12/12/2011
Full Moon
Lunar Eclipse
The Earth between the Moon and the Sun.
5 degree angle
November 8, 2003
Earth / Moon system is tilted at 5 degree angle from
the Earth / Sun system. At full moon the Moon is not
always directly behind the Earth in relation to the
Sun. However every 6 months or so……….
Lunar Eclipse
Lunar Eclipse
11.08.2003
Penumbra – partial shadow
Moon in Earth’s Shadow
Umbra – complete shadow
NOT TO SCALE
Lunar Eclipse
Lunar Eclipse Colors
• In penumbra only slight dimming is
noticeable.
• Unlike solar eclipses, a lunar eclipse
can be seen by anyone on the nighttime side of the Earth.
• Lunar eclipses last longer (smaller
object, the Moon, passes through
the Earth’s larger shadow.)
Penumbral Lunar Eclipse
• Moon will show color during totality due
to scattering of light in the Earth’s
Atmosphere.
• Color intensity indicates clarity of
atmosphere.
Less atmospheric dust
– Tan / yellow-orange
– Orange
– Red
– Dark red-dark brown
More atmospheric dust
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12/12/2011
Measuring the Diameter and
Distance of the moon from an eclipse
Negative image of an eclipse
How Tall?
Images from the eclipse
can be used to
measure the diameter
and distance of the
Moon.
Lunar Image
Earth’s shadow
Rock = 3.5 (TMart)
Geometry of a Lunar Eclipse
IF the sun was a great distance from the Earth and
the Moon, the shadows would be cylindrical.
Geometry of a Lunar Eclipse
Picture of Moon
Picture of Earth
=
Real Moon
Real Earth
x
#
= #
#
Shadow of Earth
In this case, the Earth’s shadow would be the same size as the
Earth. To find the diameter of the Moon, simply compare the
diameter of the shadow of the Earth to the diameter of the Moon.
Geometry of a Lunar Eclipse
Umbra Shadows of Earth and
Moon are conical.
Geometry of a Lunar Eclipse
• On average during a solar eclipse, Moon’s
shadow cone comes to a point on the surface
of the Earth.
• Therefore, the Moon’s shadow size is reduced
by the diameter of the Moon, in the distance
between the Earth and the Moon.
• Therefore during a lunar eclipse, at the same
distance, the Earth’s shadow will be reduced
by approximately the same amount. (the
diameter of the Moon)
NOT TO SCALE
2
12/12/2011
Geometry of Solar & Lunar Eclipses
Geometry of a Lunar Eclipse
Distance between Earth and Moon
Moon
Earth’s Shadow
In a solar eclipse,
Moons shadow
reduced to a point.
Remember that the
Earth’s shadow has been
reduced by the size of
the Moon.
In a Lunar Eclipse, Earth’s
Shadow reduced by the
diameter of the Moon
Calculating Distance to The Moon
Once diameter of the Moon is known, it is possible to
calculate the distance from the Earth to the Moon.
Calculating Diameter of the Moon
Im = diameter of lunar image
Ies = diameter of image of Earth shadow
De = diameter of Earth
Dm = diameter of Moon
Im
(Ies + Im)
=
Angular diameter of Moon
angle a
Circumference
of lunar orbit
Dm
De
(Im / (Ies+Im)) De = Dm
A =
Diameter of Moon
360
Circumference of lunar orbit
De = 12,756 km (Earatosthenes measurement for
earth’s circumference divided by p)
NOT TO SCALE
Remember Eratosthenes Pizza
If you have 1 piece of pizza…… by measuring the central
angle A and the outside arc length d, then it is possible to
determine the circumference of the pizza.
A
The ratio of angle A (the slice) to
360o (the whole pizza) is the same
as the ratio of length d to the
circumference of the whole pizza.
A
d
=
A
360o
C
Calculating Distance to The Moon
• Angular diameter of the moon is its
apparent size in degrees. (.518 o )
• Once the Circumference of the lunar
orbit is known, The distance to the
moon may be calculated by dividing the
circumference by 2p.
d
Arc length d
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