6/18/2023 0 Comments Elliptical orbitThe left-hand scale is for the difference from mean lunation, while the right-hand scale is for the true anomaly. This relationship is quite apparent when viewed graphically.įigure 4-1 plots the difference from mean lunation (histogram) and the Moon's true anomaly (diagonal curves) for every New Moon from 2008 through 2010. Similarly, when New Moon occurs near apogee (true anomaly = 180°), the length of the lunation reaches a maximum (e.g., Dec 27). Table 4-1 shows that when New Moon occurs near perigee (true anomaly = 0°), the length of the lunation is at a minimum (e.g., Jun 03). In other words, it is the orbital longitude of the Moon with respect to perigee. The true anomaly is the angle between the Moon's position and the point of perigee along its orbit. What is the cause of this odd behavior? The last column in Table 4-1 gives a clue it contains the Moon's true anomaly at the instant of New Moon. Table 4-1 New Moon and Lunation Length in 2008 ![]() The duration now increases with each succeeding lunation until the maximum value of the year is reached of 06h 49m longer than the mean (Dec 27). The first lunation of the year (Jan 08) was 03h 23m longer than the mean.Ĭontinuing through 2008, the length of each lunation drops and reaches a minimum of 05h 48m shorter than the mean value (Jun 03). The third column is the difference between the actual and mean lunation. The first column lists the decimal date of every New Moon throughout the year (Terrestrial Dynamical Time), while the second column gives the duration of each lunation. The duration of the lunation actually varies from its mean value by up to seven hours.įor instance, Table 4-1 contains details for all lunations in 2008. The major problem with such calendars is that the year, based on the solar calendar, is not evenly divisible by a whole number of lunations.Ĭonsequently, most lunar calendars are actually lunisolar calendars (e.g., Chinese, Hebrew, and Hindu) that include intercalary months to keep the seasons in step with the year. Historically, the phases of the Moon have been used as the basis of lunar calendars by many cultures around the world. When the synodic month is measured from New Moon to New Moon, it is sometimes referred to as a lunation, and we will follow that usage here. This explains why the mean synodic month is longer than the sidereal month.Īccording to astronomical convention, New Moon is defined as the instant when the geocentric ecliptic longitudes of the Sun and Moon are equal. This is nearly 2.21 days longer than the sidereal month.Īs the Moon revolves around Earth, both objects also progress in orbit around the Sun.Īfter completing one revolution with respect to the stars, the Moon must continue a little farther along its orbit to catch up to the same position it started from relative to the Sun and Earth. The mean length of the synodic month is 29.53059 days (29d 12h 44m 03s). ![]() The Moon has no light of its own but shines by reflected sunlight.Īs a consequence, the geometry of its orbital position relative to the Sun and Earth determines the Moon's apparent phase. The most familiar lunar cycle is the synodic month because it governs the well-known cycle of the Moon's phases. Nevertheless, these instantaneous parameters are of value in understanding the Moon's complex motions particularly with respect to the three major orbital cycles that govern eclipses. The ever changing distances and relative positions between the Sun, Moon, and Earth, the inclination of the Moon's orbit, the oblateness of Earth, and (to a lesser extent) the gravitational attraction of the other planets all act to throw the Moon's orbital parameters into a constant state of change.Īlthough the Moon's position and velocity can be described by the classic Keplerian orbital elements, such osculating elements are only valid for a single instant in time (Chapront-Touze' and Chapront, 1991). ![]() The mutual gravitational force between the Sun and Moon is over twice as large as between the Moon and Earth.įor this reason, the Sun plays a dominant role in perturbing the Moon's motion. These three cycles and the harmonics between them determine when, where, and how solar and lunar eclipses occur. However, there are three other orbital periods or months that are crucial to the understanding and prediction of eclipses. The lunar orbital period with respect to the stars (sidereal month) is 27.32166 days (27d 07h 43m 12s). Thus, the Moon's center-to-center distance from Earth varies with mean values of 363,396 km at perigee to 405,504 km at apogee. The Moon revolves around Earth in an elliptical orbit with a mean eccentricity of 0.0549. Eclipses and the Moon's Orbit Fred Espenak, NASA's GSFC Index
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