Mastering Astronomy Chapters 3 & 3 Assignment

Suppose that two asteroids are orbiting the Sun on nearly identical orbits, and they happen to pass close enough to each other to have their orbits altered by this gravitational encounter. If one of the asteroids ends up moving to an orbit that is closer to the Sun, what happens to the other asteroid?

It will end up on an orbit that is farther from the Sun.

One tidal bulge faces toward the Moon because that is where the gravitational attraction between Earth and the Moon is strongest. Which of the following best explains why there is also a second tidal bulge?

The second tidal bulge arises because gravity weakens with distance, essentially stretching Earth along the Earth-Moon line.

You have found that tides on Earth are determined primarily by the position of the Moon, with the Sun playing only a secondary role. Why does the Moon play a greater role in causing tides than the Sun?

because the gravitational attraction between Earth and the Moon varies more across Earth than does the gravitational attraction between Earth and the Sun

Earth orbits in the shape of a/an ______ around the Sun.

ellipse

We never see a crescent Jupiter from Earth because Jupiter __________.

is farther than Earth from the Sun

Rapidly moving comets have more ______ energy than slowly moving ones.

kinetic

As the cloud shrinks in size, its rate of rotation _____________ because ___________

speeds up its total angular momentum is conserved.

Consider Earth and the Moon. As you should now realize, the gravitational force that Earth exerts on the Moon is equal and opposite to that which the Moon exerts on Earth. Therefore, according to Newton's second law of motion __________

the Moon has a larger acceleration than Earth, because it has a smaller mass

Any particular location on Earth experiences __________.

two high tides and two low tides each day

Suppose that the Sun were to collapse from its current radius of about 700,000 km to a radius of only about 6000 km (about the radius of Earth). What would you expect to happen as a result?

A tremendous amount of gravitational potential energy would be converted into other forms of energy, and the Sun would spin much more rapidly.

The following diagrams are the same as those from Part A. This time, rank the pairs from left to right based on the size of the acceleration the asteroid on the left would have due to the gravitational force exerted on it by the object on the right, from largest to smallest.

Asteroid to sun Asteroid to Earth Asteroid to moon Asteroid to asteroid Asteroid to hydrogen atom

Earth is located at one _______ of the Moon's orbit.

Focus

As you watch the video, notice that the size of the tidal bulges varies with the Moon's phase, which depends on its orbital position relative to the Sun. Which of the following statement(s) accurately describe(s) this variation?

Low tides are lowest at both full moon and new moon. High tides are highest at both full moon and new moon.

Most people are familiar with the rise and fall of ocean tides. Do tides also affect land?

Yes, though land rises and falls by a much smaller amount than the oceans.

When would a new Venus be highest in the sky?

at noon

Due to its much higher density, water heated to 80 degrees (Celsius) contains more _______ energy than air at the same temperature.

thermal

The following five diagrams show pairs of astronomical objects that are all separated by the same distance d. Assume the asteroids are all identical and relatively small, just a few kilometers across. Considering only the two objects shown in each pair, rank the strength, from strongest to weakest, of the gravitational force acting on the asteroid on the left.

Asteroid to sun Asteroid to Earth Asteroid to moon Asteroid to asteroid Asteroid to hydrogen atom

Kepler's first law states that the orbit of each planet is an ellipse with the Sun at one focus. Which of the following statements describe a characteristic of the solar system that is explained by Kepler's first law?

Earth is slightly closer to the Sun on one side of its orbit than on the other side. The Sun is located slightly off-center from the middle of each planet's orbit.

Consider again the diagrams from Part D, which are repeated here. Again, imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. This time, rank the positions from left to right based on the distance the asteroid will travel during a one-week period when passing through each location, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

Notice the similarity between what you have found here and what you found for the comet in Part B. Kepler's second law tells us any object will sweep out equal areas in equal times as it orbits the Sun, which means the area triangles are shorter and squatter when the object is nearer to the Sun, so that the object covers a greater distance during any particular time period when it is closer to the Sun than when it is farther away.

As shown in the video, Earth has two tidal bulges at all times. Approximately where are these bulges located?

One faces the Moon and one faces opposite the Moon

The video shows a collapsing cloud of interstellar gas, which is held together by the mutual gravitational attraction of all the atoms and molecules that make up the cloud. As the cloud collapses, the overall force of gravity that draws the cloud inward _____________ because __________

gradually becomes stronger the strength of gravity follows an inverse square law with distance.

An asteroid that is moving farther from the Sun is gaining ________ energy.

gravitational potential

As the cloud shrinks in size, its central temperature _______ as a result of its _________

increases gravitational potential energy being converted to thermal energy.

When would you expect to see Venus high in the sky at midnight?

never

According to Kepler's second law, Pluto will be traveling fastest around the Sun when at ______

perihelion

The mathematical form of Kepler's third law measures the period in years and the _______ in astronomical units (AU).

semimajor axis

Consider the hypothetical observation "a planet beyond Saturn rises in west, sets in east." This observation is not consistent with a Sun-centered model, because in this model __________.

the rise and set of all objects depends only on Earth's rotation

Each of the four diagrams below represents the orbit of the same comet, but each one shows the comet passing through a different segment of its orbit around the Sun. During each segment, a line drawn from the Sun to the comet sweeps out a triangular-shaped, shaded area. Assume that all the shaded regions have exactly the same area. Rank the segments of the comet's orbit from left to right based on the length of time it takes the comet to move from Point 1 to Point 2, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

Although Kepler wrote his laws specifically to describe the orbits of the planets around the Sun, they apply more generally. Kepler's second law tells us that as an object moves around its orbit, it sweeps out equal areas in equal times. Because all the areas shown here are equal, the time it takes the comet to travel each segment must also be the same.

According to Kepler's second law, Jupiter will be traveling most slowly around the Sun when at ________

Aphelion

Consider again the set of observations from Part A. This time, classify each observation according to whether it is consistent with only the Earth-centered model, only the Sun-centered model, both models, or neither model. (Note that an observation is "consistent" with a model if that model offers a simple explanation for the observation.)

Earth-centered only -a planet beyond Saturn rises in west, sets in east Sun-Centered only -Mercury goes through a full cycle of phases -positions of nearby stars shift slightly back and forth each year Both models -stars circle daily around north or south celestial pole -Moon rises in east, sets in west -a distant galaxy rises in east, sets in west each day Neither model -we sometimes see a crescent Jupiter

The following diagrams show five pairs of asteroids, labeled with their relative masses (M) and distances (d) between them. For example, an asteroid with M=2 has twice the mass of one with M=1 and a distance of d=2 is twice as large as a distance of d=1. Rank each pair from left to right based on the strength of the gravitational force attracting the asteroids to each other, from strongest to weakest.

M=2; d=1; m=2 m=1; d=1; m=2 m=1; d=1; m=1 m=1; d=2; m=2 m=1; d=2; m=1

The following diagrams all show the same star, but each shows a different planet orbiting the star. The diagrams are all scaled the same. (For example, you can think of the tick marks along the line that passes through the Sun and connects the nearest and farthest points in the orbit as representing distance in astronomical units (AU).) Rank the planets from left to right based on their average orbital distance from the star, from longest to shortest. (Distances are to scale, but planet and star sizes are not.)

Note that the line that passes through the star and connects the nearest and farthest points of the planet's orbit is called the major axis, and half this line is the semimajor axis — which we consider the planet's average distance from the star.

Kepler's second law states that as a planet orbits the Sun, it sweeps out equal areas in equal times. Which of the following statements describe a characteristic of the solar system that is explained by Kepler's second law?

Pluto moves faster when it is closer to the Sun than when it is farther from the Sun.

Consider the following observations. Classify each observation based on whether it is a real observation (a true statement of something we can actually see from Earth) or one that is not real (a statement of something that does not really occur as seen from Earth).

Real -Mercury goes through a full cycle of phases -Moon rises in east, sets in west -stars circle daily around north or south celestial pole -positions of nearby stars shift slightly back and forth each year -a distant galaxy rises in east, sets in west each day Not real -we sometimes see a crescent Jupiter -a planet beyond Saturn rises in west, sets in east

The following diagrams are the same as those from Part A. This time, rank the planets from left to right based on the amount of time it takes each to complete one orbit, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. (Distances are to scale, but planet and star sizes are not.)

Recall that the time it takes a planet to complete an orbit is called its orbital period. The pattern found in this Part illutrates one of the ideas that are part of Kepler's third law: Planets with larger average orbital distances have longer orbital periods.

The video states that the planetary orbits are shown to scale. Which statement correctly describes the way the planet sizes are shown compared to their orbits?

The planets are all much too large compared to their orbits.

The following diagrams are the same as those from Parts A and B. This time, rank the planets from left to right based on their average orbital speed, from fastest to slowest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. (Distances are to scale, but planet and star sizes are not.)

This pattern illustrates another of the ideas that are part of Kepler's third law: Planets with larger average orbital distances have slower average speeds.

An apple contains _______ energy that your body can convert into other forms energy

chemical potential

The extent to which Mars' orbit differs from a perfect circle is called its ________

eccentricity

In Ptolemy's Earth-centered model for the solar system, Venus's phase is never full as viewed from Earth because it always lies between Earth and the Sun. In reality, as Galileo first recognized, Venus is __________.

full whenever it is on the opposite side of the Sun from Earth

The light from Polaris travels through space in the form of _______ energy.

radiative

The following diagrams are the same as those from Part A. This time, rank the five positions of the spaceship from left to right based on the strength of the gravitational force that the Moon exerts on the spaceship, from strongest to weakest.

Gravity follows an inverse square law with distance, which means the force of gravity between the Moon and the spaceship increases as the spaceship approaches the Moon. Now continue to Part C for activities that look at the effects of both distance and mass on gravity.

Each of the following diagrams shows a planet orbiting a star. Each diagram is labeled with the planet's mass (in Earth masses) and its average orbital distance (in AU). Assume that all four stars are identical. Use Kepler's third law to rank the planets from left to right based on their orbital periods, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. (Distances are to scale, but planet and star sizes are not.)

Kepler's third law tells us that the orbital period of the planet depends on its average distance from its star, but not on the planet's mass. As Newton later showed with his version of Kepler's third law, this is actually an approximation that works well whenever the planet's mass is small compared to the mass of the star.

The following diagrams are the same as those from Part A. Again considering only the two objects shown in each pair, this time rank the strength, from strongest to weakest, of the gravitational force acting on the object on the right.

Asteroid to sun Asteroid to Earth Asteroid to moon Asteroid to asteroid Asteroid to hydrogen atom

Let's now consider possible scientific claims. Recall that a scientific claim is falsifiable if it could in principle be shown to be false by observations or experiments, even if those observations or experiments have not yet been performed. Classify each claim according to whether or not it is falsifiable.

Falsifiable -The chemical content of the universe is mostly hydrogen and helium. -Earth is at the center of the solar system. -The Sun is at the center of the solar system. -The observable universe contains approximately 100 billion galaxies. Not Falsifiable -We are all playthings in a computer program created by advanced aliens. -The laws of nature are magnificent and beautiful. -The universe was created by God.

Consider again the diagrams from Parts A and B, which are repeated here. Again, assume that all the shaded areas have exactly the same area. This time, rank the segments of the comet's orbit based on the speed with which the comet moves when traveling from Point 1 to Point 2, from fastest to slowest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

From Parts A and B, you know that the comet takes the same time to cover each of the four segments shown, but that it travels greater distances in the segments that are closer to the Sun. Therefore, its speed must also be faster when it is closer to the Sun. In other words, the fact that that the comet sweeps out equal areas in equal times implies that its orbital speed is faster when it is nearer to the Sun and slower when it is farther away.

In Ptolemy's Earth-centered model for the solar system, Venus always stays close to the Sun in the sky and, because it always stays between Earth and the Sun, its phases range only between new and crescent. The following statements are all true and were all observed by Galileo. Which one provides evidence that Venus orbits the Sun and not Earth?

We sometimes see gibbous (nearly but not quite full) Venus.

Imagine that Venus is in its full phase today. If we could see it, at what time would the full Venus be highest in the sky?

at noon

Each of the four diagrams below represents the orbit of the same asteroid, but each one shows it in a different position along its orbit of the Sun. Imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. Rank the positions based on the area that would be swept out by a line drawn between the Sun and the asteroid during the one-week period, from largest to smallest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

Kepler's second law tells us that the asteroid will sweep out equal areas in equal time intervals. Therefore, the area swept out in any one week period must always be the same, regardless of the asteroid's location in its orbit around the Sun.

Let's start with an example from history. Listed below are a series of claims regarding United States President John F. Kennedy (1917-1963). Classify each statement according to whether or not it is falsifiable.

Falsifiable -Kennedy was the 35th president of the United States. -Kennedy died from a bullet in his brain. Not Falsifiable -The murder of John F. Kennedy was an act of evil. -If he'd lived, Kennedy would have ended the Vietnam War. -Kennedy's murder was orchestrated by an undetectable shadow government of the United States. -Kennedy's death was the will of God

Each of the following diagrams shows a spaceship somewhere along the way between Earth and the Moon (not to scale); the midpoint of the distance is marked to make it easier to see how the locations compare. Rank the five positions of the spaceship from left to right based on the strength of the gravitational force that Earth exerts on the spaceship, from strongest to weakest. (Assume the spaceship has the same mass throughout the trip; that is, it is not burning any fuel.)

Gravity follows an inverse square law with distance, which means the force of gravity between Earth and the spaceship weakens as the spaceship gets farther from Earth.

Consider again the diagrams from Parts D and E, which are repeated here. Again, imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. This time, rank the positions (A-D) from left to right based on how fast the asteroid is moving at each position, from fastest to slowest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

Just as you found for the comet in Parts A through C, the asteroid must be traveling at a higher speed during parts of its orbit in which it is closer to the Sun than during parts of its orbit in which it is farther away. You should now see the essence of Kepler's second law: Although the precise mathematical statement tells us that an object sweeps out equal areas in equal times, the key meaning lies in the idea that an object's orbital speed is faster when nearer to the Sun and slower when farther away. This idea explains why, for example, Earth moves faster in its orbit when it is near perihelion (its closest point to the Sun) in January than it does near aphelion (its farthest point from the Sun) in July.

Consider again the diagrams from Part A, which are repeated here. Again, assume that all the shaded areas have exactly the same area. This time, rank the segments of the comet's orbit from left to right based on the distance the comet travels when moving from Point 1 to Point 2, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

Kepler's second law tells us that the comet sweeps out equal areas in equal times. Because the area triangle is shorter and squatter for the segments nearer to the Sun, the distance must be greater for these segments in order for all the areas to be the same.

Kepler's third law states that a planet's orbital period, p, is related to its average (semimajor axis) orbital distance, a, according to the mathematical relationship p^2=a^3. Which of the following statements describe a characteristic of the solar system that is explained by Kepler's third law?

Venus orbits the Sun faster than Earth orbits the Sun. Inner planets orbit the Sun at higher speed than outer planets.

Nuclear fusion in stars converts some of the _______ energy of hydrogen nuclei into light and heat.

mass-