Notes
1. It should be noted that the conclusions in this article are based on scriptures, historical sources, and astronomy, in all of which there are elements of uncertainty. The interpretation of scripture as it relates to history is often very difficult; history itself is by nature inexact, and astronomical calculations can only be accurate to within certain tolerances. Moreover, judging the relative importance of data is a subjective enterprise, especially when conflicting evidence comes from different fields. However, the consistency discovered in the scriptures is thought to be of interest to Latter-day Saints.

2. See also Harold W. Hoehner, Chronological Aspects of the Life of Christ (Grand Rapids, Mich.: Zondervan, 1977).

3. Jubilees 49:1 and Josephus (Wars, 6.9.3).

4. John tells us that the triumphal entry occurred on the fifth day before Passover. (John 12:1, 12–13.) Reckoning inclusively from Friday (14 Nisan) as the first day, Sunday (16 Nisan) is the third day after Friday, and Monday (10 Nisan) is the fifth day before Friday. See Hoehner, p. 72.

5. This Waving of the Sheaf ceremony on 16 Nisan should not be confused with the Feast of Firstfruits (Pentecost) that occurred fifty days later. (Lev. 23:16–21.)

6. The Pharisees (and modern Jews) interpreted “Sabbath” as “feast day” and offered the grain on 16 Nisan, the second day of Passover. But the Sadducees interpreted “Sabbath” as “Saturday,” the weekly Sabbath, and presented the firstfruits on the Sunday after Passover. (See Hoehner, pp. 83–84.) Because 16 Nisan fell on Sunday in a.d. 33, both Sadducees and Pharisees presented the firstfruits on the morning proposed for Jesus’ resurrection.

6. The Pharisees (and modern Jews) interpreted “Sabbath” as “feast day” and offered the grain on 16 Nisan, the second day of Passover. But the Sadducees interpreted “Sabbath” as “Saturday,” the weekly Sabbath, and presented the firstfruits on the Sunday after Passover. (See Hoehner, pp. 83–84.) Because 16 Nisan fell on Sunday in a.d. 33, both Sadducees and Pharisees presented the firstfruits on the morning proposed for Jesus’ resurrection.

7. H. Schauss, Guide to Jewish Holy Days (New York: Schocken, 1969), p. 80.

8. Stephen D. Ricks, “The Appearance of Elijah and Moses in the Kirtland Temple and the Jewish Passover,” Brigham Young University Studies 23 (Fall, 1983), pp. 483–86.

9. Teachings of the Prophet Joseph Smith, comp. Joseph Fielding Smith (Salt Lake City: Deseret Book Co. 1938), p. 337.

10. Ibid., p. 340.

11. Ibid.

12. The modern Hebrew calendar keeps synchronized with the solar cycle by intercalating years according to a fixed 19-year Metonic cycle, which is only approximately accurate. Moreover, it uses fixed values of the solar and lunar mean motion, whereas the “Jewish calendar” used in this analysis takes into account the slowly varying lengths of the day, month, and year. Similarly, our Gregorian calendar is only an approximation to the true solar calendar, but, fortunately, it is accurate to within one day back to the Savior’s lifetime.

13. Equations for the slowly decreasing length of the tropical year and synodic lunar month in mean solar days were used from C. W. Allen, Astrophysical Quantities (London: Atholone Press, 1976), pp. 19–20. They give an average value for the solar year (between a.d. 33–1836) of 365.242324 days and for the lunar synodic month of 29.530590 days.

14. Note that these results have been derived for the true (astronomical) solar and lunisolar calendars. The modern Gregorian and Hebrew calendars will not repeat as long, due to the arbitrary method of inserting leap days and leap months. Thus, in general, when a realignment interval is applied to other dates, they may differ by one day on the Gregorian calendar or perhaps even by a month on the Hebrew calendar, although they would be identical on a true solar or lunisolar calendar.

15. All historical dates are assigned consecutive numbers to facilitate such calculations: 3 April a.d. 33 was Julian day number 1,733,206 and 3 April 1836 being day 2,391,738. (See W. Stahlman and O. Gingerich, Solar and Planetary Longitudes for Years -2500 to +2000 by 10-Day Intervals, Madison: University of Wisconsin Press, 1963, pp. 311, 546.)

16. See, for example, G. Abell, Exploration of the Universe (New York: Holt, Rinehart and Winston, 1969), pp. 184–85.

17. For example, the length of the saros depends on the inclination of the moon’s orbit to the earth’s. See Forest Ray Moulton, An Introduction to Celestial Mechanics (New York: Dover, 1970), p. 343.

18. In this case, the eclipse occurred one lunar month later on 1 May 1836. See T. Oppolzer, Canon of Eclipses (New York: Dover, 1962), p. 372.

19. In fact, one way of looking at the two realignment properties of the 100-saros period is that, while only the lunisolar realignment is necessary for the Jewish calendar to repeat, the orbital realignment feature is also necessary for the Judean calendar to do so.

20. I calculated lunar and solar longitudes for every Easter morning (3:00 U.T.) from a.d. 1 to a.d. 3000, using the equations of Herman Goldstine, New and Full Moons, 1001 b.c. to a.d. 1651 (Philadelphia: American Philosophical Society, 1973); and Robert R. Newton, Medieval Chronicles and the Rotation of the Earth (Baltimore: Johns Hopkins Press, 1972), p. 643, equation 18.8. Of Easters that fell on April 3, 16 Nisan, the longitudes for the year 1836 most nearly equal those of a.d. 33.

21. If the reader is not sufficiently impressed, note that the saros century is also a realignment interval for the solar year and the synodic period of Mercury, 115.877538 days, as given in Stahlman and Gingerich, p. xv.

* The “best fit” criterion is that the distance the belt must travel to align the worst pulley must be smaller than the corresponding distance for any smaller number of turns. This criterion was adapted from H. R. P. Ferguson and R. W. Forcade, “Generalization of the Euclidean Algorithm for Real Numbers to All Dimensions Higher Than Two,” Bull. of Am. Math. Soc. 1 (November 1979), pp. 912–14.

** Arthur Berry, A Short History of Astronomy (New York: Dover, 1961), p. 19. The Babylonians are known to have been aware of the saros since at least several centuries b.c. It is not known whether such knowledge dates back to the time of Abraham, who lived in that same area about 2000 b.c.

Notes
John P. Pratt has a Ph.D. in astronomy and is a senior scientific analyst with the Eyring Research Institute. He is the father of five children and is Sunday School president in his Kaysville, Utah, ward.

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