Sky & Telescope - January 2024 - 64

Eclipse Geometry
Drift of Lunar Nodes
Ecliptic
MIGRATING NODES Five sample
tracks of the Moon through its descending
node in lunar saros 45, each separated
by almost 380 years, or 7 exeligmos
cycles. Note how the slow, eastward
migration of the node (indicated by the
blue tick marks) causes the Moon to
cut successively more northerly slices
into Earth's shadow. The full 85-eclipse
series ends about 1,500 years after the
Moon first entered the southern penumbra
in 1352 BC. (The Moon's 5° orbital
tilt is exaggerated for clarity.)
Eastward nodal migration
an eclipse. This occurs most famously after 223 months (of
about 29.53 days each), which coincidentally corresponds to
242 draconic months (of about 27.21 days each). The result is
the 6,5851
eyed Babylonian astronomers.
But there's a subtler movement of the nodes that's only
apparent when one stacks all the eclipses of a saros together.
If one could flip through them like an animated cartoon, the
node would appear to shift eastward along the ecliptic path
by almost half a degree with each eclipse in the saros cycle.
As a result, over the 85 eclipses in saros 45, for example, the
Moon's position at the moment of eclipse ventures very slowly
upward as the node migrates, as shown in the diagram above.
A lunar eclipse through the Moon's descending node starts
as the Moon slices through the lowest part of the penumbra.
In succeeding eclipses, as the node nudges east, it inches
up until the Moon reaches the umbra for a group of total
eclipses. Gamma approaches zero as the Moon cuts through
the center of Earth's umbral shadow. As the node continues
to shift eastward over the centuries, the intersections with
Earth's shadow cuts northward of the ecliptic into positive
gamma territory. Then, about 1,500 years after the Moon first
Saros 139 Eclipse Sample
Eclipse Date
Lunar
Time
March 7, 1970
March 18, 1988
March 29, 2006
April 8, 2024
April 20, 2042
April 30, 2060
May 11, 2078
17:38:30
1:58:56
10:12:23
18:18:29
2:17:30
10:10:00
17:56:55
Longitude
347°
357.8°
8.4°
19.0°
29.3°
39.8°
50.4°
touched the southern half of the penumbra at the start of the
saros cycle, it departs the northern penumbra, and the party
is over for this series.
/3-day saros match-up discovered long ago by keenApril's
Eclipse in Context
The April 8, 2024, total solar eclipse belongs to saros cycle
series 139, a 13-century-long family of 71 ascending-node
eclipses that began in May 1501 - around the time young
Copernicus was studying law in Italy while his heart lay with
Ptolemy's astronomy. The sequence won't end until July 2763,
which means we're not yet at the mid-point of this cycle. We
can discern some near-term trends by looking at the six solar
eclipses bracketing April's totality in the table below.
The saros interval of 18 years, 11 days, and about 8 hours
between eclipses presents itself clearly. The April 8th event is
one of three exeligmos eclipses in our sample - the other two
being March 7, 1970, and May 11, 2078. The time of maximum
eclipse for all three is remarkably similar, occurring at
17:39, 18:18, and 17:57 UT, respectively.
During this one-century snapshot of saros 139, the
Moon's distance from the ascending node decreases by less
than ½° each time, falling to under 4° for the April eclipse.
Ascending
node
342.26°
353.3°
4.28°
15.3°
26.34°
37.38°
48.43°
Lunar
perigee
324.8°
337.13°
349.53°
1.85°
14.14°
26.37°
38.54°
Moon's offset
from node
4.74°
4.5°
4.12°
3.7°
2.96°
2.42°
1.97°
Moon's offset
from perigee Gamma (γ)
22.2°
20.67°
18.87°
17.15°
15.16°
13.43°
11.86°
0.4473
0.4188
0.3843
0.3431
0.2956
0.2422
0.1838
64 JANUARY 2024 * SKY & TELESCOPE
February 25, AD 164
July 12, 216 BC
November 25, 595 BC
April 13, 973 BC
August 29, 1352 BC
BEATRIZ INGLESSIS / S&T
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