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2. Eclipses and the Motion of the Moon
The Solar System
Eclipses and the Motion of the Moon

3. Phases of the Moon Figure 3-2 Why the Moon Goes Through Phases
This figure shows the Moon at eight positions on its orbit, along with
photographs of what the Moon looks like at each position as seen from
Earth. The changes in phase occur because light from the Sun illuminates
one half of the Moon, and as the Moon orbits the Earth we see varying
amounts of the Moon’s illuminated half. It takes about 291⁄2 days for the
Moon to go through a complete cycle of phases. (Photographs from Yerkes
Observatory and Lick Observatory)
Teaching Note: Point out the inner circle shows the Moon’s motion around the Earth. The photographic images show the Moon as seen by the observer standing on the Earth.

4. ‘Tilt’ of the Moon’s Orbit
Figure 3-6 The Inclination of the Moon’s Orbit
This drawing shows the Moon’s
orbit around the Earth (in yellow) and part of the Earth’s orbit around the
Sun (in red). The plane of the Moon’s orbit (shown in brown) is tilted by
about 5° with respect to the plane of the Earth’s orbit, also called the
plane of the ecliptic (shown in blue). These two planes intersect along a
line called the line of nodes.

5. Figure 3-7 Conditions for Eclipses
Eclipses can take place only if the
Sun and Moon are both very near to or on the line of nodes.
Only then can the Sun, Earth, and Moon all lie along a straight line. A solar
eclipse occurs only if the Moon is very near the line of nodes at new
moon; a lunar eclipse occurs only if the Moon is very near the line of
nodes at full moon. If the Sun and Moon are not near the line of nodes,
the Moon’s shadow cannot fall on the Earth and the Earth’s shadow
cannot fall on the Moon.

6. Question
What essential condition must be met if a lunar or solar eclipse is to occur?
The Moon must be at 1st or 3rd quarter phase.
The Sun must lie in the direction of Virgo.
The Sun and the Moon must lie on ─ or be very close to ─ the line of nodes, defined by the intersection of the Moon and Earth orbital planes.
The Moon must be full.
The Sun must be closer to the Earth than the Moon.

7. Total Lunar Eclipse Figure 3-9 Total Lunar Eclipse
This sequence of nine photographs was taken
over a 3-hour period during the lunar eclipse of January 20, The
sequence, which runs from right to left, shows the Moon moving through
the Earth’s umbra. During the total phase of the eclipse (shown in the
center), the Moon has a distinct reddish color. (Fred Espenak,
NASA/Goddard Space Flight Center; ©2000 Fred Espenak, MrEclipse.com)

8. Why Moon is Red During Lunar Eclipse

9. Figure 3-11 The Geometry of a Total Solar Eclipse
During a total solar eclipse, the tip of the Moon’s umbra reaches the Earth’s
surface. As the Earth and Moon move along their orbits, this tip traces an
eclipse path across the Earth’s surface. People within the eclipse path see
a total solar eclipse as the tip moves over them. Anyone within the
penumbra sees only a partial eclipse. The inset photograph was taken
from the Mir space station during the August 11, 1999, total solar eclipse
(the same eclipse shown in Figure 3-10). The tip of the umbra appears as
a black spot on the Earth’s surface. At the time the photograph was
taken, this spot was 105 km (65 mi) wide and was crossing the English
Channel at 3000 km/h (1900 mi/h). (Photograph by Jean-Pierre Haigneré,
Centre National d’Etudes Spatiales, France/GSFS)

10. Total Solar Eclipse Figure 3-10 A Total Solar Eclipse
(b) When the Moon completely covers the Sun’s disk during a total eclipse, the faint
solar corona is revealed. (Fred Espenak, MrEclipse.com)

11. An Annular Eclipse Figure 3-12 An Annular Solar Eclipse
This composite of six photographs taken at
sunrise in Costa Rica shows the progress of an annular eclipse of the Sun
on December 24, (Five photographs were made of the Sun, plus one
of the hills and sky.) Note that at mideclipse the limb, or outer edge, of
the Sun is visible around the Moon. (Courtesy of Dennis di Cicco)

12. The Saros Cycle
A solar eclipse occurs when there is a new moon and the line of nodes points toward the Sun.
An integral number of lunar months, which is days, must elapse for the proper alignment of the line of nodes to occur again.
But, the orbital plane of the Moon’s orbit precesses and thus, the line of nodes moves with respect to the stars.
The line of nodes takes days to move from one alignment with the Sun to the next identical alignment. This period is called the eclipse year.
When a whole number of lunar months elapse that is equal to a whole number of eclipse years, the alignments are the same as before and an eclipse will take place.
223 lunar months equals 19 eclipse years which equals 6585 days, an interval called the Saros.

13. The Saros Cycle
A more accurate calculation yields a value that is 1/3 of a day longer, or days (18 years, days). Eclipses separated by the saros interval are said to form an eclipse series.
But, if you want to see an eclipse at almost the same place on Earth … you’ll have to wait longer than a Saros interval.
Because of the extra one-third day, the Earth will have rotated by an extra 120° when the next solar eclipse of a particular series occurs. The eclipse path will thus be one-third of the way around the world from you.
Therefore, you must wait three full saros intervals (54 years, 34 days) before the eclipse path comes back around to your part of the Earth.
Ancient Babylonians likely knew about the Saros interval …

14. Saros Cycle Eclipse Paths
Figure Eclipse Paths for Total Eclipses, 1997–2020
This map shows the eclipse paths for all 18 total solar eclipses occurring from 1997 through
2020. In each eclipse, the Moon’s shadow travels along the eclipse path in
a generally eastward direction across the Earth’s surface. (Courtesy of Fred
Espenak, NASA/Goddard Space Flight Center)

15. Early Greek science started ~ 600 B.C.E. around the Ionian Sea

16. Arguments for Spherical Earth
Aristotle’s Argument
Question This photograph of the Earth was taken by the crew of
the Apollo 8 spacecraft as they orbited the Moon.
Earth’s shadow on Moon is curved!

17. Arguments for Spherical Earth
Ship’s mast is still visible above horizon but ship has disappeared below horizon. Earth’s surface is curved!

18. To Polaris
Start at equator and walk north … measure angle of North Star above the horizon.
900
450 00
900
450
Equator 00

19. Eratosthenes ‘Measures the Earth’
About 240 B.C., Eratosthenes, the librarian of Alexandria, learned that at noon in Syene, near what is now called Aswan, on the day of the summer solstice, the sun’s reflection was visible in the water of a deep well (therefore, Syene stands almost exactly on the Tropic of Cancer). This showed that the sun was directly overhead and that its rays therefore pointed in a straight line toward the center of the Earth.
On the same day at noon, Eratosthenes knew that a shadow cast by a vertical obelisk at Alexandria shows that the Sun’s rays strike the Earth at an angle of 7.2 degrees. Light rays from the distant Sun are parallel, so we may account for the difference only by the curve of the earth.

20. Data Every educated Greek citizen knew a little math … S = 5000 stades
θ = 7.2 degrees

21. The ‘Size’ of the Earth S = 5000 stadia 7.20 / 3600 = 1 / 50 S
Therefore S / C = 1 / 50
C = 50 S
= 50 (5000 stadia)
= 250,000 stadia C
Figure Eratosthenes’s Method of Determining the Diameter of the Earth
Around 200 B.C., Eratosthenes used observations of the Sun’s position at
noon on the summer solstice to show that Alexandria and Syene were
about 7° apart on the surface of the Earth. This angle is about one-fiftieth
of a circle, so the distance between Alexandria and Syene must be about
one-fiftieth of the Earth’s circumference.
1 stade = 1/6 km
C = 42,000 km
The modern value is 40,000 km!

22. Question
If, on the 1st day of summer (the summer solstice), rays from the Sun illuminated the bottom of a deep well in Syene, then ____
An obelisk in Alexandria would cast no shadow at the same time.
The Sun must be about to enter a total solar eclipse.
The well must have had water in it, otherwise Eratosthenes couldn’t have seen the bottom.
Syene must lie somewhere on the Tropic of Cancer.
Syene must lie east of Alexandria.

23. Aristarchus (310 – 264 BCE) Distance to Sun & Moon
Figure Aristarchus’s Method of Determining Distances to the Sun and
Moon
Aristarchus knew that the Sun, Moon, and Earth form a right
triangle at first and third quarter phases. Using geometrical arguments,
he calculated the relative lengths of the sides of these triangles, thereby
obtaining the distances to the Sun and Moon.

24. Distance to Sun & Moon dS = 19 dm dS dm 15 ¼ days 870 α θ 30 30 θ 870
Figure Aristarchus’s Method of Determining Distances to the Sun and
Moon
Aristarchus knew that the Sun, Moon, and Earth form a right
triangle at first and third quarter phases. Using geometrical arguments,
he calculated the relative lengths of the sides of these triangles, thereby
obtaining the distances to the Sun and Moon.
14 ¼ / 29 ½ = 2 α / 3600 = 0.483
sin θ = dm / dS = 0.052
2 α = x 3600 = 1740
dS = 19 dm
α = 870
θ = 30

25. Size of Sun & Moon ½ 0 dS = 722 DE dM = 38 DE dS = 19 x dM dM
dM = 1/3 x 720 x DE / 2π

26. Aristarchus vs Today Aristarchus Modern Moon’s Diameter 0.33 DE
Moon’s Distance
38 DE
30 DE
Sun’s Diameter
6.33 DE
109 DE
Sun’s Distance
722 DE
1.18 x 106 DE
Earth’s Diameter
(Eratosthenes)
13,000 km
12,756 km

27. Question
How did the ancient Greek astronomer Aristarchus of Samos determine that the Moon's diameter was about 1/3 that of the Earth?
by measuring it with calipers.
he made a really good guess.
by sighting the Moon with his thumb held at arm’s length.
by measuring the time for the Moon to move through the Earth's shadow during a lunar eclipse.
by sighting it with a telescope.