Slide 1

The Motion of the Planets

The planets are orbiting the sun almost exactly in the plane of the Ecliptic.

Jupiter

MarsEarth

Venus

Mercury

Saturn

The Moon is orbiting Earth in almost the same plane (Ecliptic).

Slide 2

Inferior planets are visible only at small angular distances from the Sun

Slide 3

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 4

The Cycles of the MoonChapter 3

Slide 5

I. The Changeable MoonA. The Motion of the MoonB. The Cycle of Phases

II. The TidesA. The Cause of the TidesB. Tidal Effects

III. Lunar EclipsesA. Earth's ShadowB. Total Lunar EclipsesC. Partial and Penumbral Lunar Eclipses

Outline

Slide 6

IV. Solar EclipsesA. The Angular Diameter of the Sun and MoonB. The Moon's ShadowC. Total Solar Eclipses

V. Predicting EclipsesA. Conditions for an EclipseB. The View From SpaceC. The Saros Cycle

Outline (continued)

Slide 7

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 8

Lunar Phases

Slide 9

The Phases of the Moon (2)• The Moon orbits Earth in a sidereal period of 27.32 days.

27.32 days

EarthMoon

Fixed direction in space

Slide 10

The Phases of the Moon (2)

• The Moon’s synodic period (to reach the same position relative to the sun) is 29.53 days (~ 1 month).

Fixed direction in space

Earth

Moon

Earth orbits around Sun => Direction toward Sun

changes!

29.53 days

Synodic period defines the cycle of lunar phases

Slide 11

Tides

Newton’s law of gravitation

Slide 12

Integrate over the mass distributionIn the Earth’s body

Tides

Slide 13

The TidesCaused by the difference of the Moon’s gravitational attraction on the water on Earth

2 tidal maxima

Excess gravity pulls water towards the

moon on the near sideForces are balanced at the center of the Earth

12-hour cycleExcess centrifugal force pushes water away from the moon on the far side

Slide 14

Spring and Neap TidesThe 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

Slide 15

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 16

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).

We always see the same side of the moon facing Earth.

Slide 17

Acceleration of the Moon’s Orbital Motion

Earth’s tidal bulges are slightly tilted in the direction of Earth’s rotation.

Gravitational force pulls the moon slightly forward along its orbit.

Slide 18

Effects of tides1. 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 19

Modulated by ellipticity of the Earth’s and Moon’s orbits

Tides - reality

Slide 20 p. 28

Eclipses

Slide 21

Why not every new and full moon??

Slide 22

Moon’s orbit is tilted by 5o from the ecliptic

Slide 23 Fig. 3-15, p. 36

1. The moon should be at one of the nodes – crossing the plane of the earth’s orbit2. The line of nodes should point at the sun

For an eclipse to occur,

Slide 24

Conditions for Eclipses

A solar eclipse can only occur if the moon passes a node near new moon.

The moon’s orbit is inclined against the ecliptic by ~ 50.

A lunar eclipse can only occur if the moon passes a node near full moon.

Slide 25

Lunar EclipsesEarth’s shadow consists of a zone of partial shadow, the Penumbra, and a zone of full shadow, the Umbra.

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

Slide 27

A Total Lunar Eclipse (1)

Note a circular shadow: from this observation Aristotle concluded that Earth is a sphere!

Slide 28

Lunar Eclipses: 2002-2012

Typically, 1 or 2 lunar

eclipses per year.

Slide 29

How come that the Moon can eclipse the Earth??

Solar Eclipses

Accidentally, they have almost the same angular sizes!

Earth-Moon system to scale

Slide 30

Angular diameter (rad) = Linear diameter

Distance

180 degrees = radian

(rad) = L/D

(deg) = (rad)180/

Slide 31

distance)(

size)linear (rad)(

D

L

D

L 265,206rad)(265,206)arcsec(

radian = 180 degrees

DL

Convert from radian to arcseconds:

arcsec206265 arcsec3600180

deg180

rad1

1 deg = 60 arcmin = 3600 arcsec

Note units!!

Small Angle Formula

Slide 32

D

L

2arctan2rad)(

rad)(265,206)arcsec(

radian = 180 degrees

DL

Convert from radian to arcseconds:

arcsec206265 arcsec3600180

deg180

rad1

1 deg = 60 arcmin = 3600 arcsec

Note units!!

Exact Formula

Slide 33

Small Angle Formula

(SLIDESHOW MODE ONLY)

Slide 34

Moon: = 3476 km

384000 km= 0.0091 rad = 0.5 deg

Sun: =1.4106 km

1.5108 km= 0.0093 rad = 0.5 deg

Very close!

Slide 35

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.

Slide 36

Umbra is below 270 km in diameterIt moves at 1600 km/hrTotal eclipse lasts for not more than 7.5 min

Slide 37

Total Solar Eclipse

Prominences

Chromosphere and Corona

Slide 38

Solar Atmosphere Revealed

Slide 39

Diamond Ring Effect

Slide 40

Moon’s orbit is elliptical -> when the moon is in apogee, umbra does not reach the earth -> annular eclipse

Slide 41

Annular Solar Eclipses

The angular sizes of the moon and the sun vary, depending on their distance from Earth.

When Earth is near perihelion, and the moon is near apogee, we see an annular solar eclipse.

Perigee Apogee Perihelion Aphelion

Slide 42

Solar Eclipses: 2002-2012Approximately 1 total solar eclipse per year

Slide 43

The Saros Cycle

Saros cycle: 18 years, 11 days, 8 hours

Repeats in one place every 3 cycles, or ~ 54 yr 1 month