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Rarity of Tidal Alignments.

An interesting pattern evident from the accompanying table of eclipses is that the dates of these tide-raising configurations fall in groups, separated by intervals of more than 1,000 years when no such events can occur at all.

Simultaneous close groupings of all five lines (Earth-Moon, Earth-Sun, major axis of the Moon's orbit, lunar line of nodes, major axis of Earth's orbit) did not occur at all in the 20th century, because two of these lines currently can coincide only in September, while another pair can align only in early January.

The time between successive alignments of the major axis of the Moon's orbit with the lunar line of nodes is 2.9985 mean Gregorian years, giving 34 such events during the 20th century: September 30, 1901; September 29, 1904; September 29, 1907; . . . ; September 11, 1997; September 11, 2000.

The mean time between successive occurrences of Earth's perihelion is the anomalistic year of 365.2596 days, with dates that currently fall in early January (with some scatter due to the gravitational action of the Moon): January 2, 1901; January 1, 1902; January 4, 1903; . . . ; January 3, 1999; January 3, 2000.

The very slow drift of these dates through the calendar will eventually allow for nearly simultaneous alignments of all the lines only after more than another 1,000 years have elapsed from the present day!
Eclipses with Earth near Perihelion and Moon near Perigee

    Date        Misalignment   Eclipse type

-1868   Nov.12    7[degrees]     lunar
-1775   Nov.19    5[degrees]     solar
-1700   Nov.15    7[degrees]     lunar
-1691   Nov. 6   10[degrees]     lunar
-1598   Nov.13    7[degrees]     solar
-1505   Nov.20    9[degrees]     lunar
 -399   Dec. 1    7[degrees]     lunar
 -306   Dec. 8    9[degrees]     solar
 -222   Nov.25    5[degrees]     lunar
 -129   Dec. 2    3[degrees]     solar
  -36   Dec. 7    8[degrees]     lunar
   48   Nov.24    9[degrees]     solar
 1247   Dec.13    7[degrees]     lunar
 1340   Dec.19    8[degrees]     solar
 1424   Dec. 6   10[degrees]     lunar
 1442   Dec.17    5[degrees]     lunar
 1517   Dec.13    7[degrees]     solar
 1535   Dec.24    9[degrees]     solar
 1610   Dec.30   10[degrees]     lunar
 1712   Dec.28    9[degrees]     solar
 3089   Jan.18    7[degrees]     lunar
 3182   Jan.26    7[degrees]     solar
 3275   Feb. 2   10[degrees]     lunar
 3284   Jan.24    6[degrees]     lunar
 3359   Jan.21    6[degrees]     solar
 3377   Jan.31    7[degrees]     solar
 3452   Jan.29    7[degrees]     lunar
 3554   Jan.27    9[degrees]     solar
Rare Tidal Alignment of December 1340

Calculated by      Modern                       Medieval
modern methods     description                  equivalent

Dec. 13, 8h UT     Winter solstice              Sun enters Capricorn
Dec. 13, 15h       Earth at perihelion          Sun at "opposite aux"
Dec. 19, 9h        Moon at ascending node       Moon at "head of Dragon"
Dec. 19, 11h       Lunar perigee                Moon "opposite true aux"
Dec. 19, 17h 32m   New Moon, solar eclipse[*]   Moon, Sun in conjunction
Dec. 20-21         Increased tidal range

Calculated by      Calculated from
modern methods     Alfonsine Tables

Dec. 13, 8h UT     Dec. 13, 1h UT
Dec. 13, 15h       Dec. 12, 16h
Dec. 19, 9h        Dec. 19, 8h
Dec. 19, 11h       Dec. 19, 7h
Dec. 19, 17h 32m   Dec. 19, 17h 36m
Dec. 20-21         Dec. 20-21

[*] The eclipse itself was not visible from England or France.
The path of totality crossed South America.
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Publication:Sky & Telescope
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Geographic Code:1USA
Date:Apr 1, 2000
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