Detailed Explanation
A more detailed explanation is best considered in terms of the path of the Sun and Moon on the celestial sphere, as shown in the first diagram. This shows the imaginary sphere of the sky, surrounding the Earth at the center. The Earth is aligned so that the North Pole is pointing straight up.
The Sun follows the ecliptic, which is tilted at an angle of e = 23.5° to the equator, and completes one revolution around the Earth in one year.
The Moon follows its path (shown dotted) which is inclined at an angle of about i = 5° to the ecliptic, and completes one revolution around the Earth in one month. The two points at which its path crosses the ecliptic are known as the nodes, shown as N1 and N2, and the line connecting them is known as the line of nodes. Due to precession of the lunar orbit, these crossing points, the nodes, slowly move around the ecliptic, taking 18.6 years, the nodal period, to complete one cycle.
From the diagram, it can be seen that when the line of nodes aligns with the equator, the Moon's orbit reaches either the steepest or the shallowest angle with the equator: the 5° tilt of the Moon's orbit either adds to or subtracts from the declination of the ecliptic. This is when a standstill occurs.
The effect of this on the declination of the Moon is shown in the second diagram. During the course of a month, as the Moon follows its path around the Earth, its declination swings from –m° to +m°, where m is a number in the range (e – i) ≤ m ≤ (e + i). At a minor standstill (which will happen in 2015), its declination during the month varies from –(e – i) = –18.5° to +(e – i) = 18.5°. During 2006, which was a major standstill, the declination of the Moon varied during each month from about –(e + i) = –28.5° to +(e + i) = 28.5°.
However, an additional subtlety further complicates the picture. The Sun's gravitational attraction on the Moon pulls it toward the plane of the ecliptic, causing a slight wobble of about 9 arcmin within a 6-month period. In 2006, the effect of this was that, although the 18.6-year maximum occurred in June, the maximum declination of the Moon was not in June but in September, as shown in the third diagram.
Read more about this topic: Lunar Standstill
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