The Motion of the Planets

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The Motion of the Planets
The planets are orbiting the sun almost exactly
in the plane of the Ecliptic.
Jupiter
Venus
Mars
Earth
Mercury
Saturn
The Moon is orbiting Earth in almost the same
plane (Ecliptic).
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Inferior planets are visible only at small
angular distances from the Sun
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The Motion of the Planets
Mercury appears at most 28 from the sun. It can
occasionally be seen shortly after sunset in the
west or before sunrise in the east. Venus appears
at most 46 from the sun. It can occasionally
be seen for at most a few hours after sunset in
the west or before sunrise in the east.
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The Cycles of the Moon

• Chapter 3

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Outline
I. The Changeable Moon A. The Motion of the
Moon B. The Cycle of Phases II. The Tides A.
The Cause of the Tides B. Tidal Effects III.
Lunar Eclipses A. Earth's Shadow B. Total Lunar
Eclipses C. Partial and Penumbral Lunar Eclipses
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Outline (continued)
IV. Solar Eclipses A. The Angular Diameter of
the Sun and Moon B. The Moon's Shadow C. Total
Solar Eclipses V. Predicting Eclipses A.
Conditions for an Eclipse B. The View From
Space C. The Saros Cycle
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The Phases of the Moon (1)
From Earth, we see different portions of the
Moons surface lit by the sun, causing the phases
of the Moon.
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Lunar Phases
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The Phases of the Moon (2)

• The Moon orbits Earth in a sidereal period of
  27.32 days.

27.32 days
Earth
Moon
Fixed direction in space
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The Phases of the Moon (2)
Fixed direction in space
29.53 days
Earth
Moon
Earth orbits around Sun gt Direction toward Sun
changes!

• The Moons synodic period (to reach the same
  position relative to the sun) is 29.53 days ( 1
  month).

Synodic period defines the cycle of lunar phases
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Tides
Newtons law of gravitation
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Tides
Integrate over the mass distribution In the
Earths body
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The Tides
Caused by the difference of the Moons
gravitational attraction on the water on Earth
Excess gravity pulls water towards the moon on
the near side
Forces are balanced at the center of the Earth
? 2 tidal maxima
Excess centrifugal force pushes water away from
the moon on the far side
? 12-hour cycle
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Spring and Neap Tides

• The Sun is also producing tidal effects, about
  half as strong as the Moon.
• Near Full and New Moon, those two effects add up
  to cause spring tides.
• Near first and third quarter, the two effects
  work at a right angle, causing neap tides.

Spring tides
Neap tides
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Effects of tides

• Slow down the rotation of earth

• Seabed slips under the water bulges
• Friction slows down the rotation
• The day was 18 hours long 900 million yr ago

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The Tidally-Locked Orbit of the Moon
The Earth also exerts tidal forces on the moons
rocky interior that slow down its rotation. ? It
is rotating with the same period around its axis
as it is orbiting Earth (tidally locked). ? We
always see the same side of the moon facing Earth.
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Acceleration of the Moons Orbital Motion
Earths tidal bulges are slightly tilted in the
direction of Earths rotation.
Gravitational force pulls the moon slightly
forward along its orbit.
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Effects of tides
1. Synchronization of the rotational and orbital
period
2. Tides cause the heating of the interiors of
the interacting bodies
3. If the bodies are too close to each other,
they can be disrupted by tides (Roche
limit).
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Tides - reality
Modulated by ellipticity of the Earths and
Moons orbits
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Eclipses
p. 28
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Why not every new and full moon??
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Moons orbit is tilted by 5o from the ecliptic
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For an eclipse to occur,

1. The moon should be at one of the nodes crossing
   the plane of the earths orbit
2. The line of nodes should point at the sun

Fig. 3-15, p. 36
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Conditions for Eclipses
The moons orbit is inclined against the ecliptic
by 50.
A solar eclipse can only occur if the moon passes
a node near new moon.
A lunar eclipse can only occur if the moon passes
a node near full moon.
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Lunar Eclipses
Earths shadow consists of a zone of partial
shadow, the Penumbra, and a zone of full shadow,
the Umbra.
If the moon passes through Earths full shadow
(Umbra), we see a lunar eclipse.
If the entire surface of the moon enters the
Umbra, the lunar eclipse is total.
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(No Transcript)
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A Total Lunar Eclipse (1)
Note a circular shadow from this observation
Aristotle concluded that Earth is a sphere!
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Lunar Eclipses 2002-2012
Typically, 1 or 2 lunar eclipses per year.
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Solar Eclipses
Earth-Moon system to scale
How come that the Moon can eclipse the Earth??
Accidentally, they have almost the same angular
sizes!
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Linear diameter
Angular diameter (rad)
?(rad) L/D
Distance
?(deg) ?(rad)?180/?
180 degrees ? radian
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Small Angle Formula
Convert from radian to arcseconds

• radian 180 degrees

1 deg 60 arcmin 3600 arcsec
Note units!!
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Exact Formula
Convert from radian to arcseconds

• radian 180 degrees

1 deg 60 arcmin 3600 arcsec
Note units!!
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Small Angle Formula
(SLIDESHOW MODE ONLY)
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3476 km
Moon
?
0.0091 rad 0.5 deg
384000 km
1.4?106 km
Sun
?
0.0093 rad 0.5 deg
1.5?108 km
Very close!
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Solar Eclipses
The sun appears approx. as large in the sky (same
angular diameter 0.50) as the moon. ? When the
moon passes in front of the sun, the moon can
cover the sun completely, causing a total solar
eclipse.
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Umbra is below 270 km in diameter It moves at
1600 km/hr Total eclipse lasts for not more than
7.5 min
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Total Solar Eclipse
Chromosphere and Corona
Prominences
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Solar Atmosphere Revealed
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Diamond Ring Effect
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Moons orbit is elliptical -gt when the moon is in
apogee, umbra does not reach the earth -gt annular
eclipse
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Annular Solar Eclipses
When Earth is near perihelion, and the moon is
near apogee, we see an annular solar eclipse.
The angular sizes of the moon and the sun vary,
depending on their distance from Earth.
Perigee
Apogee
Aphelion
Perihelion
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Solar Eclipses 2002-2012
Approximately 1 total solar eclipse per year
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The Saros Cycle
Saros cycle 18 years, 11 days, 8 hours
Repeats in one place every 3 cycles, or 54 yr
1 month