**MOON PHASE** Weather data – Derived Variables

*(Vantage Pro2, Vantage VUE and Vantage Pro, and all WeatherLink 5.Xversions and later)*

Parameters Used: Latitude, Longitude, Time and Date, Time Zone, Daylight Savings Time Setting

Sufficient accuracy is obtained from the following formula for *i*, the phase angle:

*i* = 180° – *D* – 6.289° sin *M’* + 2.1° sin *M* – 1.274° sin (*2D* – *M’*) – 0.658° sin *2D*

where

- D is the mean elongation of the moon (the maximum angular distance between the earth and the moon)
- M’ is the moon’s mean anomaly (angular distance, measured from where the moon is closest to the earth in its orbit, if it moved around the earth at a constant angular velocity)
- M is the sun’s mean anomaly (angular distance, measured from where the earth is closest to the sun in its orbit, if it moved around the earth at a constant angular velocity)

and the terms in the equation provide increasing amounts of mean accuracy to calculate the phase angle as follows (hr:min):

- D = 20:57
- 6.289° sin M’ = 8:35
- 2.1° sin M = 4:26
- 1.274° sin (2D – M’) = 1:56
- 0.658° sin 2D = 0:38

Note: these equations assume that the sun and moon both revolve around the earth, for simplicity. However, when addressing the positions in orbit, it is actually the earth revolving around the sun, so this should be understood when trying to understand the physical meaning described in the definitions.

The equations for *D*, *M*‘ and *M* are as follows:

*D* = 297.8501921 + 12.19074911 **days *

*M’* = 134.9633964 + 13.06499295 *days

M = 357.52911 + 0.985600281 *days,

Where days (in days and fractions of days) is the number of days since Jan 1st, 2000 at 12:00 UTC

Local time needs to be converted to UTC in order to be used in the formulas:

UTC = Local Time – Time Zone Offset (including adding one hour for daylight savings if and when in use)

The phase angle is modified so that it can be used to determine whether the moon is waxing (illuminated portion increasing in size) or waning (decreasing in size):

**If i >= 180°, then k = 1 – (k / 2)**

Now, the phase angle can be used to determine which phase the moon is in:

*i* = (*i* * 8) + 0.5

The result is interpreted as follows:

- 0 = New Moon,
- 1 = Waxing Crescent,
- 2 = First Quarter,
- 3 = Waxing Gibbous,
- 4 = Full Moon,
- 5 = Waning Gibbous,
- 6 = Last Quarter,
- 7 = Waning Crescent

WEATHERLINK BULLETIN GRAPHIC

*k* is the fraction of the moon’s disk that is illuminated. It is used to draw the moon phase icon in the Bulletin.

*k* = (1 + cos *i*)/ 2

*k* is a number between zero and one that indicates how much of the moon’s disk should be drawn as lit. It indicates the “terminator’s” (boundary between light and dark face) position on the observed face of the moon.

*k* can also be interpreted as listed below

0.00 = New Moon

0.25 = First Quarter

0.50 = Full Moon

0.75 = Last Quarter

**REFERENCE**

Meeus, Jean: “Astronomical Algorithms“. Willman-Bell, Richmond, VA, 2nd Ed. 1998.

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