CHAPTER 3 | CYCLES OF THE MOON 43
Predicting Eclipses
A Chinese story tells of two astronomers, Hsi and Ho, who
were too drunk to predict the solar eclipse of October 22, 2137
bc. Or perhaps they failed to conduct the proper ceremonies to
scare away the dragon that, according to Chinese tradition, was
snacking on the sun’s disk. When the emperor recovered from
the terror of the eclipse, he had the two astronomers beheaded.
Making exact eclipse predictions requires a computer and
proper software, but some ancient astronomers could make edu-
cated guesses as to which full moons and which new moons
might result in eclipses. Th ere are three good reasons to reproduce
their methods. First, it is an important chapter in the history of
science. Second, it will illustrate how apparently complex phe-
nomena can be analyzed in terms of cycles. Th ird, eclipse predic-
tion will exercise your scientifi c imagination and help you
visualize Earth, the moon, and the sun as objects moving through
space.Conditions for an Eclipse
You can predict eclipses by thinking about the motion of the sun
and moon in the sky. Imagine that you can look up into the sky
from your home on Earth and see the sun moving along the eclip-
tic and the moon moving along its orbit. Because the orbit of the
moon is tipped slightly over 5 degrees to the plane of Earth’s orbit,
you see the moon follow a path tipped by the same angle to the
ecliptic. Each month, the moon crosses the ecliptic at two points
called nodes. It crosses at one node going southward, and two
weeks later it crosses at the other node going northward.
Eclipses can only occur when the sun is near one of the
nodes of the moon’s orbit. Only then can the new moon cross in
front of the sun and produce a solar eclipse, as shown in
■ Figure 3-13a. Most new moons pass too far north or too far
south of the sun to cause an eclipse. When the sun is near one
node, Earth’s shadow points near the other node, and a full moon
can enter the shadow and be eclipsed. A lunar eclipse doesn’t
happen at every full moon because most full moons pass too far
north or too far south of the ecliptic and miss Earth’s shadow.
You can see a partial lunar eclipse illustrated in ■ Figure 3-13b.
So, there are two conditions for an eclipse: Th e sun must be
near a node, and the moon must be crossing either the same node
(solar eclipse) or the other node (lunar eclipse). Th at means, of
course, that solar eclipses can occur only when the moon is new,
and lunar eclipses can occur only when the moon is full.
Now you know the ancient secret of predicting eclipses. An
eclipse can occur only in a period called an eclipse season, during
which the sun is close to a node in the moon’s orbit. For solar
eclipses, an eclipse season is about 32 days long. Any new moon
during this period will produce a solar eclipse. For lunar eclipses,
the eclipse season is a bit shorter, about 22 days. Any full moon
in this period will encounter Earth’s shadow and be eclipsed.3-4
images of the partially eclipsed sun can also be seen in the shadows
of trees as sunlight peeks through the tiny openings between the
leaves and branches. Th is can produce an eerie eff ect just before
totality as the remaining sliver of sun produces thin crescents of
light on the ground under trees. Once totality begins, it is safe to
look directly. Th e totally eclipsed sun is fainter than the full moon.
SunlightPinholeImage of partially
eclipsed sun■ Figure 3-12
A safe way to view the partial phases of a solar eclipse. Use a pinhole in a
card to project an image of the sun on a second card. The greater the dis-
tance between the cards, the larger (and fainter) the image will be.
SCIENTIFIC ARGUMENT
If you were on Earth watching a total solar eclipse, what would
astronauts on the moon see when they looked at Earth?
Building this argument requires that you change your point of view
and imagine seeing the eclipse from a new location. Scientists
commonly imagine seeing events from multiple points of view as
a way to develop and test their understanding. Astronauts on the
moon could see Earth only if they were on the side that faces
Earth. Because solar eclipses always happen at new moon, the near
side of the moon would be in darkness, and the far side of the
moon would be in full sunlight. The astronauts on the near side of
the moon would be standing in darkness, and they would be look-
ing at the fully illuminated side of Earth. They would see Earth at
full phase. The moon’s shadow would be crossing Earth; and, if the
astronauts looked closely, they might be able to see the spot of
darkness where the moon’s umbral shadow touched Earth. It would
take hours for the shadow to cross Earth.
Standing on the moon and watching the moon’s umbral shadow
sweep across Earth would be a cold, tedious assignment. Perhaps
you can imagine a more interesting assignment for the astronauts.
What would astronauts on the moon see while people on Earth
were seeing a total lunar eclipse?