Essential Cosmic Perspective : Ch. 3 HW & Quiz

The shadow cast by a simple stick or obelisk allowed ancient people to

tell the time of day

On (Figure 1), you can see Kepler's third law (p2=a3p2=a3) from the fact that __________.

the data fall on a straight line

An original observation of Galileo's that helped to overturn the ancient Earth-centered model was

the phases of Venus

Galileo's contribution to astronomy included:

making observations and conducting experiments that dispelled scientific objections to the Sun-centered model.

The Moon takes roughly 28 days to complete one orbit around Earth. If the orbital radius of the Moon were twice its actual value, its orbital period would be

more than 56 days

In Ptolemy's Earth-centered model, when would Venus appear directly behind the Sun as viewed from Earth?

never

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

never

When would a new Venus be highest in the sky?

noon

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

What is Eris's average distance (semimajor axis) from the Sun?

67.7

Earth is closer to the Sun in January than in July. Therefore, in accord with Kepler's second law:

Earth travels faster in its orbit around the Sun in January than in July.

Which of the following was not a major advantage of Copernicus's Sun-centered model over the Ptolemaic model?

It made significantly better predictions of planetary positions in our sky.

According to Kepler's third law:

Jupiter orbits the Sun at a faster speed than Saturn.

You discover an asteroid that orbits the Sun with the same 1-year orbital period as Earth. Which of the following statements must be true?

The asteroid's average (semimajor axis) distance from the Sun is 1AU1AU.

As a comet orbits around the Sun, its maximum speed is twice its minimum speed. What can we say about its orbit?

The comet is twice as far from the Sun at aphelion as at perihelion.

In the Greek geocentric model, the retrograde motion of a planet occurs when:

The planet actually goes backward in its orbit around Earth.

Which of the following orbits has the largest semimajor axis?

The semimajor axis is half of the distance across the ellipse in its longest direction (which means half of the major axis), which is also the planet's average distance from the Sun. Therefore, the ellipse that measures the longest across is the one with the largest semimajor axis.

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

Jupiter orbits the Sun at an average distance of 5.2035.203 AUAU and takes 11.86years11.86years to complete each orbit. Based on these facts, which statement is true?

11.86^2=5.203^3

All of the following statements are true. Which one can be explained by Kepler's third law?

Venus orbits the Sun at a faster orbital speed than Earth.

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 p2=a3p2=a3. 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.

Which of the following can you observe about Venus with the naked eye? Select all that apply.

Venus sometimes shines brightly in the western sky shortly after sunset. Venus sometimes shines brightly in the eastern sky shortly before dawn

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.

When we say that a planet has a highly eccentric orbit, we mean that:

in some parts of its orbit it is much closer to the Sun than in other parts.

When Einstein's theory of gravity (general relativity) gained acceptance, it demonstrated that Newton's theory had been

incomplete.

We never see a crescent Jupiter from Earth because Jupiter __________

is farther than Earth from the Sun

Why wasn't the Sun-centered model of Copernicus immediately adopted after he proposed it?

it was not noticeably more accurate than the old Ptolemaic model

A planet is discovered orbiting the star 51 Peg with a period of four days (0.01 years). 51 Peg has the same mass as the Sun. Mercury's orbital period is 0.24 years, and Venus's is 0.62 years. The average orbital radius of this planet is

less than Mercury's

Which of the following is not true about a scientific theory?

A theory is essentially an educated guess.

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.

Why do the planets orbit the Sun (i.e. why don't they crash into the Sun)?

Although the planets experience a force of gravity from the Sun, since they are moving, their trajectories bend around the Sun rather than lead directly into the Sun.

Earth is slightly closer to the Sun in January than in July. How does the area swept out by Earth's orbit around the Sun during the 31 days of January compare to the area swept out during the 31 days of July?

Both areas are the same.

Suppose two comets, comet A and comet B, were orbiting the Sun, having the same average orbital radii. If comet A had a higher eccentricity than comet B, which comet would, during some portion of its orbit, have the highest orbital speed?

Comet A.

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.

How does its average distance compare to that of Pluto?

Eris orbits farther than Pluto.

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.

If an astronomer claims to have discovered an object with a very eccentric orbit, which of the following best describes the orbital trajectory of the object?

It looks like a very squashed oval

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.

Which of the following paths could not be a real orbit for a planet around the Sun?

Kepler's first law tells us that the orbit of a planet must be an ellipse with the Sun at one focus. Therefore, the path that shows the Sun in the center of the ellipse, rather than at a focus, cannot be the real orbital path of a planet. (Note that the circular path is allowed because a circle is an ellipse in which both foci are at the center.)

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.

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.

All of the following statements are true. Which one can be explained by Kepler's second law?

Mars moves faster in its orbit when it is closer to the Sun than when it is farther from the Sun.

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.

Two planets are observed going around a star. Planet Xoron has an orbital period that is twice as long as planet Krypton. Which planet has a shorter average orbital radius?

Planet Krypton

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.

Which of the following are the three key hallmarks of science?

Science progresses through the creation and testing of models of nature that explain the observations as simply as possible. Models must make testable predictions that will force us to revise or abandon the model if they do not agree with observations. Modern science seeks explanations for observed phenomena that rely solely on natural causes.

Approximately how fast is Jupiter orbiting the Sun?

a little less than 15 km/s

An asteroid with an average orbital distance of 2 AUAU will orbit the Sun at an average speed that is __________.

a little slower than the orbital speed of Mars

Tycho Brahe's contribution to astronomy included:

collecting data that enabled Kepler to discover the laws of planetary motion.

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

Based on the video, which Venus phase would be impossible to see (from Earth) if Venus orbited Earth as described in Ptolemy's Earth-centered model?

gibbous (nearly full)

If Earth's orbit were very eccentric, but the average distance from the Sun were still 1 AU, its orbital period

would still be one year