Navigation Exercise 3

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The Moon does not always follow the same path through the sky at the same time; instead, it varies on an eighteen year cycle due to the Dragon Saros. Wherefore determining the actual location is too advanced for this guidebook. Ignoring the variation of the Moon due to Auge, it is possible to find the average or expected position of the Moon at any time, and the time and angle of Moon Rise and Moon Set. Beyond the Arctic Circle, this method is unreliable. The method used is the same as for the Sun, except as the Lunar Declination changes far more rapidly, this is calculated for the precise time instead of the entire day.

You will need to know

• Current Latitude (negative for Southern Hemisphere)
• Days from Equinox (negative during Northern Winter)
• Current Time

Alusian Constants

These values vary for other planes.

• Days in a Year = 364.
• Full Moons in a Year = 13.
• Days between Full Moons = 28.
• Days for Moon to pass through the Zodiac = 26.
• Average Moonday Length = 24 hrs 53' 20".
• Maximum Declination = 28.8 degrees.

Lunar Declination

Unlike the Sun's seasonal declination, the Moon's declination changes significantly during one day. You need to calculate the Declination at the current time

• Current Lunar Declination = ArcSine(Sine((Days from Equinox + time since midnight) / 26 * 360) * Sine(Maximum Declination))

First Results

• Hours of Moonlight = Moonday/2 + (ArcSine(Tan(Current Lunar Declination)*Tan(Latitude)))/180 * Moonday

• Lunar Dawn (Hours) = Moonday /2 - Hours of Moonlight /2
• Lunar Dusk (Hours) = Moonday /2 + Hours of Moonlight /2
• Moon Bearing at Lunar Dawn = ArcCosine(-Sine(Lunar Declination at Dawn)/Cosine(Latitude))
• Moon Bearing at Lunar Dusk = 360 - ArcCosine(-Sine(Lunar Declination at Dusk)/Cosine(Latitude))
• Moon Elevation at Lunar Zenith = (90-Latitude) + (Lunar Declination at Zenith)

Second Results

• Day Progression = (Number of hours from Lunar Zenith) * 360 / Moonday
• Moon X-Axis = Cosine(Day Progression)*Cosine(Current Lunar Declination)*Sine(Latitude) - Sine(Current Lunar Declination)*Cosine(Latitude)
• Moon Y-Axis = -Sine(Day Progression)*Cosine(Current Lunar Declination)
• Moon Z-Axis = Cosine(Day Progression)*Cosine(Current Lunar Declination)*Cosine(Latitude) + Sine(Current Lunar Declination)*Sine(Latitude)

Note X-Axis² + Y-Axis² + Z-Axis² = 1

Final Results

• Moon Bearing = ArcTan(Moon Y-Axis / Moon X-Axis)
• Moon Elevation = ArcSin(Moon Z-axis)

To determining the actual location, you will need to allow for the correct Moon Zenith, the regression of the elliptical orbit relative to the sun, and the progression of the nodes. You'll need to find the Lunar Declination at Zenith, by approximating Lunar Zenith, calculating the Lunar Declination at this time, and use this to calculate a more precise Zenith estimate. Three iterations give a precision of +/- 2 minutes outside the Arctic circle. Calculating the Draconic and Anomalistic progressions is too hard to outline here.