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.