The Motion of the Planets
The planets are orbiting the sun almost
exactly in the plane of the Ecliptic.
Venus
Mercury
The Moon is orbiting Earth in almost the
same plane (Ecliptic).
Slide 1
Inferior planets are visible only at small
angular distances from the Sun
Slide 2
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.
Slide 3
Chapter 3
The Cycles of the Moon
Slide 4
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
Slide 5
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
Slide 6
The Phases of the Moon (1)
From Earth, we
see different
portions of the
Moon’s surface
lit by the sun,
causing the
phases of the
Moon.
Slide 7
Lunar Phases
Slide 8
The Phases of the Moon (2)
• The Moon orbits Earth in a sidereal period of
27.32 days.
27.32 days
Moon
Earth
Fixed direction in space
Slide 9
The Phases of the Moon (2)
Fixed direction in
space
29.53 days
Earth
Moon
Earth orbits around Sun =>
Direction toward Sun
changes!
• The Moon’s synodic
Slide 10
period (to reach the same
position relative to the
sun) is 29.53 days (~ 1
month).
Synodic period
defines the cycle of
lunar phases
Tides
Newton’s law of gravitation
Slide 11
Tides
Integrate over the mass distribution
In the Earth’s body
Slide 12
The Tides
Caused by the
difference of the Moon’s
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
Excess centrifugal
force pushes water
away from the moon
on the far side
Slide 13

2 tidal maxima
 12-hour cycle
Spring and Neap Tides
Spring 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.
Neap tides
Slide 14
• Near first and
third quarter, the
two effects work
at a right angle,
causing neap
tides.
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
Slide 15
The Tidally-Locked Orbit of the Moon
The Earth also
exerts tidal forces
on the moon’s rocky
interior that slow
down its rotation.

It is rotating with
the same period
around its axis as it
is orbiting Earth
(tidally locked).

Slide 16
We always see
the same side of the
moon facing Earth.
Acceleration of the Moon’s Orbital
Motion
Earth’s tidal bulges are
slightly tilted in the direction
of Earth’s rotation.
Slide 17
Gravitational force
pulls the moon slightly
forward along its orbit.
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).
Slide 18
Tides - reality
Modulated by ellipticity of the Earth’s and Moon’s orbits
Slide 19
Eclipses
Slide 20
p. 28
Why not every new and full moon??
Slide 21
Moon’s orbit is tilted by 5o from the ecliptic
Slide 22
For an eclipse to occur,
1.
2.
Slide 23
The moon should be at one of the nodes – crossing the plane of the earth’s orbit
The line of nodes should point at the sun
Fig. 3-15, p. 36
Conditions for Eclipses
The moon’s orbit is inclined against the ecliptic by ~ 50.
A solar eclipse can only
occur if the moon passes a
node near new moon.
Slide 24
A lunar eclipse can only
occur if the moon passes a
node near full moon.
Lunar Eclipses
Earth’s
shadow
consists of a
zone of partial
shadow, the
Penumbra,
and a zone of
full shadow,
the Umbra.
Slide 25
If the moon passes through Earth’s full shadow
(Umbra), we see a lunar eclipse.
If the entire surface of the moon enters
the Umbra, the lunar eclipse is total.
Slide 26
A Total Lunar Eclipse (1)
Slide 27
Note a circular shadow: from this observation Aristotle
concluded that Earth is a sphere!
Lunar Eclipses: 2002-2012
Typically, 1 or
2 lunar
eclipses per
year.
Slide 28
Solar Eclipses
Earth-Moon system to scale
How come that the Moon can eclipse the Earth??
Accidentally, they have almost the same angular sizes!
Slide 29
Angular diameter (rad) =
180 degrees =  radian
Slide 30
Linear diameter
Distance
(rad) = L/D
(deg) = (rad)180/
Small Angle Formula
L(line arsiz e )
 (rad) 
D(distance )
Convert from radian to arcseconds:
L
D

 radian = 180 degrees
1 deg = 60 arcmin = 3600 arcsec
1 rad 
180

de g 
180

3600arcse c 206265arcse c
L
 (arcse c)  206,265 (rad)  206,265
D
Slide 31
Note units!!
Exact Formula
 L 
 (rad)  2 arctan 
 2D 
Convert from radian to arcseconds:
L
D

 radian = 180 degrees
1 deg = 60 arcmin = 3600 arcsec
1 rad 
180

de g 
180

3600arcse c 206265arcse c
 (arcse c)  206,265 (rad)
Slide 32
Note units!!
Small Angle Formula
Slide 33
(SLIDESHOW MODE ONLY)
Moon:
Sun:
=
3476 km
= 0.0091 rad = 0.5 deg
384000 km
=
1.4106 km
1.5108
Very close!
Slide 34
km
= 0.0093 rad = 0.5 deg
Solar Eclipses
The sun appears approx. as large in the sky (same angular
diameter ~ 0.50) as the moon.

Slide 35
When the moon passes in front of the sun, the moon can
cover the sun completely, causing a total solar eclipse.
Umbra is below 270 km in diameter
It moves at 1600 km/hr
Total eclipse lasts for not more than 7.5 min
Slide 36
Total Solar Eclipse
Chromosphere and Corona
Prominences
Slide 37
Solar Atmosphere Revealed
Slide 38
Diamond Ring Effect
Slide 39
Moon’s orbit is elliptical -> when the moon is in apogee,
umbra does not reach the earth -> annular eclipse
Slide 40
Annular Solar Eclipses
When Earth is near perihelion, and
the moon is near apogee, we see
an annular solar eclipse.
Perigee
Slide 41
Apogee
Perihelion
Aphelion
The angular
sizes of the
moon and the
sun vary,
depending on
their distance
from Earth.
Solar Eclipses: 2002-2012
Approximately 1 total solar eclipse per year
Slide 42
The Saros Cycle
Saros cycle: 18 years,
11 days, 8 hours
Slide 43
Repeats in one place every
3 cycles, or ~ 54 yr 1 month