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A SHORT COURSEA SHORT COURSEinin

ASTRONOMYASTRONOMY

CHAPTER 5CHAPTER 5

SUN - EARTH - MOONSUN - EARTH - MOONRELATIONSHIPSRELATIONSHIPS

Dr. William J. BuslerDr. William J. BuslerAstrophysical Chemistry 439Astrophysical Chemistry 439

A. Phases of the MoonA. Phases of the Moon• The lunar phases are based on two principles:

(1) The Moon orbits the Earth each month, and (2) The Moon shines by reflected sunlight.

New

1st Quarter

Waxing Phases

Full

Gibbous

Gibbous

Crescent

Crescent

Last Quarter

Waning Phases

Earth

Sunset

NoonMidnight

Sunrise

The inner circle of Moon pictures shows the Moon as seen from above the Earth’s north pole, i.e., with its lighted surface facing the Sun. (Assume that the Sun is off to the right, about 400 times the Earth-Moon distance.) The outer circle shows the Moon as it appears from the Earth, i.e., as it displays its phases.

A. Phases of the MoonA. Phases of the Moon• Approximate times of moonrise, transit, and moon-

set. (Review concept of circumpolarity to see why this varies with the Moon’s position on the ecliptic.)

• Note: “Early morning” means between midnight and sunrise; “morning” means between sunrise and noon.

Phase

NewWaxing Crescent

First QuarterWaxing Gibbous

FullWaning Gibbous

Last QuarterWaning Crescent

Rise

sunrisemorning

noonafternoon

sunsetevening

midnightearly morning

Transit

noonafternoon

sunsetevening

midnightearly morning

sunrisemorning

Set

sunsetevening

midnightearly morning

sunrisemorning

noonafternoon

A. Phases of the MoonA. Phases of the Moon• Earthshine: Lunar illumination from the Earth.• The Sun’s light is “twice reflected”; i.e., it bounces

off the Earth, dimly illuminates the dark part of the Moon, and is seen again from the Earth.

• Earthshine is best seen at the time of the crescent Moon, when the Earth is nearly “full” as seen from the Moon.

A. Phases of the MoonA. Phases of the Moon• Fraction of the Moon’s surface as seen from the

Earth:• To a first approximation, we see the same side of

the Moon all the time, since it rotates once on its axis as it makes one revolution around the Earth, and both motions are in the same direction (eastward).

• However, we can see more than 60% of the Moon over a period of time, due to three factors (all of which comprise libration):

A. Phases of the MoonA. Phases of the Moon• 1. Although the Moon’s rotational speed is

constant, its orbital velocity is not, due to its elliptical orbit. Therefore, sometimes its rotation is ahead of its revolution, sometimes behind, allowing us to see “around the edge” of the Moon.

• 2. The Moon’s axis of rotation is tilted 61/2° from the perpendicular to its orbital plane (cf. 231/2° for the Earth). This allows us to see “over (and under) the poles” of the Moon.

• 3. During each night, parallax from the Earth’s rotation allows us to see around the edge of the Moon to a slight extent.

A. Phases of the MoonA. Phases of the Moon• Lunar misnomers: A number of popular terms

regarding the Moon are inaccurate. The most egregious include the following:

• 1. “Half-Moon”: The correct term for the half-illuminated phase of the Moon is “first quarter” or “last quarter”.

• 2. “Dark side of the Moon”: There is no area on the Moon which is always in darkness. What is usually intended is the “far side” of the Moon.

A. Phases of the MoonA. Phases of the Moon• Lunar malapropisms: In cartoons (and in news-

papers in general), it seems that any attempt to depict the phase of the Moon correctly is a total waste of time.

A. Phases of the MoonA. Phases of the Moon• Lunar malapropisms: In cartoons (and in news-

papers in general), it seems that any attempt to depict the phase of the Moon correctly is a total waste of time.

A. Phases of the MoonA. Phases of the Moon• Lunar malapropisms: In cartoons (and in news-

papers in general), it seems that any attempt to depict the phase of the Moon correctly is a total waste of time.

A. Phases of the MoonA. Phases of the Moon• Lunar months: There are two ways of describing

the lunar month:

• The Moon’s sidereal period (one revolution around the Earth with respect to the stars) is 27.3 days.

• The Moon’s synodic period (one revolution around the Earth with respect to the Sun; i.e., from one new Moon to the next) is 29.5 days.

A. Phases of the MoonA. Phases of the Moon

Sun M A

B

M

M 1

2

E

E

At position A, the Moon is directly opposite the Sun (full), and is seen against the background of the stars of a certain constellation. At B-1, 27.3 days later, (the Moon’s sidereal period), the Moon has made one revolution and is

seen against the same starry background. But it is not opposite the Sun, since the Earth has moved during the month. The Moon has to move 2.2 more days before becoming full again (position B-2). Therefore, the Moon’s synodic period is 29.5 days. (Cf. solar and sidereal day, in Chapter 2: The Sky and the Earth.)

B. EclipsesB. Eclipses• 1. Solar: These can only occur at the time of the

new Moon; also, the Moon must be precisely on the ecliptic.

• (The Moon’s orbital plane is inclined 5° to the ecliptic, the Earth’s orbital plane, so eclipses do not occur every month.)

• The geometry of a solar eclipse is shown below:

Not toscale!

Sun E M

B. EclipsesB. Eclipses• Because of a remarkable coincidence, the Sun and

Moon appear to be same size in the sky: 0.5°.• Although the Sun is 400 times the diameter of the

Moon, it is also 400 times as far away.• Depending on the precise distances of the Sun and

Moon at the time of the eclipse, and the position of the observer, several types of solar eclipses can occur:

B. EclipsesB. Eclipses

Total Annular

During a total solar eclipse, the blocked-out Sun looks like this from inside the umbra, the inner shadow cone. Note the corona surrounding the Sun.

Partial

Sun Moon

As seen from anywhere in the penumbra, the outer shadow cone, the partial eclipse looks like the Moon is taking a bite out of the Sun.

If the Moon is too far away to block the Sun entirely, the umbra does not reach the Earth’s surface. Directly below the umbra, the eclipse is annular (ring-shaped).

B. EclipsesB. Eclipses

B. EclipsesB. Eclipses

Total Solar Eclipse of 7-11-91

Astrophotograph by Tony and Daphne Hallas

Total Solar Eclipse of 6-30-73

Astrophotograph by Hans Vehrenberg

Diamond Ring

B. EclipsesB. Eclipses• Total solar eclipses occur frequently (about every

18 months), but you must be on the path of totality (usually only a few miles wide) to see one.

• Since the path is such a small fraction of the Earth’s surface, most people have never witnessed a total solar eclipse.

B. EclipsesB. Eclipses• 2. Lunar: These can only occur when the Moon

is full and is on the ecliptic.

• When the Moon is inside the Earth’s umbra, the lunar eclipse is total and can be seen from anywhere on the nighttime side of the Earth.

• When the Moon is partially in the umbra, the eclipse is partial.

Sun M E

(Not to scale!)

umbra

penumbra

B. EclipsesB. Eclipses• When the Moon is in the penumbra, it is darkened

only slightly. Even during totality, the Moon is visible; it may look red, due to light refracted by and through the Earth’s atmosphere.

• Eclipses occur in cycles. There is a maximum of seven eclipses per year (solar + lunar).

Sun M E

(Not to scale!)

umbra

penumbra

Total Lunar Eclipse

Lunar eclipses are especially

red and dark after

large volcanic

eruptions.

C. TidesC. Tides• Tides are caused by the differential gravitational

pull of the Moon and the Sun on the Earth.• The Moon is much closer; therefore, the difference

in pull of the Moon on the near vs. the far side of the Earth is greater, so it has more effect than the Sun.

• Therefore, the tidal bulges point towards and away from the Moon.

C. TidesC. Tides• The greatest difference in ocean levels occurs at

the time of the new or full Moon, when the Sun, Earth, and Moon are aligned.

• These are called “spring” tides, but the word has nothing to do with the season.

• As the Earth rotates through the bulges and troughs, tides flow in and out twice a day.

Sun M E M

“Spring” tides

C. TidesC. Tides• The least difference occurs when the Moon is at right

angles to the Sun; the Sun cancels some of the Moon’s effect. (This occurs at the first and last quarter.)

• These are called “neap” tides.• There are still two sets of tides per day, but the

difference is not so extreme.

Sun

M

E

M

“Neap” tides

C. TidesC. Tides• The very greatest tides occur when an eclipse takes

place during spring tides.

• The shape of the coastline and the latitude are also important, as is the distance of the Moon.

• The friction of the Earth turning through the tidal bulges has important effects:

• 1. The Earth’s rotation slows by one second every 60,000 to 120,000 years.

C. TidesC. Tides• 2. As a result of tidal friction, the tidal bulges

don’t point directly toward and away from the Moon, but are somewhat counterclockwise.

• Thus, the tides lag behind the Moon’s transit.

Sun E M

C. TidesC. Tides• 3. The tidal bulges pull on the Moon, drawing it

into a higher orbit (3 - 5 centimeters per year).

• Eventually the day and the Moon’s orbital period will become equal at about 50 of our days.

• Then, the same side of the Earth will face the Moon all the time.

Sun E M

T H E E N DT H E E N D