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Physics 1025: Lecture 11 Lunar and Solar Eclipses: visibility, duration, frequency
Announcements
Definitions: umbra (region of total shadow), 859,000 mi from earth, 232,000 mi for moon
penumbra (region of partial shadow)
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Note for moon perigee = 221,463 miles, apogee = 252,710 miles so moon’s umbra doesn’t always reach
all the way to earth
2012: May 20 annular solar mainly for Pacific Ocean
June 4 partial lunar for Americas except east coast
Nov. 28 penumbral lunar for Far East and Australia
Dec. 11 total solar for Australia and Pacific Ocean
Some years there are more than the usual quota of 2 lunars and 2 solars due to eclipse ‘seasons’
occurring at end of calendar year. In 2012 there are 2 solars (one annular, 1 total), and 1 partial lunar
and one penumbral lunar.
What you see:
Lunar: The full moon must be above the horizon to be seen. Penumbral stages not too visible. At
totality, earth’s atmosphere refracts light around earth so moon is lit and can be orange or red
in color, depending on clouds, dust in atmosphere or it can be charcoal grey. Moon dims from
-12 to -7 or so.
Solar: Total (moon near perigee) moon gradually covers sun, just before totality you see shadow
bands, Bailey’s Beads and then the lovely corona, possibly a diamond ring just before and after
totality.
Annular (moon near apogee so too small to obscure sun) you just see moon moving across, if
central leaving an annulus at eclipse maximum – hardly worth viewing.
lunar
Total solar
Annular solar
Factors determining whether an eclipse will occur and your chances of seeing it:
Duration
Lunar: Thickness of shadow cone of earth at moon’s distance is 5700 miles and moon travels
through at 2000 miles/hr. Thus moon remains partly in shadow about 4 hours and
totality lasts about an hour if eclipse is central.
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Solar: moon’s footprint on earth is 167 miles across maximum, and it moves with moon at
2000 miles/hr. However, earth rotates along under the shadow in same direction,
lengthening duration of the eclipse. E.g. at equator earth moves 1000 miles/hr so net
speed of shadow is only 1000 miles/hr, giving tmax = 167/1000 ~ 9.6 minutes at best
Relative frequency of occurrence
For lunar eclipse moon must be in shadow cone M2, whereas for a solar eclipse moon must be within
wider shadow cone M1. The relative frequency of occurence is thus the ratio M2/M1 which calculates out
to a ratio of lunar to solar eclipses of 1 to 1.5 or 2 lunars to 3 solars. There must be at least one solar
every time the sun is near a node, but for lunar the sun can slip by a node between 2 full moons without
a lunar happening. There can be as many as 7 eclipses in 1 year (5 solar and 2 lunar) or as few as 2 (both
solar).
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Visibility
Lunar: half the world looks out and sees this, plus more who rotate around during the eclipse duration
Solar: only those directly under the small shadow see the solar
Alignment of phases (nodes)
The moon’s orbit is inclined 5˚ to ecliptic (else we’d see eclipses every new and full moon). A node is the
place in moon’s orbit where it crosses ecliptic; the line of the nodes connects ascending with descending
node and keeps roughly the same orientation in space (though in fact the nodes regress westward with
a period of 18.6 years). The earth’s shadow always lies in ecliptic plane, named for the place that
eclipses can occur, but moon’s shadow is in this plane only when moon is at a node. So eclipses can
occur only when moon is at a node. Note sun must also be near a node, i.e. in line with earth and moon.
Conclusion: for an eclipse to occur the moon must be full or new and at a node. Another way to put it is
that the line of nodes must be in line with the sun and the moon must be full or new for an eclipse to
occur. There are 2 eclipse seasons 6 months apart and there can be 2 solar and 1 lunar each season.
There is no problem predicting the exact position of sun and moon and predicting eclipses with modern
computers. However, even the ancient Babylonians noted that eclipses reoccur at intervals of 18 years
11 1/3 days, a period called the Saros, and they allegedly predicted eclipses on the basis of this. So we
have whole families of eclipses recorded from antiquity since 2137 BC from ancient China, and later in
the Greek literature, the Bible and popular works by Mark Twain. Note because of the 1/3 day
increment in the Saros, successive eclipses of one Saros cycle occur 1/3 of the way further around the
earth, as well as working their way north from Antarctica; it takes about 1200 years for one full cycle.
There are some useful drawings below concerning eclipses.
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Region where
eclipse can
happen
Asc. Node
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ecliptic
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12˚/d
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No eclipses
Eclipses can
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SCV
new C
full
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Eclipses can
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