Figure 2. The problem of aligning different calendrical periods is analogous to aligning arrows on pulleys of different circumferences. (A) Our Gregorian calendar attempts to align the day (earth’s rotation) with the solar year (seasons). (B) The lunisolar calendar adds the complication of including the lunar month (moon’s phases). (C) The interval from the proposed Resurrection date to Elijah’s return realigned a calendar that also includes the week (7 days).
A realignment interval for the set of pulleys is a number of turns of the smallest one which brings all of the arrows back to the vertical point better than any smaller number of turns.
The seemingly simple problem of finding a realignment interval for several cycles is, in fact, a very difficult problem in number theory;* fortunately, however, it is easily solved with a computer by “brute force”—by simply checking every possible combination of numbers for the best fit.
For our solar calendar, 4 years is a realignment interval, whereas 400 years is not because there is at least one better solution with a smaller number of years (12,053 days divided by 33 years = 365.2424 days).
Figure 2b depicts the more complex problem of realigning the lunisolar calendar, which also includes the lunar month, the period of the moon’s phases. The modern Hebrew calendar employs a realignment interval, called the Metonic cycle, that has been known since at least five centuries before Christ: 19 years very nearly equal 235 lunar months. This means that the lunisolar calendar requires leap months as well as leap days.
Figure 2c represents the problem of realigning the Jewish calendar described in the text, also including the week as a cycle. The realignment intervals include 68, 152, 220, and 372 years. For example, in this century Easter falls on 3 April, 16 Nisan (Jewish) in the years 1904 and 1988, being 68 and 152 years after 1836, respectively. For longer realignment intervals, the variable lengths of the year and day must be considered. The realignment interval of 1,803 years discussed in the text is better than any other until 5,382 years have elapsed.
The Saros
Perhaps the greatest contribution to astronomy from ancient Chaldea was the discovery of a period of 6,585 days (18.03 years) called the saros, after which eclipses might repeat.**
An eclipse occurs when the sun, moon, and earth form a straight line. Solar eclipses occur at a new moon, when the earth is in the moon’s shadow; lunar eclipses are at full moon, when the moon passes into the earth’s shadow. (See Figure 1.)
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Figure 1. A solar eclipse can occur at a new moon, or a lunar eclipse at a full moon, when the sun, earth, and moon are approximately in a straight line. The reddening of a lunar eclipse is caused by light being refracted into the earth’s shadow by the atmosphere. Note that a total solar eclipse is only visible to the small area of the earth in the center of the new moon’s shadow, whereas a total lunar eclipse can be visible to the entire night-time half of the earth.
For a given series of eclipses to reoccur, three conditions need to be fulfilled:
1. The phase (full or new) of the moon must be the same, which is why similar eclipses are always separated by a whole number of lunar months of 29.53059 days.
2. The moon must be near the place where its path crosses the sun’s apparent path. The period of such crossings is 27.21222 days.
3. The moon needs to be at about the same distance from the earth in order to completely cover the sun in total solar eclipses. (The moon’s distance from the earth changes because its orbit is not circular, which makes its apparent size vary by about 10 percent.) This reoccurs in intervals of 27.55455 days.
Thus, the problem of predicting when eclipses will repeat is a question of finding a realignment interval for those three cycles. (See Figure 2.) After an eclipse, when will all three cycles again coincide? One of the very best realignment intervals is the saros of 6,585.32 days.
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Figure 2. The saros (18.03 years) is a realignment interval after which eclipses may repeat. It realigns the periods in which the moon is at the same phase (such as new or full), at the same distance, and at the point of intersection of the moon’s orbit with the sun’s apparent path. Eclipse cycles can only reoccur when the sun, moon, and earth are once more in proper alignment—illustrated here by all three arrows pointing nearly straight up again.
As discussed in the text, the return of Elijah occurred 100 saros periods after the proposed date of the Savior’s resurrection.
[illustration] “The Lord Jesus Christ,” by Del Parson
[illustration] A Jewish family celebrating the Passover Feast. The cup in the center of the table is for the Prophet Elijah, who is expected to return on a Passover to herald the coming of the Messiah. (Illustrated by Robert Barrett.)
[illustration] On Easter Sunday, 3 April 1836, the Prophet Elijah returned during Passover and fulfilled Malachi’s prophecy (see Mal. 4:5–6) when he restored priesthood keys in the Kirtland Temple.
