Ch 3: The Solar System

Mars Landscape

LEARNING OUTCOMES

  • Understand the origin of the solar system by recognizing the similarities and differences between the Inner (terrestrial) and outer (Jovian) planets
  • Describe gravity and explain how it impacts Earth's moon and satellites
  • Explain the motions of the moon that create phases and eclipses
  • Know the formula for eccentricity and know the relationship between orbital shape and eccentricity 
  • Explain the differences between geostationary and polar satellite orbits

Formation of the Solar System

Stars are born in clouds like the one in the picture. Gravity pulls material together. When it is extremely dense, it begins nuclear fusion. That is, it becomes a star. We can see places where stars are being born right now. Of course, it takes visible light a long time to travel to us. So what we see right now may have happened many millions or even billions of years ago. Our solar system began about 5 billion years ago. The sun, planets, and other solar system object all formed at about the same time. The leading hypothesis for how they formed is called the nebular hypothesis.

The sun and planets formed from a giant cloud of gas and dust. This was the solar nebula. The cloud contracted and began to spin. As it contracted, its temperature and pressure increased. The cloud spun faster and formed into a disk. Scientists think the solar system at that time looked like these disk-shaped objects in the Orion Nebula. New stars are forming in the Orion Nebula today. Gravity pulled a lot of material to the center of the cloud. Temperatures and pressures at the center of the cloud were extreme. It was so hot that nuclear fusion reactions began. A star was born—the sun. In these reactions, hydrogen fuses to make helium. Extreme amounts of energy are released.

An artist’s painting of a protoplanetary disk.

Meanwhile, the outer parts of the disk were cooling off. Matter condensed from the cloud. Small pieces of dust started clumping together. These clumps collided and combined with other clumps. Gravity brought more clumps together to make larger bodies. Gravity at the center of the disk attracted to rock and metal. Lighter material remained farther out in the disk. Eventually, these small bodies grew to become the planets and moons that we find in our solar system today.

THE PLANETS
Since gravity pulled the heavy material inward, the inner planets—Mercury, Venus, Earth, and Mars—are made of rock and metal. The outer planets—Jupiter, Saturn, Uranus, and Neptune—condensed farther from the Sun (
Figure below). They are made from lighter materials such as hydrogen, helium, water, ammonia, and methane. Out by Jupiter and beyond, where it’s very cold, these materials form solid particles. There are many comparable characteristics between the planets.  Each planet has a unique size, orbit, tilt, interior and surface characteristics.  Look at this NASA website for those characteristics. http://solarsystem.nasa.gov/planets/compchart.cfm  Dwarf planets, comets, and asteroids formed along with the planets.  The chart below is of some of the physical properties of the planets and moons.  Do you know what these properties represent?

Average orbit distance  Equatorial Circumference  Surface area  Orbital Velocity
Perihelion  Volume   Equatorial surface gravity  Orbital eccentricity
Aphelion   Mass  Escape velocity  Equatorial Inclination
Equatorial radius  Density  Rotational Period  Min/Max surface temperature

 

The Sun and planets (note that this image is old enough to include Pluto, which is no longer considered one of the planets).

The nebular hypothesis explains the basic features of the solar system:

    • The orbits of the planets lie in nearly the same plane. The sun is at the center.
    • The planets revolve in the same direction.
    • The planets mostly rotate in the same direction.
    • The axes of rotation of the planets are mostly nearly perpendicular to the orbital plane.
    • The oldest moon rocks are 4.5 billion years.

 

The Inner Planets

The inner planets, or terrestrial planets, are the four planets closest to the Sun: Mercury, Venus, Earth, and Mars. The figure below shows the relative sizes of these four inner planets. 

This composite shows the relative sizes of the four inner planets. From left to right, they are Mercury, Venus, Earth, and Mars.

Unlike the outer planets, which have many satellites, Mercury and Venus do not have moons, Earth has one, and Mars has two. Of course, the inner planets have shorter orbits around the Sun, and they all spin more slowly. Geologically, the inner planets are all made of cooled igneous rock with iron cores, and all have been geologically active, at least early in their history. None of the inner planets has rings.

SHORT YEAR, LONG DAYS, EXTREME TEMPERATURES
Mercury is named for the Roman messenger god. Mercury was a messenger because he could run extremely fast. The Greeks gave the planet this name because Mercury moves very quickly in its orbit around the Sun. Mercury orbits the Sun in just 88 Earth days. Mercury has a very short year, but it also has very long days. Mercury rotates slowly on its axis, turning exactly three times for every two times it orbits the Sun. Therefore, each day on Mercury is 58 Earth days long.  Mercury is very close to the Sun, so it can get very hot. Mercury also has virtually no atmosphere. As the planet rotates very slowly, the temperature varies tremendously. Indirect sunlight, the surface can be as hot as 427 C (801 F). On the dark side, the surface can be as cold as –183 C (–297 F)! The coldest temperatures may be on the insides of craters. Most of Mercury is extremely dry. Scientists think that there may be a small amount of water, in the form of ice, at the planet's poles. The poles never receive direct sunlight.

MERCURY
The smallest planet, Mercury, is the planet closest to the Sun. Because Mercury is so close to the Sun, it is difficult to observe from Earth, even with a telescope. However, the Mariner 10 spacecraft, shown in Figure below, visited Mercury from 1974 to 1975.

(a) Mariner 10 made three flybys of Mercury in 1974 and 1975. (b) A 2008 image of compiled from a flyby by MESSENGER.

The surface of Mercury is covered with craters, like Earth’s moon. Ancient impact craters mean that for billions of years Mercury hasn’t changed much geologically. Also, with very little atmosphere, the processes of weathering and erosion do not wear down structures on the planet.

Pictured below is a diagram of Mercury's interior (Figure below). Mercury is one of the densest planets. Scientists think that the interior contains a large core made mostly of melted iron. The inner core may be solid. Mercury's core takes up about 85% of the planet's radius.

VENUS
Venus’ thick clouds reflect sunlight well, so Venus is very bright. When it is visible, Venus is the brightest object in the sky beside the Sun and the Moon. Because the orbit of Venus is inside Earth’s orbit, Venus always appears close to the Sun. When Venus rises just before the Sun rises, the bright object is called the morning star. When it sets just after the Sun sets, it is the evening star.

Of the planets, Venus is most similar to Earth in size and density. Venus is also our nearest neighbor. The planet’s interior structure is similar to Earth’s, with a large iron core and a silicate mantle (Figure below). But the resemblance between the two inner planets ends there.

Venus’s interior is similar to Earth’s.

Atmosphere
Clouds on Earth are made of water vapor. Venus's clouds are a lot less pleasant. They are made of carbon dioxide, sulfur dioxide, and large amounts of corrosive sulfuric acid! Scientists think the color of sunlight on Venus is reddish-brown.

The atmosphere of Venus is so thick that the pressure on the surface of Venus is very high. In fact, it is 90 times greater than the pressure at Earth’s surface! The thick atmosphere causes a strong greenhouse effect. As a result, Venus is the hottest planet. Even though it is farther from the sun, Venus is even much hotter than Mercury. Temperatures at the surface reach 465 C (860 F). That’s hot enough to melt lead!

Surface
The surface of Venus is shrouded by thick clouds. Radar images show a complex surface. There are volcanoes and craters like other planets and moons. The surface is not nearly as complex as the surface of Earth. There are a large number of craters on Venus. However, there are not nearly as many as on Mercury or the Moon. So the planet's surface must be fairly young. This suggests that the planet experiences volcanism and has a hot interior.

Volcanoes
Venus has more volcanoes than any other planet. There are between 100,000 and one million volcanoes on Venus! Most of the volcanoes are now inactive. Pictured below is an image made using radar data (Figure below). The volcano is Maat Mons. Lava beds are in the foreground.

Radar image of the Maat Mons volcano on Venus with lava beds in the foreground.

Motion and Appearance
Venus is the only planet that rotates clockwise as viewed from its the North Pole. All of the other planets rotate counterclockwise. Venus turns slowly, making only one turn every 243 days. This is longer than a year on Venus! It takes Venus only 225 days to orbit the Sun.

Because the orbit of Venus is inside Earth’s orbit, Venus always appears close to the Sun. You can see Venus rising early in the morning, just before the Sun rises. For this reason, Venus is sometimes called “the morning star.” When it sets in the evening, just after the Sun sets, it may be called “the evening star”. Since planets only reflect the Sun’s light, Venus should not be called a star at all! Venus is very bright because its clouds reflect sunlight very well. Venus is the brightest object in the sky beside the Sun and the Moon.

MARS
Mars is the fourth planet from the Sun. The Red Planet is the first planet beyond Earth’s orbit. 
Mars’ atmosphere is thin compared to Earth's. This means that there is much lower pressure at the surface. Mars also has a weak greenhouse effect, so temperatures are only slightly higher than they would be if the planet did not have an atmosphere. The Martian climate is most like Earth's of any planet in the solar system.

Exploration
Mars is the easiest planet to observe. As a result, it has been studied more than any other planet besides Earth. People can stand on Earth and observe the planet through a telescope. We have also sent many space probes to Mars. A car-sized robotic rover, Curiosity, arrived on the Red Planet in August 2012. Curiosity joins Opportunity, which has been active since 2004.

No humans have ever set foot on Mars. NASA and the European Space Agency have plans to send people to Mars. The goal is to do it sometime between 2030 and 2040. The expense and danger of these missions are phenomenal.

Surface Features
Mars has mountains, canyons, and other features similar to Earth. But it doesn’t have as much geological activity as Earth. There is no evidence of plate tectonics on Mars. There are also more craters on Mars than on Earth. But there are fewer craters than on the Moon. What does this suggest to you regarding Mars' tectonic history? Pictured below is an image of the Martian surface (Figure below).

Mars is Earth's second nearest neighbor planet.

A Red Planet
Viewed from Earth, Mars is red. This is due to large amounts of iron in the soil. The ancient Greeks and Romans named the planet Mars after the god of war because the planet's red color reminded them of blood. Mars has only a very thin atmosphere made up mostly of carbon dioxide.

Volcanoes
Mars is home to the largest volcano in the solar system: Olympus Mons (Figure below). Olympus Mons is a shield volcano. The volcano is similar to the volcanoes of the Hawaiian Islands. But Olympus Mons is a giant, about 27 km (16.7 miles/88,580 ft) tall. That's three times taller than Mount Everest! At its base, Olympus Mons is about the size of the entire state of Arizona, about 624 km (374 miles) across.

The largest volcano in the solar system, Olympus Mons.

Canyons
Mars also has the largest canyon in the solar system, Valles Marineris (Figure below). This canyon is 4,000 km (2,500 miles) long. That's as long as Europe is wide! One-fifth of the circumference of Mars is covered by the canyon. Valles Marineris is 7 km (4.3 miles) deep. How about Earth's Grand Canyon? Earth's most famous canyon is only 446 km (277 miles) long and about 2 km (1.2 miles) deep. Valles Marineris is thought to be a tectonic crack in the Martian crust.

The largest canyon in the solar system, Valles Marineris

Is There Water on Mars?
Water on Mars can't be a liquid. This is because the pressure of the atmosphere is too low. The planet does have a lot of water; it is in the form of ice. The south pole of Mars has a very visible ice cap. Scientists also have evidence that there is also a lot of ice just under the Martian surface. The ice melts when volcanoes erupt. At these times liquid water flows across the surface.

Curiosity, the rover, has found evidence of a flowing stream on Mars. Layers of smooth, water-polished pebbles have been photographed. This is exactly what you would see in a stream on Earth. There are many surface features that look like water-eroded canyons. Since there was liquid water on Mars, scientists think that life might have existed there in the past. One of Curiosity's tasks is to sample the soil to search for carbon and other evidence of life.

Two Martian Moons
Mars has two very small, irregular moons, Phobos (Figure below) and Deimos. These moons were discovered in 1877. They are named after the two sons of Ares, who followed their father into war. The moons were probably asteroids that were captured by Martian gravity.

Phobos is Mars’ larger moon. It has a 6.9 mile (11.1 km) radius.

The Outer Planets

The four planets farthest from the Sun are the outer planets. The figure below shows the relative sizes of the outer planets and the Sun. These planets are much larger than the inner planets and are made primarily of gases and liquids, so they are also called gas giants.

This image shows the four outer planets and the Sun, with sizes to scale. From left to right, the outer planets are Jupiter, Saturn, Uranus, and Neptune.

The gas giants are made up primarily of hydrogen and helium, the same elements that make up most of the Sun. Astronomers think that hydrogen and helium gases comprised much of the solar system when it first formed. Since the inner planets didn’t have enough mass to hold on to these light gases, their hydrogen and helium floated away into space. The Sun and the massive outer planets had enough gravity to keep hydrogen and helium from drifting away.

 All of the outer planets have numerous moons. They all also have planetary rings, composed of dust and other small particles that encircle the planet in a thin plane.

JUPITER

Jupiter is the largest planet in our solar system. Jupiter is named for the king of the gods in Roman mythology. The Romans named the largest planet for their most important god. They followed the tradition of the Greeks, who had similarly named the planet Zeus. The Romans built a temple to Jupiter on the hill.

Jupiter is truly a giant! The planet has 318 times the mass of Earth and over 1,300 times Earth’s volume. So Jupiter is much less dense than Earth. Because Jupiter is so large, it reflects a lot of sunlight. When it is visible, it is the brightest object in the night sky beside the Moon and Venus. Jupiter is quite far from Earth. The planet is more than five times as far from Earth as the Sun. It takes Jupiter about 12 Earth years to orbit once around the Sun.

A Ball of Gas and Liquid
Since Jupiter is a gas giant, could a spacecraft land on its surface? The answer is no. There is no solid surface at all! Jupiter is made mostly of hydrogen, with some helium, and small amounts of other elements. The outer layers of the planet are gas. Deeper within the planet, the intense pressure condenses the gases into a liquid. Jupiter may have a small rocky core at its center.

A Stormy Atmosphere
Jupiter's atmosphere is unlike any other in the solar system! The upper layer contains clouds of ammonia. Ammonia is a different colored band. These bands rotate around the planet. The ammonia also swirls around in tremendous storms. The Great Red Spot (Figure below) is Jupiter's most noticeable feature. The spot is an enormous, oval-shaped storm. It is more than three times as wide as Earth! Clouds in the storm rotate counterclockwise. They make one complete turn every six days or so. The Great Red Spot has been on Jupiter for at least 300 years. It may have been observed as early as 1664. It is possible that this storm is a permanent feature on Jupiter. No one knows for sure.

The Great Red Spot has been on Jupiter since we've had telescopes powerful enough to see it.

Moons and Rings
Jupiter has lots of moons. As of 2012, we have discovered over 66 natural satellites of Jupiter. Four are big enough and bright enough to be seen from Earth using a pair of binoculars. These four moons were first discovered by Galileo in 1610. They are called the Galilean moons. The figure below shows the four Galilean moons and their sizes relative to each other (Figure below). These moons are named Io, Europa, Ganymede, and Callisto. The Galilean moons are larger than even the biggest dwarf planets, Pluto and Eris. Ganymede is the biggest moon in the solar system. It is even larger than the planet Mercury!

The Galilean moons are as large as small planets.

Scientists think that Europa is a good place to look for extraterrestrial life. Europa is the smallest of the Galilean moons. The moon's surface is a smooth layer of ice. Scientists think that the ice may sit on top of an ocean of liquid water. How could Europa have liquid water when it is so far from the Sun? Europa is heated by Jupiter. Jupiter's tidal forces are so great that they stretch and squash its moon. This could produce enough heat for there to be liquid water. Numerous missions have been planned to explore Europa, including plans to drill through the ice and send a probe into the ocean. However, no such mission has yet been attempted.

Photos from the Voyager missions showed that Jupiter has a ring system. This ring system is very faint, so it is very difficult to observe from Earth.
 

SATURN
Saturn is the second-largest planet in the solar system (Figure below). Saturn’s mass is about 95 times Earth's mass. The gas giant is 755 times Earth’s volume. Despite its large size, Saturn is the least dense planet in our solar system. Saturn is actually less dense than water. This means that if there were a bathtub big enough, Saturn would float! In Roman mythology, Saturn was the father of Jupiter. Saturn orbits the Sun once about every 30 Earth years.

Saturn is the least dense planet in our solar system.

Composition
Saturn’s composition is similar to Jupiter's. The planet is made mostly of hydrogen and helium. These elements are gases in the outer layers and liquids in the deeper layers. Saturn may also have a small solid core. Saturn's upper atmosphere has clouds in bands of different colors. These clouds rotate rapidly around the planet. But Saturn has fewer storms than Jupiter. Thunder and lightning have been seen in the storms on Saturn.

Rings
Saturn's rings were first observed by Galileo in 1610. Remember that his telescope was not very good. He didn't know they were rings and thought that they were two large moons. One moon was on either side of the planet. In 1659, the Dutch astronomer Christiaan Huygens realized that they were rings circling Saturn’s equator. The rings appear tilted. This is because Saturn is tilted about 27 degrees to its side.

The Voyager 1 spacecraft visited Saturn in 1980. Voyager 2 followed in 1981. These probes sent back detailed pictures of Saturn, its rings, and some of its moons (Figure below). From the Voyager data, we learned what Saturn’s rings are made of. They are particles of water and ice with a little bit of dust. There are several gaps in the rings. These gaps were cleared out by moons within the rings. Gravity attracts dust and gas to the moon from the ring. This leaves a gap in the rings. Other gaps in the rings are caused by the competing forces of Saturn and its moons outside the rings.

The rings of Saturn.

Scientists think that there are two possibilities for how Saturn's rings formed. One possibility is the breakup of one of Saturn’s moons. The other possibility is from material that never made it into the planet when Saturn originally formed.

Moons
As of 2012, 62 natural moons have been identified around Saturn. Only seven of Saturn’s moons are round. All but one is smaller than Earth’s moon. Some of the very small moons are found within the rings. All the particles in the rings are like little moons because they orbit around Saturn. Someone must decide which ones are large enough to call moons.

Saturn’s largest moon, Titan, is about one and a half times the size of Earth’s moon. Titan is even larger than the planet Mercury. The picture below compares the size of Titan to Earth (Figure below). Scientists are very interested in Titan. The moon has an atmosphere that is thought to be like Earth’s first atmosphere with nitrogen and methane. This atmosphere was around before life developed on Earth. Like Jupiter's moon, Europa, Titan may have a layer of liquid water under a layer of ice. Scientists now think that there are lakes on Titan's surface. Don't take a dip, though. These lakes contain liquid methane and ethane instead of water! Methane and ethane are compounds found in natural gas.

This composite image compares Saturn’s largest moon, Titan (right), to Earth (left).

URANUS
Uranus is named for the Greek god of the sky, the father of Saturn. Astronomers pronounce the name “YOOR-uh-nuhs.” Uranus was not known to ancient observers. The planet was first discovered with a telescope by the astronomer William Herschel in 1781.

Uranus is faint because it is very far away. Its distance from the Sun is 2.8 billion kilometers (1.8 billion miles). A photon from the Sun takes about 2 hours and 40 minutes to reach Uranus. Uranus orbits the Sun once about every 84 Earth years.

An Icy Blue-Green Ball
Uranus is a lot like Jupiter and Saturn. The planet is composed mainly of hydrogen and helium. There is a thick layer of gas on the outside. Further on the inside is liquid. But Uranus has a higher percentage of icy materials than Jupiter and Saturn. These materials include water, ammonia, and methane. Uranus is also different because of its blue-green color. Clouds of methane filter out red light. This leaves a blue-green color. The atmosphere of Uranus has bands of clouds. These clouds are hard to see in normal light. The result is that the planet looks like a plain blue ball.

Uranus is the least massive outer planet. Its mass is only about 14 times the mass of Earth. Like all of the outer planets, Uranus is much less dense than Earth. Gravity is actually weaker than on Earth’s surface. If you were at the top of the clouds on Uranus, you would weigh about 10 percent less than what you weigh on Earth.

The Sideways Planet
All of the planets rotate on their axes in the same direction that they move around the Sun. Except for Uranus. Uranus is tilted on its side. Its axis is almost parallel to its orbit. So Uranus rolls along like a bowling ball as it revolves around the Sun. How did Uranus get this way? Scientists think that the planet was struck and knocked over by another planet-sized object. This collision probably took place billions of years ago.

Rings and Moons of Uranus
Uranus has a faint system of rings, as shown in the Figure below. The rings circle the planet’s equator. However, Uranus is tilted on its side. So the rings are almost perpendicular to the planet’s orbit.

This image from the Hubble Space Telescope uses infrared light filters to show the faint rings of Uranus.

We have discovered 27 moons around Uranus. All but a few are named for characters from the plays of William Shakespeare. The five biggest moons of Uranus, Miranda, Ariel, Umbriel, Titania, and Oberon, are shown in Figure below.

The five biggest moons of Uranus, Miranda, Ariel, Umbriel, Titania, and Oberon.

NEPTUNE
Neptune (Figure below) is the eighth planet from the Sun. Neptune is so far away you need a telescope to see it from Earth. Neptune is the most distant planet in our solar system. It is nearly 4.5 billion kilometers (2.8 billion miles) from the sun. One orbit around the Sun takes Neptune 165 Earth years.

Neptune has a great dark spot at the center-left and a small dark spot at the bottom center.

Extremes of Cold and Wind
Like Uranus, Neptune is blue. The blue color is caused by gases in its atmosphere, including methane. Neptune is not a smooth looking ball-like Uranus. The planet has a few darker and lighter spots. When Voyager 2 visited Neptune in 1986, there was a large dark-blue spot south of the equator. This spot was called the Great Dark Spot. When the Hubble Space Telescope photographed Neptune in 1994, the Great Dark Spot had disappeared. Another dark spot had appeared north of the equator. Astronomers believe that both of these spots represent gaps in the methane clouds on Neptune.

Neptune's appearance changes due to its turbulent atmosphere. Winds are stronger than on any other planet in the solar system. Wind speeds can reach 1,100 km/h (700 mph). This is close to the speed of sound! The rapid winds surprised astronomers. This is because Neptune receives little energy from the Sun to power weather systems. It is not surprising that Neptune is one of the coldest places in the solar system. Temperatures at the top of the clouds are about –218°C (–360°F).

Neptune’s Rings and Moons
Like the other outer planets, Neptune has rings of ice and dust. These rings are much thinner and fainter than Saturn's. Neptune's rings may be unstable. They may change or disappear in a relatively short time.

Neptune has 13 known moons. Only Triton (Figure below) has enough mass to be round. Triton orbits in the direction opposite Neptune's orbit. Scientists think Triton did not form around Neptune. The satellite was captured by Neptune’s gravity as it passed by.

Neptune's moon, Triton.

Universal Gravity

Any two objects in the universe, with masses  m_1 and  m_2  with their centers of mass at a distance  r  apart will experience a force of mutual attraction along the line joining their centers of mass equal to:\vec{F_G}=\frac{Gm_1m_2}{r^2} && \text{Universal Gravitation, }\intertext{where G is the Gravitational constant:}G = 6.67300\times10^{-11} \mathrm{m^3 kg^{-1} s^{-2}}

 

This a minute video about gravity.

 

Here is an illustration of this law for two objects, for instance the earth and the sun: 

 

 

In 1798, Henry Cavendish designed and created an apparatus and experiment to determine the density of the planet and the value of the gravitational constant, His apparatus involved a light, rigid rod about 2-feet long with two small lead spheres attached to the ends. The rod was suspended by a thin wire. When the rod rotated, the twisting of the wire pushed backward to restore the rod to the original position. 

FORCE OF GRAVITY
In the mid-1600s, Newton wrote that the sight of a falling apple made him think of the problem of the motion of the planets. He recognized that the apple fell straight down because the earth attracted it and thought this same force of attraction might apply to the moon. It further occurred to him that the motion of the planets might be controlled by the gravity of the sun. He eventually proposed the universal law of gravitational attraction asF=G \frac{m_1m_2}{d^2}

where and m_2 are the masses being attracted, d is the distance between the centers of the masses, G is the universal gravitational constant, and is the force of attraction. The formula for gravitational attraction applies equally to two rocks resting near each other on the earth and to the planets and the sun. The value for the universal gravitational constant, G, was determined by Henry Cavendish (using the apparatus described in the introduction) to be 6.67 × 10-11 N·m2/kg2.

The moon is being pulled toward the earth and the earth toward the moon with the same force but in the opposite direction. The force of attraction between the two bodies produces a greater acceleration of the moon than the earth because the moon has a smaller mass. Even though the moon is constantly falling toward the earth, it never gets any closer. This is because the velocity of the moon is perpendicular to the radius of the earth (as shown in the image above) and therefore the moon is moving away from the earth. The distance the moon moves away from the orbit line is exactly the same distance that the moon falls in the time period. This is true of all satellites and is the reason objects remain in orbit. In the case of orbiting bodies, the centripetal force is the gravitational force, and they undergo imperfect circular motion.

Example Problem: Since we know the force of gravity on a 1.00 kg ball resting on the surface of the earth is 9.80 N, and we know the radius of the earth is 6380 km, we can use the equation for the gravitational force to calculate the mass of the earth.

Solution: m_e=\frac{Fd^2}{Gm_1}=\frac{(9.80 \ \text{m/s}^2)(6.38 \times 10^{6} \ \text{m})^2}{(6.67 \times 10^{-11} \ \text{N} \cdot \text{m}^2 / \text{kg}^2)(1.00 \ \text{kg})}=5.98 \times 10^{24} \ \text{kg}

 

 

The Moon

One of the most unique features of planet Earth is its large Moon. Unlike the only other natural satellites orbiting an inner planet, those of Mars, the Moon is not a captured asteroid. Understanding the Moon’s birth and early history reveals a great deal about Earth’s early days.

FEATURES OF THE MOON
To determine how the Moon formed, scientists had to account for several lines of evidence:

  • The Moon is large; not much smaller than the smallest planet, Mercury.
  • Earth and Moon are very similar in composition.
  • Moon’s surface is 4.5 billion years old, about the same as the age of the solar system.
  • For a body its size and distance from the Sun, the Moon has very little core; Earth has a fairly large core.
  • The oxygen isotope ratios of Earth and Moon indicate that they originated in the same part of the solar system.
  • Earth has a faster spin than it should have for a planet of its size and distance from the Sun.
  • The surface features are lunar highlands, mare, and craters.

Astronomers have carried out computer simulations that are consistent with these facts and have detailed a birth story for the Moon. A little more than 4.5 billion years ago, roughly 70 million years after Earth formed, planetary bodies were being pummeled by asteroids and planetoids of all kinds. Earth was struck by a Mars-sized asteroid (Figure below).

An artist’s depiction of the impact that produced the Moon.

The tremendous energy from the impact melted both bodies. The molten material mixed up. The dense metals remained on Earth but some of the molten, rocky material was flung into an orbit around Earth. It eventually accreted into a single body, the Moon. Since both planetary bodies were molten, the material could differentiate out of the magma ocean into core, mantle, and crust as they cooled. Earth’s fast spin is from energy imparted to it by the impact.

MOON'S ROTATION
The moon DOES rotate --- one rotation for each revolution around Earth! The accompanying drawings, covering half an orbit, should make this clear. In them, we look at the moon's orbit from high above the north pole and imagine a clock dial around the moon, and a feature on it, marked by an arrow, which initially (bottom position in each drawing) points at 12 o'clock.

Moon Orbit

Half of the moon's orbit.

In the right drawing the marked feature continues to point at Earth, and as the moon goes around the Earth, it points to the hours 10, 8, and 6 on the clock dial. As the moon goes through half a revolution, it also undergoes half a rotation. If the moon did not rotate, the situation would be as in the left drawing. The arrow would continue to point in the 12-o'clock direction, and after half an orbit, people on Earth would be able to see the other side of the moon. This does not happen. The complete rotation and revolution of the moon are called a lunar month and it takes roughly 29.5 days for this to occur.

We need to go aboard a spaceship and fly halfway around the Moon before we get a view of its other side --- as did the Apollo astronauts who took the picture below.

Far Side of the Moon

The far side of the moon.

 

 

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