Since a solar eclipse is a coincidence of a new moon and
an ascending or descending lunar node,
the interval between solar eclipses must be a common multiple of
a whole synodic month
(or lunation, 29.53 days between same lunar phases)
and half a draconic month
(27.21 days between same lunar nodes).
These line up around eclipse seasons,
173.3 days apart on average.
The saros cycle of 18.03 years is 223 synodic months, 242 draconic months,
or 239 anomalistic months
(27.55 days between lunar perigees or apogees).
This multiple coincidence of phase, node, anomaly, and time of year makes the saros especially useful for prediction.
However, there are other relationships between eclipses.
Between consecutive saros series there is another interval called
the inex:
358 synodic months, 388.5 draconic months, or about 28.94 years.
George van den Bergh showed in 1955 that the interval T between any two eclipses can be expressed as T = aI + bS, where I and S are the inex and saros periods, and a and b are integers.
Some such combinations have names:
Synodic Draconic Anomalistic Eclipse
Name Formula Months Months Months Seasons
Semester 5I - 8S 6 6.511 6.43 1.02
Hepton 5S - 3I 41 44.493 43.94 6.99
Octon 2I - 3S 47 51.004 50.37 8.01
Tritos I - S 135 146.501 144.68 23.00
Saros S 223 241.999 238.99 38.00
Inex I 358 388.500 383.67 61.00
Source: F. Verleben
Between the eclipse pairs in question, 2422 days = 82 lunations = 10S - 6I or 2 heptons.
The two pairs also happen to be 3 heptons apart.
The same hepton family includes southern hemisphere eclipses in Dec 2020, Nov 2030, and Jul 2037.
Tabulated in a
saros-inex panorama,
all seven eclipses would fit on a single diagonal line of slope 5/3.
Greatest eclipse Sun Moon
Date UT Lon Lat Decl EcLat Node Saros Inex
2017-08-21 18:26 88W 37N +12 +0.43 asc 145 39
2020-12-14 16:13 68W 40S -23 -0.29 desc 142 44
2024-04-08 18:17 104W 25N +7 +0.35 asc 139 49
2027-08-02 10:06 33E 25N +18 +0.14 desc 136 54
2030-11-25 06:50 71E 44S -21 -0.39 asc 133 59
2034-03-20 10:17 22E 16N 0 +0.29 desc 130 64
2037-07-13 02:39 139E 25S +22 -0.71 asc 127 69
Sources: F. Espenak,
JPL HORIZONS
From a Moon-centric point of view, the umbra of a solar eclipse moves straight along the ecliptic, but several factors shape its path on the Earth's surface.
The terrestrial longitude of a path is directly related to the time of day (UT).
A path's terrestrial latitude is very sensitive to the Moon's
ecliptic latitude
and is also affected by the Sun's declination.
Due to the tilt of the Earth's axis, an eclipse path
slants southwest-northeast near the March equinox,
bends southward near the June solstice,
slants northwest-southeast near the September equinox,
or bends northward near the December solstice.
The Moon's motion in ecliptic latitude also contributes a slight slant,
northward at ascending node or southward at descending node,
as the umbra passes west to east.
Both the 2017-2024 and 2027-2034 eclipse pairs occur near opposite equinoxes and at similar times of day, so their paths naturally have opposite slants and similar ranges of longitude.
The 2030 and 2037 eclipse paths have similar ranges of latitude but barely cross because they occur 4 hours apart in the day.
Eclipses in the same saros series, if not widely separated in longitude, occur at the same time of year and have nearly parallel paths with few opportunities to cross.
