# Moon phase calculator

### Introduction

If you like mechanical watches, sooner or later you'll have to adjust a moon-phase dial. The way this dial work is usually very simple: a gear ratio of 118:1 driven by the hour wheel simply makes the dial rotate by half a turn every 29.5 days. This is not a bad approximation since the moon cycle has an average duration (called "synodic month") of 29 days, 12 hours 44 minutes and 3 seconds, meaning that the reading will by off by one day in about 32 months, which is acceptable considering the precision of a mechanical watch.

Now the problem is how to set this dial according to the current moon phase; even supposing that the sky is clear and the moon is clearly visible, looking at the moon is not enough to determine its age and how the dial should be rotated to indicate the correct phase. Except for new and full moon, the image displayed on the dial has not the same shape as the real moon. So unless adjusting the watch at these precise moments, it's not easy to guess the exact position.

Knowing the age of the moon is already better, since one can set the dial for a new moon and than count the ticks from there, knowing that there is one (or two) ticks per day, depending on the mechanism. It would be even easier if one could see how the dial should look like and adjust accordingly, and this is the idea of this calculator.

### Calculating the phase is not easy

In order to display a reference image of the moon to make adjustment of the dial easier, one has to start by calculating the current phase with sufficient precision. The first idea was to start from the date and time of a known new moon in the past and count a number of synodic months until the current date is found and see how many days elapsed from the last new moon. With a computer is easy to take into account the exact length of 29 days, 12 hours 44 minutes and 3 seconds and this would be hard to achieve with gears and pinions.

When this was implemented, the result was quite disappointing: the dates of the new moons were considerably off. This is because the length of a synodic month is not constant and can vary from a minimum of 29 days 6 hours and 14 minutes to a maximum of 29 days 19 hours and 12 minutes due to perturbing effects of the Sun on the Moon's eccentric orbit. On top of this, several long (or short) months can happen in a raw and the phase calculated this way can be off by almost one day. So I looked for a better way to calculate.

### The selected solution

In order to precisely calculate the correct phase, a very good reference is a book written Jean Meeus called "Astronomical Formulas For Calculators" which explains many astronomical algorithms and how to implement them. Unfortunately, there is no ready recipe for the current moon phase and several different algorithms would need to be put together. Furthermore, implementing such an algorithm wold require extensive testing to make sure the results are accurate, adding complexity to this method.

So another solution was selected: a list of known moon phases was built and we simply look for the current date into it. The list used here is based on the predictions calculated by Fred Espenak (NASA/GSFC) that are freely available. Here I included only data for the current century that should be enough for me. In the year 2100, if I'm still here, please remind me to put some fresh data on this page ;-)

The current date and time zone information are read from your browser (not from the server) because these are usually set in your locale and won't need any further calculation. Only dates within this century (from 2001 to 2100) are accepted, but this should be enough for adjusting a mechanical watch. Time is expressed in 24h format. Hit the "refresh" button of your browser to update the calculations.

### Current moon status

Last new moon: ---.

Moon age: --- (--- %).

Current synodic month length: ---.

Current date and time (just to check): ---.

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### Moon dial

The image below shows how the current moon should look like on the dial of a mechanical watch. As one can see, the shape of the moon bright surface is only a rough imitation of the real moon.

### Moon image

As a comparison, the image below shows how the current moon really looks like. Please remark that this image is based on a single picture of the moon and doesn't take into account movements like libration and is calculated with a simple geometrical model that doesn't consider effects like twilight or shades due to surface relief.