Chapter 6 The Earth-Moon System

6-1 Measuring the Moon’s Distance and Size When viewed from two different places on Earth, the parallactic shift in the Moon's position can be observed, giving the distance to the Moon. In this way Ptolemy obtained a value of 27.3 Earth diameters for the Moon's distance. Its actual distance is 30.13 Earth diameters, or about 380,000 km.

The Size of the Moon By combining knowledge of an object’s angular size with its distance we can determine its size. Angular size is the angle between two lines that start at the observer and go to opposite sides of the object. The angular size of the Moon as seen from the Earth is close to 0.5 degrees.

The Small-Angle Formula The angular size and diameter of an object are related to its distance from the observer.

Summary: Two Measuring Techniques Triangulation: The use of parallax to determine distance to an object. 2. The small angle formula relates angular size, actual diameter, and distance. If you know any two quantities you can calculate the third.

The Moon’s Changing Size The Moon’s orbit is not circular. The larger apparent diameter of the Moon occurs at perigee, or the closest distance to the Earth. The smaller apparent diameter occurs at the Moon's maximum distance, apogee. Courtesy of Galileo Project, NASA.

6-2 The Tides Low tide on the left; high tide on the right. Campobello Island, Canada. © Andrew J. Martinez/Photo Researchers, Inc.

Tidal force: A gravitational force that varies in strength and/or direction over an object, causing it to deform. Point A feels the greatest lunar gravitational force. Point B feels less. Point C feels the least. Most of the Earth is covered by water, which can flow to areas at points A and C.

The sides of the Earth nearest and farthest from the Moon experience high tide. The areas in between experience low tide. Time between high tides = about 12 hr 50 min. The Earth must make more than one complete rotation to return to the same orientation with respect to the Moon, which has also moved in that time.

The Sun also causes tides on the Earth The Sun also causes tides on the Earth. The Moon’s tidal force on the Earth is 2.2 times that of the Sun’s. Spring tide: The greatest difference between high and low tide, occurring about twice a month, when the lunar and solar tides correspond. Neap tide: The least difference between high and low tide, occurring when the solar tide partly cancels the lunar tide.

Rotation and Revolution of the Moon The Moon’s rotation period = its period of revolution. It keeps the same face toward Earth at all times. This is the result of tidal forces. On Earth, there is tidal friction between the water tidal bulges and the land masses. Tidal friction: Friction forces that result from the movement of tides on a rotating object caused by its gravitational interactions with another object.

Tidal friction between the water and the land is slowing Earth's rotation. Similar tides in the solid Moon have already slowed its rotation. Tidal friction pushes the tidal budges out of alignment with the Moon. This also causes the Moon's orbit to become larger.

Precession of the Earth The Earth is flattened by its rotation, making it oblate. The diameter across the equator is about 43 km greater than pole to pole. Oblateness: A measure of the “flatness” of a planet, calculated by dividing the difference between the largest and smallest diameters by the largest diameter.

Precession: The conical shifting of the axis of a rotating object. The differences in gravitational forces from the Moon on different parts of the Earth cause the Earth’s precession.

The Earth's axis precesses with a period of about 26,000 years, pointing to different “pole stars” over the centuries. Polaris is the pole star now. The radius of the precession circle is 23.5o. The locations of the equinoxes and solstices also change due to precession.

6-3 Earth The Interior of the Earth Density: The ratio of an object’s mass to its volume. Earth's average density is 5.52 g/cm3. For comparison: water’s density is 1 g/cm3, aluminum’s is 2.7 g/cm3, iron is 7.8 g/cm3. This tells us the interior of the Earth must have metals to make a high average density.

Crust: The thin, outermost layer of the Earth. Density is 2 Crust: The thin, outermost layer of the Earth. Density is 2.5 to 3 g/cm3. Mantle: The thick, solid layer between the crust and the core of the Earth. Density ranges from 3 to 9 g/cm3. Core: The central part of the Earth, consisting of a solid inner core surrounded by a liquid outer core. Density ranges from 9 to 13 g/cm3 and is thought to be made up of iron and nickel.

Chemical differentiation: The sinking of denser materials toward the center of planets or other objects. When the Earth formed and was in a molten state, heavier elements sunk through the less dense layers. We know the makeup of the Earth's interior primarily by detecting of waves that result from earthquakes: P waves: Seismic waves analogous to the waves produced by pushing a spring back and forth. S waves: Seismic waves analogous to the waves produced by shaking a rope up and down.

Plate Tectonics Continental drift: The gradual motion of the continents relative one another. Plate tectonics: The motion of sections of the Earth's crust (plates) across the underlying mantle.

Rift zone: A place where tectonic plates are being pushed apart, normally by molten material being forced up out of the mantle. In other locations plates are pushed together and one plate is pushed below another. There are about 12 plates. They are 50 to 100 km thick.

Earth's Atmosphere 78% nitrogen; 21% oxygen, with water vapor, carbon dioxide, ozone making up a small percentage. Most of the atmosphere - about 75% - lies within 11 km of the surface in the troposhere. Troposphere: The lowest level of the Earth’s (and some other planets’) atmosphere.

Earth’s Magnetic Field Magnetic field: A magnetic field exists in a region of space if magnetic forces can be detected in that region. The poles of the magnetic field are located near the rotation poles. The magnetic poles can wander around. The shape is similar to that of a bar magnet. The Earth’s magnetic north is actually a “south” pole (and the magnetic south is actually a “north” pole).

Dynamo model: The model that explains the Earth’s magnetic fields as due to currents within a molten iron core. Three main conditions are needed: A seed magnetic field. (The Sun's magnetic field started the process.) A conducting fluid. (The molten iron outer core.) An energy source to move the field in an appropriate pattern. (Earth’s rotation and convection in the outer core.)

Van Allen belts are regions where the magnetic field of the Earth traps charged particles from the Sun. The belts surround the Earth except near the poles. Some particles spiral along the field lines and hit the atmosphere near the poles. Aurora: Light radiated in the upper atmosphere due to impacts of charged particles.

6-4 The Moon's Surface The Moon’s surface can be divided into two types: Maria (singular mare): Lowlands of the Moon or Mars that resemble a sea when viewed from Earth. Mountainous, cratered regions. Craters on the Moon are the result of impacts of meteorites from space, not volcanic in origin. Meteorite: An interplanetary chunk of matter that has struck a planet or moon.

Lunar craters are lower than the surrounding surface and not on mountaintops. They also can overlap. On Earth, impact craters are erased by erosion and the atmosphere prevents only the largest meteoroids from reaching its surface. These reasons don’t affect the Moon. Craters form more by an explosion when the object hits rather than material just splashing away by the impact. Most impact craters are nearly circular.

Tycho is the bright crater near the bottom of this photo. Maria are the result of volcanic eruptions. They are roughly circular perhaps because they were floors of large craters. Lunar ray: A bright streak on the Moon caused by material ejected from a crater. Tycho is the bright crater near the bottom of this photo. Courtesy of NASA/JPL.

These result from bombardment by countless meteorites. The top few centimeters of the surface are made of loose powdery lava, small rocks, and spherical pieces of glass. These result from bombardment by countless meteorites. Courtesy of NASA, JSC Digital Image Collection.

The crust is 60 to 100 km thick. It is thinner on the side facing the Earth. Mountains on the Moon are formed by overlapping crater walls. The density of the Moon is 3.35 g/cm3, close to an average rock density, so it must have only a small iron core. The Moon’s magnetic field is very weak.

6-5 Theories of the Origin of the Moon Evidence indicates that the Moon formed about 4.6 billion years ago. Double planet (or co-creation) theory: holds that the Moon was formed at the same time as the Earth. They formed together from the same disk of material. This theory is ruled out because it predicts the densities of both would be the same, but they are not.

Fission theory: A theory that holds that the Moon formed when material was spun off from the Earth. The density of the Moon is similar to the Earth's crust. It is difficult to explain why the Earth was spinning so fast or how an object as massive as the Moon is thown off. The Moon does not orbit in the plane of the Earth's equator.

Capture theory: Holds that the Moon was originally solar system debris that was captured by the Earth Being on the right paths for capture is very unlikely. The Moon seems to have formed at a higher temperature than the Earth and has smaller proportions of volatiles. Volatiles: Capable of being vaporized at a relatively low temperature.

6-6 The History of the Moon Overlapping craters provide information on the order of events in the Moon's history. The ages of rocks can be determined with radioactive dating. Radioactive dating: A procedure that examines the radioactivity of a substance to determine its age. Rocks we’ve found on the Moon are as old as 4.42 billion years. Image © UC Regents/Lick Observatory.

Most craters formed between 4.2 and 3.9 billion years ago. Giant impacts near the end of that period formed the maria. The interior of the Moon was still molten and flowed to fill in the floors of those giant craters. This volcanic period ended about 3.1 billion years ago. Cratering continues today, but at a reduced rate. Micrometeorites (tiny meteorites) strike the surface, further pulverizing the soil.