Friday, January 29, 2010

Lunar Orbit: Perigee and Apogee Moon(s)

Properties of the lunar orbit
The orbit of the Moon is distinctly elliptical with an average eccentricity of 0.0549.

The non-circular form of the lunar orbit causes variations in the Moon's angular speed and apparent size as it moves towards and away from an observer on Earth.

The mean angular daily movement relative to an imaginary observer at the barycenter is 13.176358° to the east. The orientation of the orbit is not fixed in space, but precesses over time.

The Moon's elongation is its angular distance east of the Sun at any time. At new moon it is zero and the Moon is said to be in conjunction. At full moon the elongation is 180° and it is said to be in opposition. In both cases the moon is in syzygy, that is, the Sun, Moon and Earth are nearly aligned. When elongation is either 90° or 270° the Moon is said to be in quadrature.

The line of nodes of the lunar orbit (the line of the intersection of the plane of the lunar orbit with the plane of the ecliptic) has a retrograde motion, that is, it rotates towards the west (along the ecliptic) at a rate of 19°21′ per year, that is, with a period of 6,793 days or 18.60 years (nutation period).

Thus the node, or point at which the Moon's orbit crosses the ecliptic, moves steadily clockwise (viewed from celestial north), closely aligned with Earth's orbital path but in the opposite direction. The interval of time between the passage of the Moon through the same node is called the draconitic month, and is 27.2122 days. The times of the eclipses depend upon these factors.

Line of Apsides
Perigee is the distance of closest approach, whereas apogee is its farthest recession. The line joining these two points (the line of apsides) has a progressive motion or advances, that is, it slowly rotates counterclockwise in space in the plane of the Moon's orbit, that is, direct motion, making one complete revolution in 3232.575 days or about 8.85 years.

Lunar Standstill
When the ascending node of the moon's orbit coincides with the vernal equinox in the northern hemisphere, the declination of the moon in the sky reaches a maximum at 23°29′ + 5°9′ or 28°36′.

This is called the major standstill. Nine and a half years later, when the descending node has come to the same point, the angle is only 23°28′ − 5°8′ or 18°19′, and the declination of the moon is a minimum. This is the minor standstill.

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