Tuesday, March 29, 2011

Phase of the moon

The moon is second only to the sun as the most dynamic feature of our sky. It moves across the sky from east to west once every day and each month it goes from being invisible to the brightest object in the night sky and back to invisible again. These patterns result from the motions of the earth, moon and sun relative to each other.

The factors that contribute to the daily and monthly lunar cycles are:
  1. The rotation of the earth around its own axis with a period of of 24 hours.
  2. The orbit of the moon around the earth1 with a period of 27.3 days.
  3. The orientation of the earth-moon system with the sun. This determines what part of the moon is illuminated.
Daily cycle of the moon
The 24 hour it takes the earth to rotate around its own axis is the primary driver of the daily movement of both the sun and the moon across the sky. The solar day, the period between times the sun is directly overhead at one location on the earth, is equal to roughly one earth rotation: 24 hours. The apparent path of the moon takes 50 minutes longer to complete one cycle. The additional 50 minutes results from the fact that the moon orbits the earth in the same direction as the earth rotates. 24 hours and 50 minutes is the time the earth needs to complete one rotation around its axis plus the distance the moon travels over that 24 hour period. In other words, the earth needs to rotate a little more than one full rotation in order to ‘catch up’ to the moon. This is often referred to as a tidal day because of the moon's role in the tides.

Monthly cycle (phases) of the moon
The moon does not give off any light of its own. It is only visible due to reflected sunlight. As only one half of the moon’s surface is bathed in sunlight at any given time, only that half is visible. The 27.3 day period of the moon’s orbit around the earth drives the monthly cycle of moon phases. Once every 27.3 days the side of the moon facing the earth is completely bathed in sunlight (the moon is full). Then, 13.7 days after each full moon, the side facing the earth is completely dark (new moon).

The following illustration explores the relationship between the rotation of the earth, the orbit of the moon, the orientation of the earth-moon system and the appearance of the moon from earth.  A demonstration of the model can be found below.

Video demonstration

1This is a simplification. A more accurate statement is the orbit of the moon-earth system its common center of mass with a period of 27.3 days.

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