How to Calculate the Phases of the Moon

Third phase of the moon

The Moon circles the earth once every 28 days, and during that time, it presents four different aspects--phases--resulting from the relationship between the Sun, the Moon and the Earth's shadow. The phases, while regular in the sense that they change about every seven days, vary as to the exact time that the phase changes. Calculating the exact time and date of the phase change relative to your position requires you to use the Nautical Almanac and a bit of math to get your local mean time using a synchronized timepiece and your exact longitude.

Things You'll Need

• Nautical Almanac
• Your exact longitude
• Radio capable of receiving broadcasts in the High Frequency ranges
• Timepiece recently synchronized with NIST radio stations WWV or WWVH

Instructions

1. The data pages of the Nautical Almanac are organized by date. The moon data is on the pages on the right side of the book. Find a date page where there is a phase change of the moon and record the time. The time given in the almanac is the time that the phase change occurs at the Greenwich Meridian.

2. Find the longitude representing the center of the nearest time zone. At sea, the nearest line of longitude evenly divisible by 15 is the center of a time zone. It is noted as positive in west longitudes and negative in east longitudes. The zone extends 7-1/2 degrees east of that line and 7-1/2 degrees west of that line.

3. 

   Calculate the difference between the hour angle at the center of the time zone you are in and the hour angle at your location. For example, if your current longitude is W 88 degrees 14 minutes and 38 seconds, convert the longitude to decimal degrees. Do this by dividing the minutes by 60 and the seconds by 3600 (60 minutes x 60 seconds). Add the result to the number of degrees. The result is your longitude in decimal degrees.

4. 

   Subtract your longitude in decimal degrees from the line of longitude representing the center of the time zone you are in if you are East of the center of the time zone. Add your decimal degrees to the longitude if you are West of the center of the time zone. Since 1 degree represents 1/15 (0.667) of the time zone, which is 1 hour wide, multiply the result by 0.667. The result is the number of minutes to be added (if West of the zone center) or subtracted (if East of the zone center) from the Zone Time for the change of the phase of the moon indicated in the Almanac.

Tips & Warnings

• The National Institute of Standards Radio Stations WWV and WWVH broadcast in the High Frequency bands, at 2.5, 5, 10, 15 and 20 megahertz providing worldwide coverage. The stations broadcast a time signal, based on the National Institute of Standards atomic clock, every minute. The time hack, which has a 15 second countdown at the end of each minute, includes Marine storm warnings and other information.

• Do not forget to correct Zone Time for daylight saving time, if required.

References

• H.O. Pub 9, Chapter 18
• UN Food and Agricultural Organization
• The Nautical Almanac, 1996; US Government Printing Office, 1995

Resources

• About the Moon