Chapter 3 Eclipses and the Motion of the Moon

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Lunar Phases and Eclipses Guiding Questions

• Why does the Moon go through phases?
• Is there such a thing as the dark side of the
  Moon?
• What is the difference between a lunar eclipse
  and a solar eclipse?
• How often do lunar eclipses happen? When one is
  taking place, where do you have to be to see it?
• How often do solar eclipses happen? Why are they
  visible only from certain special locations on
  Earth?
• How did ancient astronomers deduce the sizes of
  the Earth, the Moon, and the Sun?

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Phases of the Moon

• new moon
• waxing Crescent
• first quarter
• waxing gibbous
• full
• waning gibbous
• third quarter
• waning crescent
• new moon

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Lunar Phases
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The phases of the Moon are caused by its orbital
motion and repeat every 29½ days.
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The phases of the Moon are caused by its orbital
motion and repeat every 29½ days.
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Check your understanding

• The full moon transits at what time?
• midnight
• An observer see the moon rising at 3am. What
  phase is it?
• Waning crescent
• A waxing quarter moon sets at what time?
• midnight

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Although the Moon will orbit Earth completely in
27.32 days (sidereal month), it takes a 29 ½ days
(synodic month) to become a new moon again
because Earth moves around the Sun.
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The Moons rotation always keeps the same face
toward the Earth.
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Moon Near side and Far side
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Synchronous Rotation the moon takes exactly the
same amount of time to orbit Earth as it does to
spin on its lunar axis.
Subsequently, there is no permanent dark side
of the Moon, each location experiences about 14
days of daylight and 14 days of night.
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Solar Eclipse

• When the new moon blocks the view of the Sun as
  seen from a particular location on Earth for
  several minutes.

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Total Solar Eclipse 4 Dec 2002

• Totality is only 2m4s
• Width of Eclipse path 87 km
• Eclipse maximum is in Southern Indian Ocean (bad
  weather predicted!)

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Solar eclipses can be either total, partial, or
annular, depending on the alignment of the Sun,
Earth, and Moon.
Total eclipse where the Sun appears to be
completely covered by the Moon. Partial eclipse
where part of the Sun appears to be covered by
the Moon. Annular eclipse where the Moon is too
close in its orbit around Earth to completely
cover the Sun.
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Annular solar Eclipse
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Lunar Eclipse

• When Earth obscures most of the sunlight from
  illuminating the full moon for several hours.

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Lunar eclipses can be either total, partial, or
annular, depending on the alignment of the Sun,
Earth, and Moon.
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Eclipses occur only when the Sun and Moon are
both on the line of nodes. Where the Moons
orbital plane intersects with Earths orbital
plane.
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Lunar eclipses can be either total, partial, or
penumbral, depending on the alignment of the Sun,
Earth, and Moon
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A solar Eclipse (Suns Corona visible)
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Solar Eclipse Movie (India, 1999)
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The Saros Cycle

• One synodic lunar month (new moon to new moon) is
  29.53 days.
• Line of nodes lines up with Earth-Sun line every
  346.6 days.
• Hence, time intervals between Solar Eclipses will
  be whenever
• 29.53N 346.6M
• where N, M are integers.
• The smallest integers which satisfy the equation
  are
• 22329.53 19346.6 6585.3 days 18yr 11.3
  days
• This interval (18yr, 11.3 days) is the Saros
  cycle. Solar eclipses repeat on the Saros cycle.
• However, the extra 0.3 days (8hr) means the next
  solar eclipse occurs at a longitude 120 W of
  observer, so next solar eclipse at (almost) the
  same longitude must be 3 Saros cycles, or 54 yr,
  34 days.
• N.B. Because of the eccentricity of the Moons
  orbit, this is not exact.

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Solar Eclipse Paths
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Aristarchus, part 2

• He also tried to determine the angle between the
  Sun and Moon at exactly ¼ phase.
• He measured 87, so that the ratio of Earth-Moon
  to Earth-Sun distance must be 201. (Correct
  angle is 89.7, distance ratio is 4001)

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87
tan(3) EM/SM 1/20
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Aristarchus, part 3

• A solar eclipse means angular sizes of Sun, Moon
  are about equal (both are 1/2), so since
  Sun-Earth distance is 20x Earth-Moon distance,
  the Sun must be 20x Moon size.
• From lunar eclipse, he already estimated Earth
  size 3x Moon size, so Sun must be 20/3 7x size
  of Earth. (actual 100x)
• Since Sun is much larger than Earth, he
  (correctly) deduced that the Earth is likely to
  orbiting the Sun (heliocentric model) and not
  vice-versa (geocentric model).
• Note this was 1,700 years before Copernicus!

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Aristarchus (c.280 BCE) Method to measure
relative sizes, distances of Moon, Earth, Sun

• He noticed the shadow of the Earth on moon during
  lunar eclipse was 2x size of the Moon.
  Correcting for converging shadows, he estimated
  the true ratio at 3x, i.e. Earth was 3x times
  diameter of Moon. (Actual 6378km /1738km 3.7x

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Ancient astronomers measured the size of the Earth

• Around 200 BC, Greek astronomer Eratosthenes used
  the observation that the Sun is 7º south of the
  zenith in Alexandria on the same day it was
  directly overhead in Syene (near Aswan).
• From this he deduced that Alexandria must be
  7/360th of the way around a spherical Earth.
  Knowing that these two cities are separated by
  about 800 km, he calculated the Earth to have a
  circumference of about 40,000 km which is quite
  close to the actual size.

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Method of Eratosthenes to measure radius of Earth
1 stadium 180 yd So C 240,000 stadii 43,000
km Earth radius R C/2? 6,875 km (accurate
value R 6,380 km)
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PRS quiz

• Solar eclipses occur when
• The moon is at full phase, line of nodes is
  along Earth-Sun line
• The moon is at new phase, line of nodes is along
  Earth-Sun line
• The moon is at new phase, line of nodes is in
  ecliptic plane
• The moon is at full phase, line of nodes is in
  ecliptic plane
• Lunar eclipses
• Can be seen over most of the Earth
• Can only be seen along a narrow (100km wide) path
  at any instant
• Are never visible in the polar regions
• Occur every other full moon.
• The reason solar eclipses are sometimes annular
  is
• The Sun is in the wrong place in the sky.
• The Moon is in a tilted orbit
• The Moon is too far away from Earth, so its
  angular size is smaller than the Sun
• The Sun and Moon are not in the ecliptic plane

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• Eratosthenes method of measuring the Earths
  size assumed
• The Earth is spherical
• The Earth is flat
• The Sun and Moon are at right angles
• The Moons orbit is circular
• The Saros cycle is approximately
• 18y 11d
• 6mo
• 346.6 days
• 29.53 days
• Suppose a solar eclipse occurs in Iowa City in
  early June 2003. Another solar eclipse can be
  expected in or near Iowa City
• Mid-December 2004
• Late June 2021
• Early July 2057
• Cant determine solar eclipses are
  unpredictable

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• The maximum time of totality for a solar eclipse
  at a given location is closest to
• A few seconds
• 8 minutes
• 2 hours
• A full 12 hour period
• During a lunar eclipse, the moon appears red.
  Why?
• The Earths shadow is red (because of the Earths
  atmosphere)
• The Moon has surface iron oxide dust which
  appears red in low light conditions
• The Earth has a slight reddish glow which
  illuminated the Moon.
• This is an optical illusion caused by the Moons
  thin atmosphere
• Why dont eclipses occur every lunar cycle?
• The Moons orbit is elliptical
• The Sun moves out of the ecliptic
• The line of nodes of the Earths orbit is
  misaligned
• The Moons orbit is tilted.

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• The method of Aristarchus to measure the relative
  size of the Earth and Moon used an observation
  of
• The angle between ¼ phase Moon and the Sun
• The size of the Earths shadow on the Moon during
  a lunar eclipse
• The length of the shadow on a vertical stick on
  the summer solstice
• The length of a solar eclipse on the Earths
  surface

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Guiding Questions

• Why does the Moon go through phases?
• Is there such a thing as the dark side of the
  Moon?
• What is the difference between a lunar eclipse
  and a solar eclipse?
• How often do lunar eclipses happen? When one is
  taking place, where do you have to be to see it?
• How often do solar eclipses happen? Why are they
  visible only from certain special locations on
  Earth?
• How did ancient astronomers deduce the sizes of
  the Earth, the Moon, and the Sun?