Motions of the
Earth and Moon
Motions of the Moon
• The Moon revolves around Earth once in 27.32 days. This is called its
sidereal period of revolution because it is measured relative to the
stars.
27.32
32 days
days. This is its sidereal period of
• The Moon rotates once in 27
rotation. Because of this, we always see the same side of the Moon
rotation
from Earth.
• As the Moon moves eastward in its orbit, the part of the illuminated
half that we see changes. The fraction of the illuminated half that is
visible from Earth is called the phase, usually expressed as a
percentage.
N
Sunlight
eastward
1
Why do we always see the same side of the Moon?
The Moon’s rotation
period is equal to its
period of revolution.
Earth
Phases of the Moon
A complete cycle
of phases is called
a lunation.
Waxing
gibbous
First
quarter
Waxing
crescent
full
New
eastward
The time to
complete a cycle of
phases is called
the synodic period
of the Moon. It is
the Moon’s period
of revolution with
respect to the Sun.
Waning
gibbous
Third
quarter
Waning
crescent
The synodic
period of the
Moon is 29.53
days. That is
about 1 week from
new to first
quarter, one week
from first quarter
to full, etc..
2
How is the time of day for an observer related to
the location of that observer on Earth?
Sunset
North Pole
Midnight
Noon
Sunlight
Sunrise
Lunar Phases and
Time of Day
Sunset
W
E
W
E
Note: eastward is the direction in which Earth
rotates. In the diagram, a line is drawn tangent to
the observer’s location, with the direction of
rotation labeled E and the opposite direction
labeled W. These two points identify the eastern
and western horizons.
North Pole
Midnight
Noon
Sunlight
E
W
W
E
Sunrise
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SS
In this diagram, the Sun
is at the vernal equinox,
so the date is near
March 20.
Lunar Phases and the
Seasons
AE
VE
What is the phase
of the Moon if
the date is March
20, and the Moon
is at the summer
solstice?
WS
An internet tutorial and practice quiz on the phases of the Moon is located at
http://www.calvin.edu/~lmolnar/moon/Tool.html.
4
Lunar and Solar Eclipses
angular diameter linear diameter
=
206265′′
distance
The maximum distance between Earth and the Sun is about 152,000,000 km, and the
diameter of the Sun’s photosphere (the region of the Sun that is normally visible) is
1,390,000 km. Calculate the angular diameter of the Sun at this distance.
d = 1.52 × 108 km
⎛D⎞
θ = 2.06265 × 105 ⎜ ⎟
⎝d⎠
θ = 1.886 × 103 arcsec
D = 1.39 × 106 km
Calculate θ.
θ = 2.06265 × 105 ×
θ = 1.886 × 103 ×
1
°
3600
1.39 × 106
1.52 × 108
θ = 0.524º
When the Moon is closest to Earth, its angular diameter is 0.549º. If it then comes
between us and the Sun, it blocks (eclipses) the photosphere. This phenomenon is called
a total solar eclipse.
The Sun’s angular diameter can be as large as 0.542º and the Moon’s as small as 0.491º.
When the Moon comes between Earth and the Sun under these conditions, a ring of the
photosphere is visible. This is called an annular eclipse.
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The Structure of a Shadow
Sun
The green sphere in the diagram represents either
Earth or the Moon. No sunlight reaches the region
labeled U. This is the darkest part (called the
umbra) of the shadow of the green sphere; it is the
region in which the Sun is totally eclipsed. P labels
the penumbra of the shadow, where the Sun is
partially eclipsed. From region A, an observer
would see an annular eclipse.
A cross section of the
shadow at the dotted
line would look like
the figure below.
umbra
penumbra
Earth-Sun-Moon Configurations for Lunar and Solar Eclipses
•
•
•
For a lunar eclipse to occur, the Moon must pass through Earth’s shadow. This
can only happen at a full Moon.
For a solar eclipse to occur, the Moon’s shadow must fall on Earth. This can
only happen when the Moon is new.
Whyy isn’t there a lunar eclipse
p at everyy full Moon and a solar eclipse
p at everyy
new Moon?
Full
Moon
New
Moon
Sun
Earth
The Moon’s orbit does not lie in the ecliptic. There
is an angle of about 5º between the plane of Earth’s
orbit and the plane of the Moon’s orbit. Because of
this, the shadows usually miss as shown at the right.
Ecliptic
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Line of Nodes
Under ideal lunar eclipse conditions, the length of Earth’s umbra is 1.4 million km and the
distance from Earth to the Moon is 363 thousand km. The diameter of Earth’s umbra at
that distance is 9500 km, and the diameter of its penumbra is 16,000 km. Since the
diameter of the Moon is only 3476 km, it is possible for the entire Moon to pass through
Earth’s umbra. The Moon is then seen totally eclipsed by anyone on Earth who can see
the Moon. Three kinds of lunar eclipse are possible: total, partial, and penumbral.
eastward
Penumbral: Moon passes through
the penumbra.
Total: all of the Moon passes through
the umbra.
Partial: only part of the Moon passes
through the umbra
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Lunar Eclipse
During the penumbral phase of a total lunar eclipse or during a penumbral eclipse, the full
Moon is slightly fainter than usual
usual. During the total phase,
phase it is not completely dark
because some sunlight is refracted (i.e., bent))toward the Moon by earth’s atmosphere. As
it passes through Earth’s atmosphere, the sunlight is also scattered. More blue light is
scattered than red, so the Moon looks orange during totality as shown in these
photographs.
Under ideal lunar eclipse conditions, the diameter of the Moon’s umbra is about 270
km, and the diameter of its penumbra is about 6000 km. Since Earth’s radius is about
6380 km, the only people who can see a total solar eclipse are those who happen to be
along the narrow path followed by the umbra; this path is called the path of totality.
Umbra
of
Moon’s
shadow
Earth
For an observer at Earth’s equator, the umbra
moves at about 1730 km/h due to the
combination of the orbital motion of the
Moon and the rotation of Earth. The time for
the umbra to pass over such an observer is
therefore no more than about 7.5 minutes.
Total eclipses at higher latitudes are even
shorter.
On the other hand, it can take as much
as 1 hour
h
and
d 45 minutes
i
for
f the
h Moon
to traverse Earth’s umbra.
There are three kinds of solar eclipse: total (photosphere completely blocked by the
Moon, partial (photosphere partially blocked by the Moon), and annular (Moon
blocks the central part of the photosphere, but leaves a thin ring of photosphere visible.
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Solar Eclipse from Satellite
Because
Earth
rotates and
the Moon
moves in its
orbit, the
shadow
moves at
more than
1000 mph.
Since the
diameter of
the umbra is
no more
than about
168 miles, a
total solar
eclipse can
last no more
than 7.5
minutes.
This is a
satellite view
of the
passage of
the Moon
Moon’ss
shadow over
the surface
of Earth
during a
total solar
eclipse.
While the
umbra
passes over
a region, the
people in
that region
see a total
solar eclipse.
Total Solar Eclipse as Seen from the Ground
Notice that just,
before the
beginning and
just before the
end of
totality,there is a
bright flash near
the edge of the
Sun. This
phenomenon is
called the
diamond ring
effect.
ff t It iis the
th
result of
sunlight passing
through a valley
on the Moon
while the rest of
the Sun is
eclipsed.
The white halo
seen during
totality is the
part of the Sun’s
atmosphere
called the
corona.
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Chromosphere and Prominences
When the photosphere is eclipsed, the outer regions of the Sun’s atmosphere can be
seen. The pink region, which has an average depth of several thousand km, is called
the chromosphere. The corona is the tenuous, but very hot, region that shows up as
a white irregular halo around the Sun during totality. The clouds of hot gas that rise
above the chomosphere into the corona are called prominences.
Predicting Eclipses
The Moon's orbit is tilted 5o 8' 43" to the plane of the ecliptic. It crosses the ecliptic
twice a month. These crossing points are called the nodes of its orbit.
Conditions for an eclipse to occur:
1. The Moon must be full (lunar eclipse) or new (solar eclipse).
2. The Sun must be near a node of the Moon’s orbit.
Eclipse season: a time interval during which the Sun is close enough to a node for
an eclipse to occur – about 32 days for solar eclipses, 22 days for lunar eclipses.
Line of nodes: a line that passes through the two nodes of the Moon’s
Moon s orbit
orbit.
Eclipse year: the amount of time for the Sun to return to a node = 346.62 days
The eclipse seasons begin 19 days earlier each year.
10
1
1 saros cycle = 18 years 11 days = 6585.321 days = 223 lunar synodic periods
3
6585.321
= 223.00
29.531
6585.321
= 19.00
346.62
If the line of nodes points toward the Sun on a given date, and the Moon is new, a solar
eclipse will occur. 6585.321 days later, an eclipse of the same type will occur – but it will
be seen 0.321 × 360 = 120o farther west.
Annular eclipse on 8/21/2017. When will the same eclipse occur again?
When will it occur again and be visible from the same location?
Total Solar Eclipses Visible from the USA
http://sunearth.gsfc.nasa.gov/eclipse/eclipse.html
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