CHAPTER 6
The Earth-Moon System
CHAPTER OUTLINE
6-1 Measuring the Moon’s Distance and Size
The Distance to the Moon
1. Using parallax, Ptolemy determined that the distance from the Earth to the Moon is
27.3 Earth diameters — close to the correct average distance of 30.13.
2. Since the Earth’s diameter is about 12,800 km, thirty Earth diameters puts the Moon at
about 380,000 km from Earth.
The Size of the Moon
1. Angular size of the Moon is close to 0.5°.
2. The Moon’s apparent diameter depends on its distance from the observer and on its
angular size.
The Small-Angle Formula
1. The diameter (width) of an object is directly proportional to its angular size and its
distance from the observer.
2. Small angle formula is accurate for angles less than 5°.
3. Small angle formula yields a value of 3,480 km (2,160 mi) for Moon’s diameter.
Summary: Two Measuring Techniques
1. The triangulation (parallax) method relies on the relationship among size of the
baseline, angle of parallax, and distance to the object.
2. Another important relationship exists among angular size, actual diameter, and
distance.
The Moon’s Changing Size
1. Larger apparent diameter of the Moon occurs at perigee—the point in the orbit of an
Earth satellite where it is closest to Earth—which is at a distance of 363,300 km.
2. Smaller apparent size of the Moon occurs at apogee—the point in the orbit of an Earth
satellite where it is farthest from Earth—which is at a distance of 405,500 km.
6-2 The Tides
1. The Moon exerts a gravitational force on each individual part of the Earth. This tidal
force varies in strength and direction over the Earth causing it to deform.
2. A unit mass on the side of the Earth closest to the Moon feels a gravitational force
from the Moon about 3% greater than the force on a unit mass at the Earth’s center,
which in turn is 3% greater than the force on a unit mass at the far side of the Earth.
3. On the side of the Earth nearest the Moon, water feels a greater force and flows to the
area under the Moon, causing a high tide.
4. A high tide on the opposite side of the Earth (farthest from the Moon) occurs because
the center of the Earth feels a greater force toward the Moon than water on that side, so
the main body of the Earth is pulled away from the water, resulting in another high tide.
5. Differential gravitational pull on the various parts of the Earth results in two areas of
the Earth experiencing high tides. On most days on the Earth there are two high tides and
two low tides.
6. As the Earth rotates on its axis, the Moon revolves around the Earth. Because the
Moon is not stationary, the Earth must turn for an additional 50 minutes each day before
a spot on the Earth returns to the same position with respect to the Moon. This is what
causes the high tides and the rising and setting of the Moon to occur about 50 minutes
later each day.
7. The Sun’s gravity also causes tides on Earth. Even though the Sun’s gravitational pull
on a unit mass of Earth is about 180 times stronger than the corresponding pull from the
Moon, the differential pull is smaller. In fact, the difference in the Moon’s pull on
opposite sides of the Earth is a bit more than 2 times greater than the difference in the
Sun’s pull.
8. A spring tide is the greatest difference between high and low tide, occurring about
twice a month when the lunar and solar tides correspond.
9. A neap tide is the least difference between high and low tide, occurring when the solar
tide partly cancels the lunar tide (i.e., when the solar tides are 90° from the Moon’s).
Rotation and Revolution of the Moon
1. The period of the Moon’s rotation exactly matches its period of revolution. This is
caused by tidal forces, and as a result the Moon keeps the same face toward Earth at all
times.
2. There are frictional forces between the solid Earth and its oceans. The Earth’s motion
tends to drag the tides along with it, so that a high tide is not directly under the Moon but
is farther to the east.
3. Tidal friction (i.e., friction forces that result from tides on a rotating object) has
slowed Earth’s rotation over time.
4. The Earth and Sun also cause Moon tides, similar to the tides on the solid Earth.
Through millions of years, the tides have slowed the Moon’s rotation until it now keeps
its same face toward the Earth.
5. As a result of tidal interactions, the Moon is pushed farther away from Earth.
6. Tides on the Earth are complicated because land masses disturb the flow of water. The
shape of the shoreline, the depth of the water, and the location of the Moon all play a part
in determining exactly when high and low tides occur at a particular location and just
how high and how low those tides are.
7. We actually see about 59% of the Moon’s surface because of libration, the small
oscillation of the Moon about its mean position, for three reasons.
(a) The Moon’s orbit about the Earth is eccentric; itss rotation sometimes leads its orbital
position and sometimes lags behind.
(b) The Moon’s equator is tilted about 1.5o from its orbit plane.
(c) As the Earth rotates, an observer on Earth’s surface is offset from the line connecting
the centers of the two objects.
Precession of the Earth
1. Precession is the conical shifting of the axis of a rotating object, also known as
wobbling.
2. The Earth is not a perfect sphere; its equatorial diameter is about 26 miles greater than
its polar diameter. Earth’s spinning on its axis causes it to flatten slightly at the poles.
3. Oblateness is a measure of the “flatness” of a planet, calculated by dividing the
difference between the largest and smallest diameter by the largest diameter.
4. The Moon’s and Sun’s gravitational forces acting on the “flattened” spinning Earth
causes its rotation axis to precess. The Earth precesses very slowly, requiring a period of
about 26,000 years.
5. As the Earth precesses, stars different from Polaris (or no visible stars) occupy the
position near the Earth’s north celestial pole. A corresponding effect is that the position
of the vernal equinox changes over the centuries.
6. The gravitational effects of other planets on the Earth are small but also cause its orbit
to precess and the ellipticity of its orbit to oscillate.
Summary: Tidal Interactions
1. Tidal phenomena are universal; they occur in any system where gravitational
interactions change in time and space.
2. Tidal interactions also occur in galaxy interactions, planetary rings, the shell of comets
around our solar system, generation of heat from friction inside bodies, spin-orbit
resonances.
6-3 Earth
The Interior of the Earth
1. Density is the ratio of an object’s mass to its volume. Earth’s average density is 5.52
g/cm3. (The density of water is 1 g/cm3; of aluminum 2.7 g/cm3; of iron 7.8 g/cm3.)
2. Earth’s interior is made up of three layers.
(a) Crust is the thin (<100 km) outermost layer of the Earth; it has a density of 2.5–3
g/cm3.
(b) Mantle is the thick (2900 km) solid layer between the crust and the Earth’s core; it
has a density of 3–9 g/cm3. The crust “floats” on top of the mantle.
(c) Core is the central part of the Earth, composed of a solid inner core and a liquid outer
core. The core is probably composed of iron and nickel and its density ranges from 9–13
g/cm3.
3. This pattern of increasing density is called chemical differentiation and is caused by
the sinking of denser materials toward the center of planets or other objects.
4. We know about the makeup of the Earth’s interior by analyzing travel times of two
types of waves generated by earthquakes: the P-waves (primary waves, analogous to
waves produced by pushing a spring back and forth), and the S-waves (secondary waves,
analogous to the waves produced by shaking a rope attached to a wall up and down).
Plate Tectonics
1. Alfred Wegener is credited with first developing the idea of continental drift—the
gradual motion of the continents relative to one another.
2. Rift zone is a place where tectonic plates are being pushed apart, normally by molten
material being forced up out of the mantle.
3. The theory of plate tectonics states that sections of the Earth’s crust move across the
underlying mantle. There are about 12 tectonic plates that extend about 50–100 km deep.
4. Over millions of years, moving plates—often crashing into one another—have caused
the continents to “drift,” mountains to be uplifted, ocean trenches to form, and
earthquakes to be unleashed.
Earth’s Atmosphere
1. Earth’s atmosphere consists of about 78% nitrogen (N2), 21% oxygen (O2), with minor
amounts of water vapor (H2O), carbon dioxide (CO2), argon (Ar), and trace amounts of
ozone (O3).
2. Troposphere is the lowest level of the Earth’s atmosphere, containing 75% of the
atmospheric mass; it is about 11 km (7 mi) deep and is where weather occurs.
3. The troposphere receives most of its heat from infrared radiation emitted from the
ground; thus, the temperature of the troposphere decreases as one goes higher.
4. About 50 km above the Earth’s surface is the ozone layer. Ozone is an efficient
absorber of the Sun’s UV radiation. This absorption causes the temperature of the Earth’s
atmosphere to peak at the ozone layer.
5. The ozone layer has protects life on Earth from harmful ultraviolet radiation. The
release of chlorofluorocarbons during the 20th century has reduced, through molecular
interactions, the amount of ozone available to protect us.
Earth’s Magnetic Field
1. A magnetic field exists in a region of space if magnetic forces can be detected there.
2. The magnetic poles of the Earth are not located at its poles of rotation. The location of
the magnetic poles changes with time.
3. According to the dynamo model, the Earth’s (and other planets’) magnetic field is due
to currents within a molten iron core.
4. The three main conditions for generating a magnetic field are: (i) a seed magnetic field,
(ii) a conducting fluid, and (iii) an energy source to move the fluid in an appropriate
pattern.
5. The Earth’s field is 0.3 – 0.7 gauss (being stronger at the poles compared to the equator), the Sun’s field in the photosphere is 0.5 – 4 gauss, and that of a typical refrigerator
magnet is about 50 gauss.
6. The Van Allen belts are doughnut-shaped regions composed of charged particles
(protons and electrons) emitted by the Sun and captured by the magnetic field of the
Earth.
7. Auroras are caused by charged particles trapped in the Earth’s magnetic field striking
atoms and molecules in the upper atmosphere.
6-4 The Moon’s Surface
1. The surface of the Moon can be divided into maria and mountainous, cratered regions.
2. Mare (plural maria) are any of the lowlands of the Moon or Mars that resemble a sea
when viewed from Earth.
3. Most craters on the Moon are the result of impacts by meteorites—an interplanetary
chunk of matter that has struck a planet or moon.
4. Earth has few impact craters because its atmosphere keeps all but the largest meteorites
from reaching the surface. Over time, erosion and tectonic plate movement has erased all
but a relative few of the largest craters. On the airless Moon, Mercury, satellites of other
planets, and even asteroids, craters remain intact and visible for billions of years.
5. Lunar ray is a bright streak on the Moon caused by material ejected from a crater.
6. The Moon’s maria are the result of volcanic action leading to massive lava flows.
7. The top few centimeters of the Moon’s surface are a fine dust, the result of
bombardment by countless meteorites.
8. The Moon’s crust ranges in depth from 60–100 km and is thinner on the side facing the
Earth.
9. Mountains on the Moon are the result of extensive cratering over eons.
10. A new theory suggests that the highlands on the Moon’s far side are the result of
debris left over from a collision between the young Moon and a large moonlet.
11. The Moon’s density is 3.35 g/cm3. Its core, if composed of iron, must be small.
12. The Moon’s weak magnetic field—10−4 times that of Earth’s magnetic field—
suggests the presence of a small iron core, though this has not been confirmed.
13. Spacecraft have found water ice in some polar craters. The extremely low
temperatures in the craters allow the existence of water ice that might have been
delivered there by comet impacts or formed by chemical reactions between the solar wind
and the moon’s surface.
14. Sensors on the Moon have detected very weak natural moonquakes. There is no evidence for plate tectonics on the Moon’s surface, and the cause of these quakes is the tidal
interactions between the Earth and Moon.
6-5 Theories of the Origin of the Moon
1. Evidence indicates that the Moon formed about 4.6 billion years ago.
2. According to the double planet theory the Earth and Moon formed at the same time
from the same rotating disk of material. The different densities of the Earth and Moon
seem to rule out this scenario.
3. According to the fission hypothesis, the large basin of the Pacific Ocean is the place
from which the Moon was ejected due to the Earth’s fast rotation. This theory cannot
explain the Moon’s current orbit nor offer an adequate rationale for what force could
have caused the Moon to be torn from the Earth.
4. According to the capture theory, the Moon was originally solar system debris that
was captured by the Earth’s gravitational field. Dynamically, a third object is required for
capture, and the chance of this happening with the Moon and Earth is highly unlikely.
5. The Moon’s chemical composition is similar to that of the Earth’s crust, but the Moon
has smaller proportions of volatile—easily vaporized—substances than the Earth.
The Large Impact Theory
1. According to the large impact theory, the Moon formed as the result of a glancing
impact between a large Mars-sized object and the Earth. This theory can explain the
relative compositions of the Earth and Moon, the Moon’s orbit, and the Earth’s rotation
rate. This theory has also been successfully modeled on a supercomputer.
6-6 The History of the Moon
1. The order of events in the Moon’s history can be pieced together by comparing
overlapping craters, overlapping rays, and the darkness of rays.
2. Radioactive dating techniques on the 840 pounds of Moon rocks brought back to
Earth by the Apollo astronauts have been indispensable in forming a model of the
Moon’s history.
3. The Moon formed about 4.6 billion years ago.
4. Most craters formed between 4.2 and 3.9 billion years ago. Giant impacts near the end
of the cratering period formed the maria.
5. After cratering ended, the Moon’s interior became hot from radioactive decay and
molten lava flowed, ending about 3.1 billion years ago. The Moon has probably remained
relatively unchanged since then.
6. Micrometeorites (tiny meteorites) still hit the Moon, but no new large crater has ever
been observed.