating date and moon phase.

[BigMoosie]

Hi, how would I create an algorith that has three inputs, d/m/y and outputs the phase of the moon. Or if anybody knows one that just inputs one number like the days since the start of the millenium it would be just as useful.

Also, for what length of time would such an equation / algorith be likely to hold true?

[Non-praying Mantis]

I think the folks in S&S might have an answer to your question.

NPM, E/C Moderator

[Oxymoron]

There isn't a formula for this - as such. The actual path of the moon is very complex because it is really governed by an n-body problem between itself, Earth, the Sun, and the other planets, with the addition of tidal forces between Earth and moon. There are power series solutions to Newton's equations - they contain many thousands of terms involving complex coefficient and the orbital elements of the various bodies - and they are only valid for "short" time frames. How long depends on how big an error you can accept :D However, the good answer is that these have been pre-calculated for you (well, astronomers) and published in an ephemeris. I would be shocked if there was not an online link to an ephemeris database which you can write a short query app for and just suck the data out without having to worry about the math (which is truly horrible).

[Huon]

http://www.nightskyobserver.com/software.htm

[BigMoosie]

I realise that it is not possible to predict accurately on a long term, but I was wonderin if there was some kind of formula, that doesnt necessarily have to be perfect but just good enough so I can put it on a website and know that it will work for the next 5 years or whatever.

[Huon]

Try this other link :
http://www.moonphasecalendar.com/moon_phase_emergency.htm

<quote>
First of all, try to stay calm. Now count the number of days (whole days and fractions thereof) since 2001 January 1, 0h UT. Next, calmly multiply this number by 850. Then, add to this number 5130. Finally, divide this number by 25101. The number you have now is the number of lunations (whole lunations and fractions thereof) that have elapsed since some new moon way back when (in December 2000). What is so nice about this algorithm is that it only requires you to remember three number (850, 5130, and 25101). Additionally, this algorithm is accurate beyond belief. Its initial synchronization with the lunar month is off by .5769 parts in 25101. To eliminate this error, just change 5130 to 5130.5769. Additionally, the length of the lunar month is matched perfectly to the accuracy of human knowledge. The only expected long term drifting will result from the slowing of the Earth's rotation.

Now for an example. Lets pretend I am having a moon phase emergency. Lets say, one afternoon, I get lost in the woods around Bristol, Florida, USA and I desperately want to know if the moon will be up before sunset. Pretend the date is March 28, 2002. First I would count the days since 2001 January 1, 0h UT. I would add 365 (to get from 2001 to 2002) and 31 (for January) and 28 (for February) and 27 (to get from March 1 to March 28) and .75 (to get from midnight to about sunset) and 85/360 (for my longitude from UT (which I think I would round off to .25)). I would get a total of 452.00 (after rounding as before mentioned). Now multiply by 850, add 5130, and divide by 25101. I would now have 15.510... . The meaningful part is the .510... which tells me that the moon is past full (.500) and should not rise until after sunset. Oh woe is me. I will be caught in the dark. The excess (.010...) can be multiplied by 24 to show that the moon will rise about .24 hours after sunset or about 14 minutes. That's not so bad. The twilight won't even have wore off before the moon gets up. So it looks like everything will be okay. Wow, that was close. (Don't forget that because the moon and Earth have elliptical orbits, this time can be expected to be off by up to 30 or so minutes. Other factors can throw things off too, most notably, extreme latitudes. But luckily in this example, latitude is not very high and 14 plus 30 is still within Florida's twilight zone.)

MOON PHASE EMERGENCY: RESOLVED

And your story can have a happy ending too if you can only remember three numbers, ...
850, 5130, and 25101.
<end quote>