Description
The saros, a period of 6585.322 days (14 normal years + 4 leap years + 11.322 days, or 13 normal years + 5 leap years + 10.322 days), is useful for predicting the times at which nearly identical eclipses will occur, and derives from three periodicities of the lunar orbit: the synodic month, the draconic month, and the anomalistic month. For an eclipse to occur, either the Moon must be located between the Earth and Sun (for a solar eclipse) or the Earth must be located between the Sun and Moon (for a lunar eclipse). This can happen only when the Moon is new or full, respectively, and repeat occurrences of these lunar phases are controlled by the Moon's synodic period, which is about 29.53 days. Most of the times during a full and new moon, however, the shadow of the Earth or Moon falls to the north or south of the other body. Thus, if an eclipse is to occur, the three bodies must also be nearly in a straight line. This condition occurs only when a full or new Moon passes close to the ecliptic plane (during an eclipse season) which is the case around the time when it passes through one of the two nodes of its orbit (the ascending or descending node). The period of time for two successive passes through the ecliptic plane at the same node is given by the draconic month, which is 27.21 days. So the conditions of an eclipse are met when the new or full moon is near one of the nodes, which occurs every 5 or 6 months (the Sun, being in conjunction or opposition to the Moon, is also at a node of the Moon's orbit at that time - this happens twice in an eclipse year). However, if two eclipses are to have the same appearance and duration, then also the distance between the Earth and Moon, as well as the Earth and Sun, must be the same for both events. The time it takes the Moon to orbit the Earth once and return to the same distance is given by the anomalistic month, which has a period of 27.55 days.
The origin of the saros comes from the recognition that 223 synodic months is approximately equal to 242 draconic months, which is approximately equal to 239 anomalistic months (this approximation is good to within about 2 hours). After one saros, the Moon will have completed roughly an integer number of synodic, draconic, and anomalistic months, and the Earth-Sun-Moon geometry will be nearly identical: the Moon will have the same phase, be at the same node, and have the same distance from the Earth. In addition, because the saros is close to 18 years in length (about 11 days longer), the earth will be nearly the same distance from the sun, and tilted to it in nearly the same orientation (same season). If one knew the date of an eclipse, then one saros later, a nearly identical eclipse should occur. Note that during this 18-year cycle, about 40 other solar and lunar eclipses take place, but with a somewhat different geometry. Note also that the saros (18.03 years) is not equal to an integer number of revolutions of the Moon with respect to the fixed stars (sidereal month of 27.32 days). Therefore, even though the relative geometry of the Earth-Sun-Moon system will be nearly identical after a saros, the Moon will be in a different position with respect to the stars. This is due to the fact that the orbit of the Moon precesses.
A complication with the saros is that its period is not an integer number of days, but contains a multiple of ⅓ of a day. Thus, as a result of the Earth's rotation, for each successive saros, an eclipse will occur about 8 hours later in the day. In the case of an eclipse of the Sun, this means that the region of visibility will shift westward by 120°, or one third of the way around the globe, and the two eclipses will thus not be visible from the same place on Earth. In the case of an eclipse of the Moon, the next eclipse might still be visible from the same location as long as the Moon is above the horizon. However, if one waits three saroses, the local time of day of an eclipse will be nearly the same. This period of three saroses (54 years 1 month, or almost 19756 full days), is known as a triple saros or exeligmos (Greek: "turn of the wheel").
Read more about this topic: Saros (astronomy)
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